# Properties

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

## 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

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

## 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 the 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