Fermat cubic,
S_2((Subscript[Γ, 0])(27)) cuspform (((η(3τ)))^2)(((η(9τ)))^2)

Normalized mod-p Fermat cubic solution-count for p=1 mod 3, by counting and by Gauss formula

IsSquare[n_]:=n==1||Mod[Union[FactorInteger[n][[All,2]]],2]=={0};
(*{#,IsSquare[#]}&/@Range[16]*)

Acount[p_]:=Module[
{s,A1,bmax,b,A2=0},
(*Print["p = ",p];*)
If[!(PrimeQ[p]&&Mod[p,3]==1),Return[False]
];
s=Length[Union[Solve[x^3+y^3==1,{x,y},Modulus->p],Solve[x^3+1==0,{x},Modulus->p]]];
(*Print["s = ",s];*)
A1=p+1-s;
bmax=Sqrt[4p/27];
For[b=1,b≤bmax,b++,
A2=4p-27b^2;
If[IsSquare[A2],
A2=Sqrt[A2];
If[Mod[A2,3]==1,A2=-A2];
Break[]
]
];
Return[{p,A1,A2}]
];

Acount[#]&/@{7,13,19,31,37,43,61,67,73,79}

Acount[#][[3]]&/@{7,13,19,31,37,43,61,67,73,79}

S_2((Subscript[Γ, 0])(27)) cuspform (((η(3τ)))^2)(((η(9τ)))^2)

nmax=79;
f[q_]:=Expand[q Product[(1-q^(3n))^2(1-q^(9n))^2,{n,1,nmax}]]/.q^b_/;b>nmax->0;
Clear[q];
f[q]
TeXForm[f[q]]
Coefficient[f[q],#]&/@{q^7,q^13,q^19,q^31,q^37,q^43,q^61,q^67,q^73,q^79}