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Properties

Label 2456.1
Level 2456
Weight 1
Dimension 172
Nonzero newspaces 6
Newform subspaces 8
Sturm bound 376992
Trace bound 2

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Defining parameters

Level: \( N \) = \( 2456 = 2^{3} \cdot 307 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 8 \)
Sturm bound: \(376992\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2456))\).

Total New Old
Modular forms 2026 782 1244
Cusp forms 190 172 18
Eisenstein series 1836 610 1226

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 168 4 0 0

Trace form

\( 172 q - q^{2} - 2 q^{3} + 11 q^{4} - 4 q^{6} - 2 q^{7} - q^{8} + 7 q^{9} + O(q^{10}) \) \( 172 q - q^{2} - 2 q^{3} + 11 q^{4} - 4 q^{6} - 2 q^{7} - q^{8} + 7 q^{9} - 4 q^{10} - 4 q^{11} - 2 q^{12} - 2 q^{14} - 4 q^{15} + 19 q^{16} - 12 q^{17} - 3 q^{18} - 2 q^{19} - 2 q^{22} - 4 q^{24} + 13 q^{25} - 4 q^{27} - 2 q^{28} - q^{32} - 4 q^{33} - 2 q^{34} - 4 q^{35} + 15 q^{36} - 2 q^{38} - 4 q^{39} - 6 q^{41} - 4 q^{42} - 4 q^{43} + 2 q^{46} - 2 q^{48} + 13 q^{49} - q^{50} - 4 q^{51} - 8 q^{54} + 2 q^{56} - 4 q^{57} - 4 q^{60} + 2 q^{62} - 6 q^{63} + 11 q^{64} - 6 q^{65} - 4 q^{66} - 4 q^{67} + 4 q^{68} - 4 q^{70} - 2 q^{71} - 3 q^{72} - 4 q^{73} + 2 q^{74} - 2 q^{75} - 2 q^{76} - 2 q^{79} + 11 q^{81} - 2 q^{82} - 4 q^{83} - 4 q^{86} - 4 q^{87} - 2 q^{88} - 6 q^{89} - 4 q^{90} + 4 q^{91} - 2 q^{94} - 4 q^{96} - 4 q^{97} - q^{98} - 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2456))\)

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
2456.1.c \(\chi_{2456}(1841, \cdot)\) None 0 1
2456.1.d \(\chi_{2456}(615, \cdot)\) None 0 1
2456.1.g \(\chi_{2456}(1843, \cdot)\) None 0 1
2456.1.h \(\chi_{2456}(613, \cdot)\) 2456.1.h.a 8 1
2456.1.h.b 8
2456.1.k \(\chi_{2456}(631, \cdot)\) None 0 2
2456.1.l \(\chi_{2456}(1553, \cdot)\) None 0 2
2456.1.n \(\chi_{2456}(325, \cdot)\) None 0 2
2456.1.o \(\chi_{2456}(1859, \cdot)\) 2456.1.o.a 2 2
2456.1.o.b 4
2456.1.s \(\chi_{2456}(33, \cdot)\) None 0 6
2456.1.u \(\chi_{2456}(287, \cdot)\) None 0 6
2456.1.w \(\chi_{2456}(475, \cdot)\) 2456.1.w.a 6 6
2456.1.y \(\chi_{2456}(261, \cdot)\) None 0 6
2456.1.z \(\chi_{2456}(205, \cdot)\) None 0 16
2456.1.ba \(\chi_{2456}(115, \cdot)\) 2456.1.ba.a 16 16
2456.1.bd \(\chi_{2456}(623, \cdot)\) None 0 16
2456.1.be \(\chi_{2456}(193, \cdot)\) None 0 16
2456.1.bi \(\chi_{2456}(19, \cdot)\) 2456.1.bi.a 32 32
2456.1.bj \(\chi_{2456}(125, \cdot)\) None 0 32
2456.1.bl \(\chi_{2456}(57, \cdot)\) None 0 32
2456.1.bm \(\chi_{2456}(79, \cdot)\) None 0 32
2456.1.bp \(\chi_{2456}(5, \cdot)\) None 0 96
2456.1.br \(\chi_{2456}(11, \cdot)\) 2456.1.br.a 96 96
2456.1.bt \(\chi_{2456}(7, \cdot)\) None 0 96
2456.1.bv \(\chi_{2456}(73, \cdot)\) None 0 96

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2456))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2456)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(307))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1228))\)\(^{\oplus 2}\)