Properties

Label 354.2
Level 354
Weight 2
Dimension 871
Nonzero newspaces 4
Newforms 16
Sturm bound 13920
Trace bound 1

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Defining parameters

Level: \( N \) = \( 354 = 2 \cdot 3 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newforms: \( 16 \)
Sturm bound: \(13920\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(354))\).

Total New Old
Modular forms 3712 871 2841
Cusp forms 3249 871 2378
Eisenstein series 463 0 463

Trace form

\( 871q + q^{2} + q^{3} + q^{4} + 6q^{5} + q^{6} + 8q^{7} + q^{8} + q^{9} + O(q^{10}) \) \( 871q + q^{2} + q^{3} + q^{4} + 6q^{5} + q^{6} + 8q^{7} + q^{8} + q^{9} + 6q^{10} + 12q^{11} + q^{12} + 14q^{13} + 8q^{14} + 6q^{15} + q^{16} + 18q^{17} + q^{18} + 20q^{19} + 6q^{20} + 8q^{21} + 12q^{22} + 24q^{23} + q^{24} + 31q^{25} + 14q^{26} + q^{27} + 8q^{28} + 30q^{29} + 6q^{30} + 32q^{31} + q^{32} + 12q^{33} + 18q^{34} + 48q^{35} + q^{36} + 38q^{37} + 20q^{38} + 14q^{39} + 6q^{40} + 42q^{41} + 8q^{42} + 44q^{43} + 12q^{44} - 52q^{45} - 92q^{46} - 68q^{47} + q^{48} - 175q^{49} - 201q^{50} - 214q^{51} - 102q^{52} - 178q^{53} - 202q^{54} - 276q^{55} + 8q^{56} - 270q^{57} - 86q^{58} - 173q^{59} - 168q^{60} - 170q^{61} - 84q^{62} - 282q^{63} + q^{64} - 264q^{65} - 191q^{66} - 164q^{67} - 98q^{68} - 208q^{69} - 184q^{70} - 160q^{71} + q^{72} - 42q^{73} - 78q^{74} - 27q^{75} + 20q^{76} + 96q^{77} + 14q^{78} + 80q^{79} + 6q^{80} + q^{81} + 42q^{82} + 84q^{83} + 8q^{84} + 108q^{85} + 44q^{86} + 30q^{87} + 12q^{88} + 90q^{89} + 6q^{90} + 112q^{91} + 24q^{92} + 32q^{93} + 48q^{94} + 120q^{95} + q^{96} + 98q^{97} + 57q^{98} + 12q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(354))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
354.2.a \(\chi_{354}(1, \cdot)\) 354.2.a.a 1 1
354.2.a.b 1
354.2.a.c 1
354.2.a.d 1
354.2.a.e 1
354.2.a.f 1
354.2.a.g 2
354.2.a.h 3
354.2.c \(\chi_{354}(353, \cdot)\) 354.2.c.a 10 1
354.2.c.b 10
354.2.e \(\chi_{354}(7, \cdot)\) 354.2.e.a 56 28
354.2.e.b 56
354.2.e.c 84
354.2.e.d 84
354.2.g \(\chi_{354}(11, \cdot)\) 354.2.g.a 280 28
354.2.g.b 280

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(354))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(354)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(118))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(177))\)\(^{\oplus 2}\)