## Defining parameters

 Level: $$N$$ = $$245 = 5 \cdot 7^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$12$$ Newform subspaces: $$46$$ Sturm bound: $$9408$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(245))$$.

Total New Old
Modular forms 2592 2215 377
Cusp forms 2113 1925 188
Eisenstein series 479 290 189

## Trace form

 $$1925q - 27q^{2} - 30q^{3} - 39q^{4} - 50q^{5} - 114q^{6} - 44q^{7} - 75q^{8} - 57q^{9} + O(q^{10})$$ $$1925q - 27q^{2} - 30q^{3} - 39q^{4} - 50q^{5} - 114q^{6} - 44q^{7} - 75q^{8} - 57q^{9} - 72q^{10} - 114q^{11} - 102q^{12} - 60q^{13} - 72q^{14} - 113q^{15} - 171q^{16} - 72q^{17} - 135q^{18} - 78q^{19} - 116q^{20} - 158q^{21} - 138q^{22} - 90q^{23} - 102q^{24} - 66q^{25} - 156q^{26} - 66q^{27} - 80q^{28} - 72q^{29} - 27q^{30} - 126q^{31} - 63q^{32} - 42q^{33} - 60q^{34} - 57q^{35} - 111q^{36} - 4q^{37} - 18q^{38} + 32q^{39} + 66q^{40} - 72q^{41} + 42q^{42} - 30q^{43} + 78q^{44} - 5q^{45} + 6q^{46} - 54q^{47} + 104q^{48} + 40q^{49} - 201q^{50} - 126q^{51} + 92q^{52} - 96q^{53} + 18q^{54} - 18q^{55} - 12q^{56} - 90q^{57} + 72q^{58} - 18q^{59} + 19q^{60} - 22q^{61} - 6q^{62} - 60q^{63} + 21q^{64} - 49q^{65} - 222q^{66} - 30q^{67} - 84q^{68} - 90q^{69} + 3q^{70} - 258q^{71} - 195q^{72} - 48q^{73} - 96q^{74} - 51q^{75} - 210q^{76} - 126q^{77} - 30q^{78} - 66q^{79} - 5q^{80} - 129q^{81} + 54q^{82} - 6q^{83} + 208q^{84} - 87q^{85} - 36q^{86} + 78q^{87} + 240q^{88} + 267q^{90} - 82q^{91} + 48q^{92} + 270q^{93} + 120q^{94} + 101q^{95} + 300q^{96} + 42q^{97} + 408q^{98} - 12q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(245))$$

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
245.2.a $$\chi_{245}(1, \cdot)$$ 245.2.a.a 1 1
245.2.a.b 1
245.2.a.c 1
245.2.a.d 2
245.2.a.e 2
245.2.a.f 2
245.2.a.g 2
245.2.a.h 2
245.2.b $$\chi_{245}(99, \cdot)$$ 245.2.b.a 2 1
245.2.b.b 2
245.2.b.c 2
245.2.b.d 2
245.2.b.e 4
245.2.b.f 4
245.2.e $$\chi_{245}(116, \cdot)$$ 245.2.e.a 2 2
245.2.e.b 2
245.2.e.c 2
245.2.e.d 2
245.2.e.e 4
245.2.e.f 4
245.2.e.g 4
245.2.e.h 4
245.2.e.i 4
245.2.f $$\chi_{245}(48, \cdot)$$ 245.2.f.a 4 2
245.2.f.b 4
245.2.f.c 24
245.2.j $$\chi_{245}(79, \cdot)$$ 245.2.j.a 4 2
245.2.j.b 4
245.2.j.c 4
245.2.j.d 4
245.2.j.e 4
245.2.j.f 4
245.2.j.g 8
245.2.k $$\chi_{245}(36, \cdot)$$ 245.2.k.a 54 6
245.2.k.b 66
245.2.l $$\chi_{245}(68, \cdot)$$ 245.2.l.a 4 4
245.2.l.b 4
245.2.l.c 8
245.2.l.d 48
245.2.p $$\chi_{245}(29, \cdot)$$ 245.2.p.a 12 6
245.2.p.b 144
245.2.q $$\chi_{245}(11, \cdot)$$ 245.2.q.a 96 12
245.2.q.b 120
245.2.s $$\chi_{245}(13, \cdot)$$ 245.2.s.a 312 12
245.2.t $$\chi_{245}(4, \cdot)$$ 245.2.t.a 312 12
245.2.x $$\chi_{245}(3, \cdot)$$ 245.2.x.a 624 24

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(245))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(245)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 2}$$