# Properties

 Label 215.2 Level 215 Weight 2 Dimension 1567 Nonzero newspaces 12 Newform subspaces 23 Sturm bound 7392 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$215 = 5 \cdot 43$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$12$$ Newform subspaces: $$23$$ Sturm bound: $$7392$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(215))$$.

Total New Old
Modular forms 2016 1815 201
Cusp forms 1681 1567 114
Eisenstein series 335 248 87

## Trace form

 $$1567q - 45q^{2} - 46q^{3} - 49q^{4} - 64q^{5} - 138q^{6} - 50q^{7} - 57q^{8} - 55q^{9} + O(q^{10})$$ $$1567q - 45q^{2} - 46q^{3} - 49q^{4} - 64q^{5} - 138q^{6} - 50q^{7} - 57q^{8} - 55q^{9} - 66q^{10} - 138q^{11} - 70q^{12} - 56q^{13} - 66q^{14} - 67q^{15} - 157q^{16} - 60q^{17} - 81q^{18} - 62q^{19} - 70q^{20} - 158q^{21} - 78q^{22} - 66q^{23} - 102q^{24} - 64q^{25} - 168q^{26} - 82q^{27} - 98q^{28} - 72q^{29} - 75q^{30} - 144q^{31} - 21q^{32} - 6q^{33} + 30q^{34} - 29q^{35} + 7q^{36} + 4q^{37} + 66q^{38} + 90q^{40} - 126q^{41} + 72q^{42} + 125q^{43} + 29q^{45} - 30q^{46} - 48q^{47} + 170q^{48} - q^{49} + 18q^{50} - 114q^{51} + 84q^{52} - 12q^{53} - 36q^{54} - 33q^{55} - 162q^{56} - 108q^{57} - 132q^{58} - 102q^{59} - 91q^{60} - 188q^{61} - 138q^{62} - 146q^{63} - 169q^{64} - 77q^{65} - 270q^{66} - 110q^{67} - 168q^{68} - 54q^{69} - 3q^{70} - 114q^{71} + 183q^{72} - 32q^{73} + 138q^{74} - 25q^{75} + 28q^{76} + 114q^{77} + 336q^{78} + 46q^{79} + 74q^{80} + 89q^{81} + 252q^{82} + 42q^{83} + 574q^{84} + 24q^{85} + 81q^{86} + 216q^{87} + 198q^{88} + 36q^{89} + 276q^{90} - 70q^{91} + 210q^{92} + 166q^{93} + 150q^{94} + q^{95} + 168q^{96} + 112q^{97} + 81q^{98} + 96q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(215))$$

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
215.2.a $$\chi_{215}(1, \cdot)$$ 215.2.a.a 1 1
215.2.a.b 3
215.2.a.c 5
215.2.a.d 6
215.2.b $$\chi_{215}(44, \cdot)$$ 215.2.b.a 6 1
215.2.b.b 14
215.2.e $$\chi_{215}(6, \cdot)$$ 215.2.e.a 2 2
215.2.e.b 4
215.2.e.c 10
215.2.e.d 12
215.2.g $$\chi_{215}(42, \cdot)$$ 215.2.g.a 40 2
215.2.i $$\chi_{215}(49, \cdot)$$ 215.2.i.a 40 2
215.2.k $$\chi_{215}(11, \cdot)$$ 215.2.k.a 42 6
215.2.k.b 54
215.2.l $$\chi_{215}(7, \cdot)$$ 215.2.l.a 4 4
215.2.l.b 4
215.2.l.c 72
215.2.p $$\chi_{215}(4, \cdot)$$ 215.2.p.a 120 6
215.2.q $$\chi_{215}(31, \cdot)$$ 215.2.q.a 72 12
215.2.q.b 96
215.2.r $$\chi_{215}(2, \cdot)$$ 215.2.r.a 240 12
215.2.u $$\chi_{215}(9, \cdot)$$ 215.2.u.a 240 12
215.2.x $$\chi_{215}(3, \cdot)$$ 215.2.x.a 480 24

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(215))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(215)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(43))$$$$^{\oplus 2}$$