## Defining parameters

 Level: $$N$$ = $$260 = 2^{2} \cdot 5 \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$20$$ Newform subspaces: $$43$$ Sturm bound: $$8064$$ Trace bound: $$9$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(260))$$.

Total New Old
Modular forms 2256 1128 1128
Cusp forms 1777 1000 777
Eisenstein series 479 128 351

## Trace form

 $$1000 q - 8 q^{2} + 4 q^{3} - 12 q^{4} - 26 q^{5} - 36 q^{6} - 20 q^{8} - 10 q^{9} + O(q^{10})$$ $$1000 q - 8 q^{2} + 4 q^{3} - 12 q^{4} - 26 q^{5} - 36 q^{6} - 20 q^{8} - 10 q^{9} - 30 q^{10} + 12 q^{11} - 24 q^{12} - 24 q^{14} + 8 q^{15} - 20 q^{16} - 18 q^{17} - 36 q^{18} - 34 q^{20} - 108 q^{21} - 72 q^{22} - 36 q^{23} - 108 q^{24} - 62 q^{25} - 100 q^{26} - 80 q^{27} - 72 q^{28} - 42 q^{29} - 66 q^{30} + 12 q^{31} - 88 q^{32} - 36 q^{33} - 60 q^{34} + 22 q^{35} - 60 q^{36} + 22 q^{37} - 24 q^{38} + 44 q^{39} - 4 q^{40} - 70 q^{41} + 24 q^{42} + 16 q^{43} + 48 q^{44} - 61 q^{45} + 84 q^{46} + 24 q^{47} + 84 q^{48} - 142 q^{49} + 52 q^{50} - 72 q^{51} + 100 q^{52} - 168 q^{53} + 72 q^{54} - 78 q^{55} + 72 q^{56} - 252 q^{57} + 68 q^{58} - 84 q^{59} + 12 q^{60} - 238 q^{61} + 12 q^{62} - 168 q^{63} - 177 q^{65} - 144 q^{66} - 108 q^{67} - 144 q^{68} - 156 q^{69} - 60 q^{70} - 96 q^{71} - 144 q^{72} - 112 q^{73} - 180 q^{74} - 142 q^{75} - 156 q^{76} - 144 q^{77} - 240 q^{78} - 40 q^{79} - 164 q^{80} - 154 q^{81} - 164 q^{82} - 96 q^{83} - 96 q^{84} - 21 q^{85} - 144 q^{86} - 96 q^{88} - 12 q^{89} - 36 q^{90} - 72 q^{92} - 12 q^{93} + 12 q^{94} - 8 q^{95} + 144 q^{96} + 32 q^{97} - 16 q^{98} + 108 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(260))$$

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
260.2.a $$\chi_{260}(1, \cdot)$$ 260.2.a.a 1 1
260.2.a.b 3
260.2.c $$\chi_{260}(209, \cdot)$$ 260.2.c.a 6 1
260.2.d $$\chi_{260}(129, \cdot)$$ 260.2.d.a 8 1
260.2.f $$\chi_{260}(181, \cdot)$$ 260.2.f.a 6 1
260.2.i $$\chi_{260}(61, \cdot)$$ 260.2.i.a 2 2
260.2.i.b 2
260.2.i.c 2
260.2.i.d 2
260.2.j $$\chi_{260}(31, \cdot)$$ 260.2.j.a 56 2
260.2.m $$\chi_{260}(57, \cdot)$$ 260.2.m.a 2 2
260.2.m.b 4
260.2.m.c 8
260.2.o $$\chi_{260}(27, \cdot)$$ 260.2.o.a 72 2
260.2.p $$\chi_{260}(103, \cdot)$$ 260.2.p.a 2 2
260.2.p.b 2
260.2.p.c 8
260.2.p.d 64
260.2.r $$\chi_{260}(177, \cdot)$$ 260.2.r.a 2 2
260.2.r.b 4
260.2.r.c 8
260.2.u $$\chi_{260}(99, \cdot)$$ 260.2.u.a 2 2
260.2.u.b 2
260.2.u.c 72
260.2.x $$\chi_{260}(101, \cdot)$$ 260.2.x.a 8 2
260.2.z $$\chi_{260}(49, \cdot)$$ 260.2.z.a 16 2
260.2.ba $$\chi_{260}(9, \cdot)$$ 260.2.ba.a 12 2
260.2.bc $$\chi_{260}(19, \cdot)$$ 260.2.bc.a 4 4
260.2.bc.b 4
260.2.bc.c 144
260.2.bf $$\chi_{260}(37, \cdot)$$ 260.2.bf.a 4 4
260.2.bf.b 4
260.2.bf.c 20
260.2.bg $$\chi_{260}(23, \cdot)$$ 260.2.bg.a 4 4
260.2.bg.b 4
260.2.bg.c 144
260.2.bj $$\chi_{260}(3, \cdot)$$ 260.2.bj.a 4 4
260.2.bj.b 4
260.2.bj.c 144
260.2.bk $$\chi_{260}(33, \cdot)$$ 260.2.bk.a 4 4
260.2.bk.b 4
260.2.bk.c 20
260.2.bn $$\chi_{260}(11, \cdot)$$ 260.2.bn.a 112 4

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(260))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(260)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(52))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(65))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(130))$$$$^{\oplus 2}$$