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Properties

Label 2312.1
Level 2312
Weight 1
Dimension 193
Nonzero newspaces 9
Newform subspaces 18
Sturm bound 332928
Trace bound 2

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Defining parameters

Level: \( N \) = \( 2312 = 2^{3} \cdot 17^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 9 \)
Newform subspaces: \( 18 \)
Sturm bound: \(332928\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2312))\).

Total New Old
Modular forms 2789 930 1859
Cusp forms 389 193 196
Eisenstein series 2400 737 1663

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 193 0 0 0

Trace form

\( 193 q + q^{2} + 2 q^{3} + q^{4} + 2 q^{6} + q^{8} + 3 q^{9} + O(q^{10}) \) \( 193 q + q^{2} + 2 q^{3} + q^{4} + 2 q^{6} + q^{8} + 3 q^{9} + 2 q^{11} - 14 q^{12} + q^{16} - 5 q^{18} + 2 q^{19} + 2 q^{22} - 14 q^{24} + q^{25} - 12 q^{27} + q^{32} + 4 q^{33} + 3 q^{36} - 14 q^{38} + 2 q^{41} - 14 q^{43} + 2 q^{44} + 2 q^{48} + q^{49} - 15 q^{50} - 12 q^{54} - 12 q^{57} + 2 q^{59} + q^{64} - 12 q^{66} + 2 q^{67} + 3 q^{72} + 2 q^{73} + 2 q^{75} + 2 q^{76} - 11 q^{81} + 2 q^{82} - 14 q^{83} - 14 q^{86} + 2 q^{88} + 2 q^{89} + 2 q^{96} + 2 q^{97} + q^{98} - 10 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2312))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
2312.1.d \(\chi_{2312}(1735, \cdot)\) None 0 1
2312.1.e \(\chi_{2312}(1155, \cdot)\) 2312.1.e.a 2 1
2312.1.e.b 4
2312.1.f \(\chi_{2312}(579, \cdot)\) 2312.1.f.a 1 1
2312.1.f.b 2
2312.1.f.c 4
2312.1.g \(\chi_{2312}(2311, \cdot)\) None 0 1
2312.1.j \(\chi_{2312}(251, \cdot)\) 2312.1.j.a 2 2
2312.1.j.b 2
2312.1.j.c 8
2312.1.l \(\chi_{2312}(327, \cdot)\) None 0 2
2312.1.m \(\chi_{2312}(399, \cdot)\) None 0 4
2312.1.p \(\chi_{2312}(155, \cdot)\) 2312.1.p.a 4 4
2312.1.p.b 4
2312.1.p.c 4
2312.1.p.d 4
2312.1.p.e 8
2312.1.q \(\chi_{2312}(653, \cdot)\) 2312.1.q.a 16 8
2312.1.t \(\chi_{2312}(65, \cdot)\) None 0 8
2312.1.w \(\chi_{2312}(135, \cdot)\) None 0 16
2312.1.x \(\chi_{2312}(35, \cdot)\) 2312.1.x.a 16 16
2312.1.y \(\chi_{2312}(67, \cdot)\) 2312.1.y.a 16 16
2312.1.z \(\chi_{2312}(103, \cdot)\) None 0 16
2312.1.bc \(\chi_{2312}(47, \cdot)\) None 0 32
2312.1.be \(\chi_{2312}(115, \cdot)\) 2312.1.be.a 32 32
2312.1.bg \(\chi_{2312}(19, \cdot)\) 2312.1.bg.a 64 64
2312.1.bj \(\chi_{2312}(15, \cdot)\) None 0 64
2312.1.bk \(\chi_{2312}(41, \cdot)\) None 0 128
2312.1.bn \(\chi_{2312}(5, \cdot)\) None 0 128

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2312))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2312)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(136))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1156))\)\(^{\oplus 2}\)