# Properties

 Label 245.2 Level 245 Weight 2 Dimension 1925 Nonzero newspaces 12 Newform subspaces 46 Sturm bound 9408 Trace bound 2

## 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

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

## 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

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