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Properties

Label 316.2
Level 316
Weight 2
Dimension 1742
Nonzero newspaces 8
Newform subspaces 15
Sturm bound 12480
Trace bound 1

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Defining parameters

Level: \( N \) = \( 316 = 2^{2} \cdot 79 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 15 \)
Sturm bound: \(12480\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(316))\).

Total New Old
Modular forms 3315 1898 1417
Cusp forms 2926 1742 1184
Eisenstein series 389 156 233

Trace form

\( 1742 q - 39 q^{2} - 39 q^{4} - 78 q^{5} - 39 q^{6} - 39 q^{8} - 78 q^{9} + O(q^{10}) \) \( 1742 q - 39 q^{2} - 39 q^{4} - 78 q^{5} - 39 q^{6} - 39 q^{8} - 78 q^{9} - 39 q^{10} - 39 q^{12} - 78 q^{13} - 39 q^{14} - 39 q^{16} - 78 q^{17} - 39 q^{18} - 39 q^{20} - 78 q^{21} - 39 q^{22} - 39 q^{24} - 78 q^{25} - 39 q^{26} - 39 q^{28} - 78 q^{29} - 39 q^{30} - 39 q^{32} - 78 q^{33} - 39 q^{34} - 39 q^{36} - 78 q^{37} - 39 q^{38} - 39 q^{40} - 78 q^{41} - 39 q^{42} - 39 q^{44} - 78 q^{45} - 39 q^{46} - 39 q^{48} - 78 q^{49} - 39 q^{50} - 39 q^{52} - 78 q^{53} - 39 q^{54} - 39 q^{56} - 78 q^{57} - 39 q^{58} - 39 q^{60} - 78 q^{61} - 39 q^{62} - 52 q^{63} - 39 q^{64} - 156 q^{65} - 39 q^{66} - 91 q^{67} - 39 q^{68} - 234 q^{69} - 39 q^{70} - 78 q^{71} - 39 q^{72} - 156 q^{73} - 39 q^{74} - 156 q^{75} - 39 q^{76} - 195 q^{77} - 234 q^{79} - 78 q^{80} - 312 q^{81} - 39 q^{82} - 117 q^{83} - 39 q^{84} - 234 q^{85} - 39 q^{86} - 78 q^{87} - 39 q^{88} - 156 q^{89} - 39 q^{90} - 156 q^{91} - 39 q^{92} - 169 q^{93} - 39 q^{94} - 78 q^{95} - 39 q^{96} - 130 q^{97} - 39 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(316))\)

We only show spaces with even 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
316.2.a \(\chi_{316}(1, \cdot)\) 316.2.a.a 1 1
316.2.a.b 1
316.2.a.c 2
316.2.a.d 2
316.2.d \(\chi_{316}(315, \cdot)\) 316.2.d.a 4 1
316.2.d.b 10
316.2.d.c 24
316.2.e \(\chi_{316}(181, \cdot)\) 316.2.e.a 2 2
316.2.e.b 12
316.2.f \(\chi_{316}(103, \cdot)\) 316.2.f.a 4 2
316.2.f.b 72
316.2.i \(\chi_{316}(21, \cdot)\) 316.2.i.a 72 12
316.2.j \(\chi_{316}(15, \cdot)\) 316.2.j.a 456 12
316.2.m \(\chi_{316}(5, \cdot)\) 316.2.m.a 168 24
316.2.p \(\chi_{316}(3, \cdot)\) 316.2.p.a 912 24

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(316))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(316)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(79))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(158))\)\(^{\oplus 2}\)