## Defining parameters

 Level: $$N$$ = $$460 = 2^{2} \cdot 5 \cdot 23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$12$$ Newform subspaces: $$22$$ Sturm bound: $$25344$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(460))$$.

Total New Old
Modular forms 6776 3498 3278
Cusp forms 5897 3250 2647
Eisenstein series 879 248 631

## Trace form

 $$3250q - 18q^{2} + 4q^{3} - 22q^{4} - 56q^{5} - 66q^{6} - 4q^{7} - 30q^{8} - 46q^{9} + O(q^{10})$$ $$3250q - 18q^{2} + 4q^{3} - 22q^{4} - 56q^{5} - 66q^{6} - 4q^{7} - 30q^{8} - 46q^{9} - 45q^{10} - 22q^{12} - 44q^{13} - 22q^{14} + 7q^{15} - 50q^{16} - 22q^{17} - 10q^{18} + 30q^{19} - 25q^{20} - 58q^{21} - 44q^{22} + 38q^{23} - 44q^{24} - 58q^{25} - 74q^{26} + 58q^{27} - 22q^{28} - 34q^{29} - 33q^{30} + 30q^{31} - 38q^{32} - 22q^{33} - 66q^{34} - 18q^{35} - 200q^{36} - 108q^{37} - 132q^{38} - 80q^{39} - 113q^{40} - 156q^{41} - 242q^{42} - 68q^{43} - 176q^{44} - 164q^{45} - 242q^{46} - 76q^{47} - 198q^{48} - 170q^{49} - 27q^{50} - 112q^{51} - 234q^{52} - 112q^{53} - 198q^{54} - 22q^{55} - 176q^{56} - 82q^{57} - 148q^{58} + 20q^{59} - 55q^{60} - 96q^{61} - 22q^{62} + 106q^{63} - 22q^{64} + 11q^{65} + 40q^{67} - 20q^{68} + 78q^{69} - 66q^{70} + 134q^{71} - 64q^{72} + 40q^{73} + 59q^{75} + 44q^{76} - 110q^{77} + 198q^{78} + 28q^{79} + 34q^{80} - 250q^{81} + 78q^{82} + 10q^{83} + 286q^{84} - 174q^{85} + 154q^{86} - 108q^{87} + 154q^{88} - 164q^{89} + 142q^{90} - 96q^{91} + 176q^{92} - 632q^{93} + 132q^{94} - 85q^{95} + 352q^{96} - 298q^{97} + 126q^{98} - 242q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(460))$$

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
460.2.a $$\chi_{460}(1, \cdot)$$ 460.2.a.a 1 1
460.2.a.b 1
460.2.a.c 1
460.2.a.d 1
460.2.a.e 2
460.2.c $$\chi_{460}(369, \cdot)$$ 460.2.c.a 12 1
460.2.e $$\chi_{460}(91, \cdot)$$ 460.2.e.a 16 1
460.2.e.b 32
460.2.g $$\chi_{460}(459, \cdot)$$ 460.2.g.a 4 1
460.2.g.b 8
460.2.g.c 56
460.2.i $$\chi_{460}(137, \cdot)$$ 460.2.i.a 8 2
460.2.i.b 16
460.2.j $$\chi_{460}(47, \cdot)$$ 460.2.j.a 132 2
460.2.m $$\chi_{460}(41, \cdot)$$ 460.2.m.a 30 10
460.2.m.b 50
460.2.o $$\chi_{460}(19, \cdot)$$ 460.2.o.a 40 10
460.2.o.b 640
460.2.q $$\chi_{460}(11, \cdot)$$ 460.2.q.a 480 10
460.2.s $$\chi_{460}(9, \cdot)$$ 460.2.s.a 120 10
460.2.w $$\chi_{460}(3, \cdot)$$ 460.2.w.a 1360 20
460.2.x $$\chi_{460}(17, \cdot)$$ 460.2.x.a 240 20

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(460))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(460)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(46))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(92))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(115))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(230))$$$$^{\oplus 2}$$