# Properties

 Label 825.6 Level 825 Weight 6 Dimension 81198 Nonzero newspaces 42 Sturm bound 288000 Trace bound 10

## Defining parameters

 Level: $$N$$ = $$825 = 3 \cdot 5^{2} \cdot 11$$ Weight: $$k$$ = $$6$$ Nonzero newspaces: $$42$$ Sturm bound: $$288000$$ Trace bound: $$10$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(\Gamma_1(825))$$.

Total New Old
Modular forms 121120 81938 39182
Cusp forms 118880 81198 37682
Eisenstein series 2240 740 1500

## Trace form

 $$81198 q - 20 q^{2} - 63 q^{3} + 286 q^{4} + 252 q^{5} - 997 q^{6} - 2168 q^{7} - 224 q^{8} + 991 q^{9} + O(q^{10})$$ $$81198 q - 20 q^{2} - 63 q^{3} + 286 q^{4} + 252 q^{5} - 997 q^{6} - 2168 q^{7} - 224 q^{8} + 991 q^{9} + 3408 q^{10} + 1534 q^{11} - 1350 q^{12} - 8888 q^{13} - 21474 q^{14} - 6852 q^{15} - 20738 q^{16} + 4766 q^{17} + 32825 q^{18} + 49668 q^{19} + 47688 q^{20} + 15500 q^{21} + 9406 q^{22} - 35484 q^{23} - 45091 q^{24} - 65948 q^{25} - 79514 q^{26} - 43278 q^{27} - 21136 q^{28} + 92216 q^{29} + 42732 q^{30} - 7350 q^{31} + 124772 q^{32} - 14267 q^{33} - 116188 q^{34} - 83800 q^{35} + 231307 q^{36} + 92702 q^{37} - 69538 q^{38} + 123500 q^{39} + 268976 q^{40} + 139480 q^{41} - 86284 q^{42} - 39276 q^{43} + 422322 q^{44} - 80448 q^{45} + 233320 q^{46} + 108718 q^{47} - 120554 q^{48} - 339046 q^{49} - 716952 q^{50} + 20514 q^{51} - 764344 q^{52} - 492654 q^{53} - 16456 q^{54} - 240964 q^{55} - 922760 q^{56} - 17078 q^{57} - 147316 q^{58} + 207542 q^{59} + 837852 q^{60} + 361584 q^{61} + 794584 q^{62} - 161468 q^{63} + 2236302 q^{64} + 454636 q^{65} + 244274 q^{66} + 383566 q^{67} - 131760 q^{68} - 127009 q^{69} - 925480 q^{70} - 135604 q^{71} + 323146 q^{72} - 808464 q^{73} - 793114 q^{74} + 329908 q^{75} - 888112 q^{76} - 131898 q^{77} + 1703564 q^{78} + 645360 q^{79} + 329368 q^{80} + 965823 q^{81} - 1433406 q^{82} - 581670 q^{83} - 1275236 q^{84} + 1138644 q^{85} + 1319168 q^{86} - 161076 q^{87} + 1869618 q^{88} + 1133848 q^{89} - 645072 q^{90} - 3605820 q^{91} - 3603558 q^{92} - 95837 q^{93} - 755040 q^{94} + 101168 q^{95} + 5555740 q^{96} + 1565726 q^{97} + 3754768 q^{98} + 2783065 q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(\Gamma_1(825))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
825.6.a $$\chi_{825}(1, \cdot)$$ 825.6.a.a 1 1
825.6.a.b 1
825.6.a.c 2
825.6.a.d 2
825.6.a.e 2
825.6.a.f 3
825.6.a.g 3
825.6.a.h 3
825.6.a.i 3
825.6.a.j 3
825.6.a.k 5
825.6.a.l 5
825.6.a.m 7
825.6.a.n 7
825.6.a.o 7
825.6.a.p 8
825.6.a.q 8
825.6.a.r 9
825.6.a.s 9
