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Properties

Label 354.2
Level 354
Weight 2
Dimension 871
Nonzero newspaces 4
Newform subspaces 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: \( 4 \)
Newform subspaces: \( 16 \)
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

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

Display 100 coefficients 10 coefficients

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 available 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

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