↑

Properties

Label 353.2
Level 353
Weight 2
Dimension 5017
Nonzero newspaces 10
Newform subspaces 15
Sturm bound 20768
Trace bound 3

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 353 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 10 \)
Newform subspaces: \( 15 \)
Sturm bound: \(20768\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(353))\).

Total New Old
Modular forms 5368 5368 0
Cusp forms 5017 5017 0
Eisenstein series 351 351 0

Trace form

\( 5017 q - 173 q^{2} - 172 q^{3} - 169 q^{4} - 170 q^{5} - 164 q^{6} - 168 q^{7} - 161 q^{8} - 163 q^{9} + O(q^{10}) \) \( 5017 q - 173 q^{2} - 172 q^{3} - 169 q^{4} - 170 q^{5} - 164 q^{6} - 168 q^{7} - 161 q^{8} - 163 q^{9} - 158 q^{10} - 164 q^{11} - 148 q^{12} - 162 q^{13} - 152 q^{14} - 152 q^{15} - 145 q^{16} - 158 q^{17} - 137 q^{18} - 156 q^{19} - 134 q^{20} - 144 q^{21} - 140 q^{22} - 152 q^{23} - 116 q^{24} - 145 q^{25} - 134 q^{26} - 136 q^{27} - 120 q^{28} - 146 q^{29} - 104 q^{30} - 144 q^{31} - 113 q^{32} - 128 q^{33} - 122 q^{34} - 128 q^{35} - 85 q^{36} - 138 q^{37} - 116 q^{38} - 120 q^{39} - 86 q^{40} - 134 q^{41} - 80 q^{42} - 132 q^{43} - 92 q^{44} - 98 q^{45} - 104 q^{46} - 128 q^{47} - 52 q^{48} - 119 q^{49} - 83 q^{50} - 104 q^{51} - 78 q^{52} - 122 q^{53} - 56 q^{54} - 104 q^{55} - 56 q^{56} - 96 q^{57} - 86 q^{58} - 116 q^{59} - 8 q^{60} - 114 q^{61} - 80 q^{62} - 72 q^{63} - 49 q^{64} - 92 q^{65} - 32 q^{66} - 108 q^{67} - 50 q^{68} - 80 q^{69} - 32 q^{70} - 104 q^{71} + 19 q^{72} - 102 q^{73} - 62 q^{74} - 52 q^{75} - 36 q^{76} - 80 q^{77} - 8 q^{78} - 96 q^{79} + 10 q^{80} - 55 q^{81} - 50 q^{82} - 92 q^{83} + 48 q^{84} - 68 q^{85} - 44 q^{86} - 56 q^{87} + 4 q^{88} - 86 q^{89} + 58 q^{90} - 64 q^{91} - 8 q^{92} - 48 q^{93} - 32 q^{94} - 56 q^{95} + 76 q^{96} - 78 q^{97} - 5 q^{98} - 20 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(353))\)

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
353.2.a \(\chi_{353}(1, \cdot)\) 353.2.a.a 1 1
353.2.a.b 3
353.2.a.c 11
353.2.a.d 14
353.2.b \(\chi_{353}(352, \cdot)\) 353.2.b.a 28 1
353.2.c \(\chi_{353}(42, \cdot)\) 353.2.c.a 2 2
353.2.c.b 8
353.2.c.c 46
353.2.d \(\chi_{353}(70, \cdot)\) 353.2.d.a 112 4
353.2.e \(\chi_{353}(22, \cdot)\) 353.2.e.a 280 10
353.2.f \(\chi_{353}(36, \cdot)\) 353.2.f.a 232 8
353.2.g \(\chi_{353}(16, \cdot)\) 353.2.g.a 280 10
353.2.i \(\chi_{353}(4, \cdot)\) 353.2.i.a 560 20
353.2.j \(\chi_{353}(2, \cdot)\) 353.2.j.a 1120 40
353.2.k \(\chi_{353}(9, \cdot)\) 353.2.k.a 2320 80