## Defining parameters

 Level: $$N$$ = $$462 = 2 \cdot 3 \cdot 7 \cdot 11$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$16$$ Sturm bound: $$46080$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(462))$$.

Total New Old
Modular forms 17760 4072 13688
Cusp forms 16800 4072 12728
Eisenstein series 960 0 960

## Trace form

 $$4072 q - 8 q^{2} + 12 q^{3} + 16 q^{4} - 72 q^{5} + 52 q^{6} - 184 q^{7} - 32 q^{8} - 200 q^{9} + O(q^{10})$$ $$4072 q - 8 q^{2} + 12 q^{3} + 16 q^{4} - 72 q^{5} + 52 q^{6} - 184 q^{7} - 32 q^{8} - 200 q^{9} - 304 q^{10} - 292 q^{11} - 112 q^{12} - 32 q^{13} + 104 q^{14} + 244 q^{15} + 64 q^{16} + 712 q^{17} + 724 q^{18} - 52 q^{19} + 96 q^{20} + 972 q^{21} - 48 q^{22} - 256 q^{23} - 208 q^{24} - 236 q^{25} + 608 q^{26} - 96 q^{27} + 64 q^{28} + 1328 q^{29} + 360 q^{30} + 872 q^{31} - 128 q^{32} + 2484 q^{33} - 624 q^{34} - 1364 q^{35} - 1288 q^{36} + 2192 q^{37} + 272 q^{38} + 40 q^{39} + 384 q^{40} - 544 q^{41} + 316 q^{42} + 4120 q^{43} + 2672 q^{44} + 840 q^{45} - 576 q^{46} - 664 q^{47} - 384 q^{48} - 11320 q^{49} - 6424 q^{50} - 9078 q^{51} - 4672 q^{52} - 7968 q^{53} - 1224 q^{54} - 3388 q^{55} + 448 q^{56} + 446 q^{57} - 1920 q^{58} - 1776 q^{59} + 1776 q^{60} - 1832 q^{61} - 3424 q^{62} - 4120 q^{63} + 1792 q^{64} - 4464 q^{65} - 160 q^{66} + 12192 q^{67} + 3328 q^{68} + 9152 q^{69} + 12288 q^{70} + 10256 q^{71} + 2848 q^{72} + 9344 q^{73} + 10176 q^{74} + 12978 q^{75} + 5536 q^{76} + 23176 q^{77} + 6512 q^{78} + 10688 q^{79} + 3968 q^{80} + 2672 q^{81} - 7352 q^{82} + 12144 q^{83} - 1680 q^{84} - 13456 q^{85} - 5296 q^{86} - 15384 q^{87} - 4000 q^{88} - 18768 q^{89} - 16952 q^{90} - 34068 q^{91} - 1536 q^{92} - 12616 q^{93} - 12112 q^{94} - 21792 q^{95} + 768 q^{96} + 11180 q^{97} + 88 q^{98} + 16248 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(462))$$

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
462.4.a $$\chi_{462}(1, \cdot)$$ 462.4.a.a 1 1
462.4.a.b 1
462.4.a.c 1
462.4.a.d 1
462.4.a.e 1
462.4.a.f 1
462.4.a.g 1
462.4.a.h 1
462.4.a.i 1
462.4.a.j 2
462.4.a.k 2
462.4.a.l 2
462.4.a.m 2
462.4.a.n 2
462.4.a.o 2
462.4.a.p 2
462.4.a.q 3
462.4.a.r 3
462.4.a.s 3
462.4.c $$\chi_{462}(197, \cdot)$$ 462.4.c.a 36 1
462.4.c.b 36
462.4.e $$\chi_{462}(307, \cdot)$$ 462.4.e.a 24 1
462.4.e.b 24
462.4.g $$\chi_{462}(419, \cdot)$$ 462.4.g.a 4 1
462.4.g.b 36
462.4.g.c 40
462.4.i $$\chi_{462}(67, \cdot)$$ 462.4.i.a 2 2
462.4.i.b 6
462.4.i.c 8
462.4.i.d 8
462.4.i.e 8
462.4.i.f 10
462.4.i.g 12
462.4.i.h 12
462.4.i.i 14
462.4.j $$\chi_{462}(169, \cdot)$$ n/a 144 4
462.4.k $$\chi_{462}(89, \cdot)$$ n/a 160 2
462.4.n $$\chi_{462}(65, \cdot)$$ n/a 192 2
462.4.p $$\chi_{462}(241, \cdot)$$ 462.4.p.a 48 2
462.4.p.b 48
462.4.s $$\chi_{462}(125, \cdot)$$ n/a 384 4
462.4.u $$\chi_{462}(13, \cdot)$$ n/a 192 4
462.4.w $$\chi_{462}(29, \cdot)$$ n/a 288 4
462.4.y $$\chi_{462}(25, \cdot)$$ n/a 384 8
462.4.ba $$\chi_{462}(19, \cdot)$$ n/a 384 8
462.4.bc $$\chi_{462}(95, \cdot)$$ n/a 768 8
462.4.bf $$\chi_{462}(5, \cdot)$$ n/a 768 8

"n/a" means that newforms for that character have not been added to the database yet

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(462))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(462)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(66))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(77))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(154))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(231))$$$$^{\oplus 2}$$