# Properties

 Label 462.8 Level 462 Weight 8 Dimension 9496 Nonzero newspaces 16 Sturm bound 92160 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$462 = 2 \cdot 3 \cdot 7 \cdot 11$$ Weight: $$k$$ = $$8$$ Nonzero newspaces: $$16$$ Sturm bound: $$92160$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{8}(\Gamma_1(462))$$.

Total New Old
Modular forms 40800 9496 31304
Cusp forms 39840 9496 30344
Eisenstein series 960 0 960

## Trace form

 $$9496 q + 32 q^{2} + 768 q^{4} - 432 q^{5} - 5168 q^{6} - 1868 q^{7} + 2048 q^{8} - 10172 q^{9} + O(q^{10})$$ $$9496 q + 32 q^{2} + 768 q^{4} - 432 q^{5} - 5168 q^{6} - 1868 q^{7} + 2048 q^{8} - 10172 q^{9} - 46144 q^{10} - 25784 q^{11} + 16640 q^{12} + 100368 q^{13} + 19744 q^{14} - 111356 q^{15} + 16384 q^{16} + 48944 q^{17} + 130576 q^{18} + 30364 q^{19} - 29184 q^{20} - 136392 q^{21} + 117312 q^{22} + 434464 q^{23} + 97280 q^{24} + 982284 q^{25} - 801536 q^{26} - 1255020 q^{27} + 100864 q^{28} - 210752 q^{29} + 1113120 q^{30} + 1358456 q^{31} + 131072 q^{32} + 2710350 q^{33} - 2097984 q^{34} - 3404764 q^{35} - 3224704 q^{36} + 68280 q^{37} + 554176 q^{38} + 2555260 q^{39} - 393216 q^{40} + 1042720 q^{41} + 4591408 q^{42} - 6901688 q^{43} - 4906496 q^{44} - 17565840 q^{45} - 721792 q^{46} + 13903720 q^{47} + 4451364 q^{49} - 4294304 q^{50} + 6308598 q^{51} - 4068864 q^{52} - 8906712 q^{53} - 6785568 q^{54} - 27596868 q^{55} + 1839104 q^{56} - 23821378 q^{57} + 62848 q^{58} + 6703752 q^{59} + 8741376 q^{60} + 13609528 q^{61} + 22583680 q^{62} + 76224686 q^{63} + 15728640 q^{64} + 15031296 q^{65} - 16822144 q^{66} - 132188328 q^{67} - 36550144 q^{68} - 85990048 q^{69} - 73427392 q^{70} - 31782992 q^{71} - 542720 q^{72} + 37802744 q^{73} + 42989952 q^{74} + 90327858 q^{75} + 25227264 q^{76} + 100797284 q^{77} + 24418496 q^{78} + 42753536 q^{79} - 2097152 q^{80} - 82168708 q^{81} + 10762912 q^{82} - 131073168 q^{83} - 25357056 q^{84} - 120102776 q^{85} - 90801728 q^{86} - 36365340 q^{87} + 16246784 q^{88} + 39446592 q^{89} + 53580448 q^{90} + 187159184 q^{91} - 17366016 q^{92} - 103831696 q^{93} - 71006656 q^{94} - 344599272 q^{95} - 7864320 q^{96} + 221777236 q^{97} + 61475744 q^{98} + 259581180 q^{99} + O(q^{100})$$

## Decomposition of $$S_{8}^{\mathrm{new}}(\Gamma_1(462))$$

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
462.8.a $$\chi_{462}(1, \cdot)$$ 462.8.a.a 1 1
462.8.a.b 3
462.8.a.c 3
462.8.a.d 4
462.8.a.e 4
462.8.a.f 4
462.8.a.g 4
462.8.a.h 4
462.8.a.i 4
462.8.a.j 5
462.8.a.k 5
462.8.a.l 5
462.8.a.m 5
462.8.a.n 5
462.8.a.o 5
462.8.a.p 5
462.8.a.q 6
462.8.c $$\chi_{462}(197, \cdot)$$ n/a 168 1
462.8.e $$\chi_{462}(307, \cdot)$$ n/a 112 1
462.8.g $$\chi_{462}(419, \cdot)$$ n/a 184 1
462.8.i $$\chi_{462}(67, \cdot)$$ n/a 184 2
462.8.j $$\chi_{462}(169, \cdot)$$ n/a 336 4
462.8.k $$\chi_{462}(89, \cdot)$$ n/a 376 2
462.8.n $$\chi_{462}(65, \cdot)$$ n/a 448 2
462.8.p $$\chi_{462}(241, \cdot)$$ n/a 224 2
462.8.s $$\chi_{462}(125, \cdot)$$ n/a 896 4
462.8.u $$\chi_{462}(13, \cdot)$$ n/a 448 4
462.8.w $$\chi_{462}(29, \cdot)$$ n/a 672 4
462.8.y $$\chi_{462}(25, \cdot)$$ n/a 896 8
462.8.ba $$\chi_{462}(19, \cdot)$$ n/a 896 8
462.8.bc $$\chi_{462}(95, \cdot)$$ n/a 1792 8
462.8.bf $$\chi_{462}(5, \cdot)$$ n/a 1792 8

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

## Decomposition of $$S_{8}^{\mathrm{old}}(\Gamma_1(462))$$ into lower level spaces

$$S_{8}^{\mathrm{old}}(\Gamma_1(462)) \cong$$ $$S_{8}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 8}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 8}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 4}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 8}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 8}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 4}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 4}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 4}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 4}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 2}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(66))$$$$^{\oplus 2}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(77))$$$$^{\oplus 4}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(154))$$$$^{\oplus 2}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(231))$$$$^{\oplus 2}$$