# Properties

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

## 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

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

## 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 the 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