Properties

Label 2916.1
Level 2916
Weight 1
Dimension 84
Nonzero newspaces 4
Newform subspaces 15
Sturm bound 472392
Trace bound 1

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Defining parameters

Level: \( N \) = \( 2916 = 2^{2} \cdot 3^{6} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 15 \)
Sturm bound: \(472392\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2916))\).

Total New Old
Modular forms 3400 732 2668
Cusp forms 160 84 76
Eisenstein series 3240 648 2592

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 84 0 0 0

Trace form

\( 84 q + O(q^{10}) \) \( 84 q + 6 q^{10} + 6 q^{37} - 6 q^{64} + 15 q^{73} - 30 q^{82} + 9 q^{91} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2916))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
2916.1.c \(\chi_{2916}(1457, \cdot)\) None 0 1
2916.1.d \(\chi_{2916}(1459, \cdot)\) 2916.1.d.a 3 1
2916.1.d.b 3
2916.1.f \(\chi_{2916}(487, \cdot)\) 2916.1.f.a 6 2
2916.1.f.b 6
2916.1.g \(\chi_{2916}(485, \cdot)\) None 0 2
2916.1.j \(\chi_{2916}(163, \cdot)\) 2916.1.j.a 6 6
2916.1.j.b 6
2916.1.j.c 6
2916.1.j.d 6
2916.1.j.e 6
2916.1.j.f 6
2916.1.j.g 6
2916.1.j.h 6
2916.1.k \(\chi_{2916}(161, \cdot)\) 2916.1.k.a 6 6
2916.1.k.b 6
2916.1.k.c 6
2916.1.n \(\chi_{2916}(55, \cdot)\) None 0 18
2916.1.o \(\chi_{2916}(53, \cdot)\) None 0 18
2916.1.r \(\chi_{2916}(19, \cdot)\) None 0 54
2916.1.s \(\chi_{2916}(17, \cdot)\) None 0 54
2916.1.v \(\chi_{2916}(7, \cdot)\) None 0 162
2916.1.w \(\chi_{2916}(5, \cdot)\) None 0 162

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2916))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2916)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(243))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(324))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(729))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(972))\)\(^{\oplus 2}\)