↑

Properties

Label 349.2
Level 349
Weight 2
Dimension 4902
Nonzero newspaces 8
Newform subspaces 10
Sturm bound 20300
Trace bound 3

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 349 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 10 \)
Sturm bound: \(20300\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(349))\).

Total New Old
Modular forms 5249 5249 0
Cusp forms 4902 4902 0
Eisenstein series 347 347 0

Trace form

\( 4902 q - 171 q^{2} - 170 q^{3} - 167 q^{4} - 168 q^{5} - 162 q^{6} - 166 q^{7} - 159 q^{8} - 161 q^{9} + O(q^{10}) \) \( 4902 q - 171 q^{2} - 170 q^{3} - 167 q^{4} - 168 q^{5} - 162 q^{6} - 166 q^{7} - 159 q^{8} - 161 q^{9} - 156 q^{10} - 162 q^{11} - 146 q^{12} - 160 q^{13} - 150 q^{14} - 150 q^{15} - 143 q^{16} - 156 q^{17} - 135 q^{18} - 154 q^{19} - 132 q^{20} - 142 q^{21} - 138 q^{22} - 150 q^{23} - 114 q^{24} - 143 q^{25} - 132 q^{26} - 134 q^{27} - 118 q^{28} - 144 q^{29} - 102 q^{30} - 142 q^{31} - 111 q^{32} - 126 q^{33} - 120 q^{34} - 126 q^{35} - 83 q^{36} - 136 q^{37} - 114 q^{38} - 118 q^{39} - 84 q^{40} - 132 q^{41} - 78 q^{42} - 130 q^{43} - 90 q^{44} - 96 q^{45} - 102 q^{46} - 126 q^{47} - 50 q^{48} - 117 q^{49} - 81 q^{50} - 102 q^{51} - 76 q^{52} - 120 q^{53} - 54 q^{54} - 102 q^{55} - 54 q^{56} - 94 q^{57} - 84 q^{58} - 114 q^{59} - 6 q^{60} - 112 q^{61} - 78 q^{62} - 70 q^{63} - 47 q^{64} - 90 q^{65} - 30 q^{66} - 106 q^{67} - 48 q^{68} - 78 q^{69} - 30 q^{70} - 102 q^{71} + 21 q^{72} - 100 q^{73} - 60 q^{74} - 50 q^{75} - 34 q^{76} - 78 q^{77} - 6 q^{78} - 94 q^{79} + 12 q^{80} - 53 q^{81} - 48 q^{82} - 90 q^{83} + 50 q^{84} - 66 q^{85} - 42 q^{86} - 54 q^{87} + 6 q^{88} - 84 q^{89} + 60 q^{90} - 62 q^{91} - 6 q^{92} - 46 q^{93} - 30 q^{94} - 54 q^{95} + 78 q^{96} - 76 q^{97} - 3 q^{98} - 18 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(349))\)

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
349.2.a \(\chi_{349}(1, \cdot)\) 349.2.a.a 11 1
349.2.a.b 17
349.2.b \(\chi_{349}(348, \cdot)\) 349.2.b.a 2 1
349.2.b.b 26
349.2.c \(\chi_{349}(122, \cdot)\) 349.2.c.a 56 2
349.2.e \(\chi_{349}(123, \cdot)\) 349.2.e.a 58 2
349.2.g \(\chi_{349}(31, \cdot)\) 349.2.g.a 756 28
349.2.h \(\chi_{349}(17, \cdot)\) 349.2.h.a 784 28
349.2.i \(\chi_{349}(9, \cdot)\) 349.2.i.a 1568 56
349.2.k \(\chi_{349}(3, \cdot)\) 349.2.k.a 1624 56