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We present nuclear magnetic resonance (NMR) and nuclear quadrupole resonance(NQR) measurements performed on single crystalline \ccag{}, a member of arecently discovered family of heavy fermion materials Ce$_2M$Al$_7$Ge$_4$ ($M$= Co, Ir, Ni, or Pd). Previous measurements indicated a strong Kondointeraction as well as magnetic order below $T_M = 1.8$ K. Our NMR spectralmeasurements show that the Knight shift $K$ is proportional to the bulkmagnetic susceptibility $\chi$ at high temperatures. A clear Knight shiftanomaly ($K \not\propto \chi$) is observed at coherence temperatures $T^* \sim17.5$ K for $H_0 \parallel \hat{c}$ and 10 K for $H_0 \parallel \hat{a}$ at the${}^{59}$Co site, and $T^* \sim 12.5$ K at the ${}^{27}$Al(3) site for $H_0\parallel \hat{a}$ characteristic of the heavy fermion nature of this compound.At high temperatures the ${}^{59}$Co NMR spin-lattice relaxation rate$T_1^{-1}$ is dominated by spin fluctuations of the 4$f$ local moments with aweak metallic background. The spin fluctuations probed by ${}^{59}$Co NMR areanisotropic and larger in the basal plane than in the $c$ direction.Furthermore, we find $(T_1TK)^{-1} \propto T^{-1/2}$ at the ${}^{59}$Co site asexpected for a Kondo system for $T > T^*$ and $T> T_K$. ${}^{59}$Co NQR \slrr{}measurements at low temperatures indicate slowing down of spin fluctuationsabove the magnetic ordering temperature $T_M \sim 1.8$ K. A weak ferromagneticcharacter of fluctuations around $\mathbf{q}=0$ is evidenced by an increase of$\chi T$ versus $T$ above the magnetic ordering temperature. We also find goodagreement between the observed and calculated electric field gradients at allobserved sites.

Nuclear magnetic resonance investigation of the heavy fermion system Ce$_2$CoAl$_7$Ge$_4$