## Defining parameters

 Level: $$N$$ = $$462 = 2 \cdot 3 \cdot 7 \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$16$$ Newform subspaces: $$61$$ Sturm bound: $$23040$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(462))$$.

Total New Old
Modular forms 6240 1353 4887
Cusp forms 5281 1353 3928
Eisenstein series 959 0 959

## Trace form

 $$1353q - 3q^{2} + q^{3} + 5q^{4} + 6q^{5} + 19q^{6} + 37q^{7} - 3q^{8} + 53q^{9} + O(q^{10})$$ $$1353q - 3q^{2} + q^{3} + 5q^{4} + 6q^{5} + 19q^{6} + 37q^{7} - 3q^{8} + 53q^{9} + 46q^{10} + 41q^{11} + 21q^{12} + 30q^{13} + 5q^{14} + 42q^{15} - 3q^{16} + 50q^{17} - 17q^{18} + 32q^{19} - 18q^{20} - 15q^{21} - 23q^{22} - 8q^{23} - 25q^{24} + 35q^{25} - 18q^{26} - 59q^{27} + 9q^{28} - 2q^{29} - 54q^{30} + 24q^{31} - 3q^{32} - 89q^{33} - 6q^{34} + 26q^{35} + 3q^{36} - 2q^{37} + 12q^{38} - 6q^{39} + 6q^{40} + 10q^{41} + 35q^{42} + 148q^{43} + 41q^{44} + 6q^{45} + 104q^{46} + 88q^{47} + q^{48} + 117q^{49} + 83q^{50} + 32q^{51} + 22q^{52} + 30q^{53} - 19q^{54} + 98q^{55} + 9q^{56} + 6q^{57} + 46q^{58} + 36q^{59} - 2q^{60} - 26q^{61} - 48q^{62} - 217q^{63} + 5q^{64} - 204q^{65} - 143q^{66} - 196q^{67} - 70q^{68} - 264q^{69} - 370q^{70} - 392q^{71} - 59q^{72} - 318q^{73} - 202q^{74} - 407q^{75} - 108q^{76} - 267q^{77} - 154q^{78} - 240q^{79} - 74q^{80} - 291q^{81} - 202q^{82} - 252q^{83} - 83q^{84} - 300q^{85} - 252q^{86} - 270q^{87} - 91q^{88} - 198q^{89} - 254q^{90} - 386q^{91} - 24q^{92} - 160q^{93} - 200q^{94} - 144q^{95} - 15q^{96} - 34q^{97} - 51q^{98} - 83q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(462))$$

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
462.2.a $$\chi_{462}(1, \cdot)$$ 462.2.a.a 1 1
462.2.a.b 1
462.2.a.c 1
462.2.a.d 1
462.2.a.e 1
462.2.a.f 1
462.2.a.g 1
462.2.a.h 2
462.2.c $$\chi_{462}(197, \cdot)$$ 462.2.c.a 12 1
462.2.c.b 12
462.2.e $$\chi_{462}(307, \cdot)$$ 462.2.e.a 8 1
462.2.e.b 8
462.2.g $$\chi_{462}(419, \cdot)$$ 462.2.g.a 4 1
462.2.g.b 4
462.2.g.c 4
462.2.g.d 4
462.2.g.e 8
462.2.i $$\chi_{462}(67, \cdot)$$ 462.2.i.a 2 2
462.2.i.b 2
462.2.i.c 2
462.2.i.d 2
462.2.i.e 4
462.2.i.f 6
462.2.i.g 6
462.2.j $$\chi_{462}(169, \cdot)$$ 462.2.j.a 4 4
462.2.j.b 4
462.2.j.c 4
462.2.j.d 4
462.2.j.e 8
462.2.j.f 8
462.2.j.g 8
462.2.j.h 8
462.2.k $$\chi_{462}(89, \cdot)$$ 462.2.k.a 4 2
462.2.k.b 4
462.2.k.c 4
462.2.k.d 8
462.2.k.e 8
462.2.k.f 8
462.2.k.g 20
462.2.n $$\chi_{462}(65, \cdot)$$ 462.2.n.a 4 2
462.2.n.b 4
462.2.n.c 4
462.2.n.d 4
462.2.n.e 24
462.2.n.f 24
462.2.p $$\chi_{462}(241, \cdot)$$ 462.2.p.a 16 2
462.2.p.b 16
462.2.s $$\chi_{462}(125, \cdot)$$ 462.2.s.a 128 4
462.2.u $$\chi_{462}(13, \cdot)$$ 462.2.u.a 32 4
462.2.u.b 32
462.2.w $$\chi_{462}(29, \cdot)$$ 462.2.w.a 48 4
462.2.w.b 48
462.2.y $$\chi_{462}(25, \cdot)$$ 462.2.y.a 24 8
462.2.y.b 24
462.2.y.c 40
462.2.y.d 40
462.2.ba $$\chi_{462}(19, \cdot)$$ 462.2.ba.a 64 8
462.2.ba.b 64
462.2.bc $$\chi_{462}(95, \cdot)$$ 462.2.bc.a 128 8
462.2.bc.b 128
462.2.bf $$\chi_{462}(5, \cdot)$$ 462.2.bf.a 256 8

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(462))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(462)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(66))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(77))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(154))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(231))$$$$^{\oplus 2}$$