825.6.a.t 10
825.6.a.u 10
825.6.a.v 13
825.6.a.w 13
825.6.a.x 13
825.6.a.y 13
825.6.c $$\chi_{825}(199, \cdot)$$ n/a 148 1
825.6.d $$\chi_{825}(824, \cdot)$$ n/a 356 1
825.6.f $$\chi_{825}(626, \cdot)$$ n/a 374 1
825.6.j $$\chi_{825}(43, \cdot)$$ n/a 360 2
825.6.k $$\chi_{825}(518, \cdot)$$ n/a 600 2
825.6.m $$\chi_{825}(16, \cdot)$$ n/a 1200 4
825.6.n $$\chi_{825}(301, \cdot)$$ n/a 760 4
825.6.o $$\chi_{825}(421, \cdot)$$ n/a 1200 4
825.6.p $$\chi_{825}(181, \cdot)$$ n/a 1200 4
825.6.q $$\chi_{825}(166, \cdot)$$ n/a 992 4
825.6.r $$\chi_{825}(31, \cdot)$$ n/a 1200 4
825.6.s $$\chi_{825}(479, \cdot)$$ n/a 2384 4
825.6.v $$\chi_{825}(379, \cdot)$$ n/a 1200 4
825.6.x $$\chi_{825}(131, \cdot)$$ n/a 2384 4
825.6.bd $$\chi_{825}(281, \cdot)$$ n/a 2384 4
825.6.bf $$\chi_{825}(266, \cdot)$$ n/a 2384 4
825.6.bi $$\chi_{825}(101, \cdot)$$ n/a 1496 4
825.6.bj $$\chi_{825}(116, \cdot)$$ n/a 2384 4
825.6.bl $$\chi_{825}(34, \cdot)$$ n/a 1008 4
825.6.bo $$\chi_{825}(134, \cdot)$$ n/a 2384 4
825.6.br $$\chi_{825}(29, \cdot)$$ n/a 2384 4
825.6.bs $$\chi_{825}(74, \cdot)$$ n/a 1424 4
825.6.bu $$\chi_{825}(239, \cdot)$$ n/a 2384 4
825.6.bv $$\chi_{825}(229, \cdot)$$ n/a 1200 4
825.6.bx $$\chi_{825}(49, \cdot)$$ n/a 720 4
825.6.by $$\chi_{825}(4, \cdot)$$ n/a 1200 4
825.6.cb $$\chi_{825}(169, \cdot)$$ n/a 1200 4
825.6.ce $$\chi_{825}(164, \cdot)$$ n/a 2384 4
825.6.cg $$\chi_{825}(41, \cdot)$$ n/a 2384 4
825.6.ci $$\chi_{825}(113, \cdot)$$ n/a 4768 8
825.6.cl $$\chi_{825}(28, \cdot)$$ n/a 2400 8
825.6.cm $$\chi_{825}(13, \cdot)$$ n/a 2400 8
825.6.cs $$\chi_{825}(23, \cdot)$$ n/a 4000 8
825.6.ct $$\chi_{825}(218, \cdot)$$ n/a 2848 8
825.6.cu $$\chi_{825}(53, \cdot)$$ n/a 4768 8
825.6.cv $$\chi_{825}(38, \cdot)$$ n/a 4768 8
825.6.cw $$\chi_{825}(7, \cdot)$$ n/a 1440 8
825.6.cx $$\chi_{825}(52, \cdot)$$ n/a 2400 8
825.6.cy $$\chi_{825}(172, \cdot)$$ n/a 2400 8
825.6.cz $$\chi_{825}(142, \cdot)$$ n/a 2400 8
825.6.df $$\chi_{825}(47, \cdot)$$ n/a 4768 8

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

## Decomposition of $$S_{6}^{\mathrm{old}}(\Gamma_1(825))$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(\Gamma_1(825)) \cong$$ $$S_{6}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 12}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 6}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 8}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 6}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 3}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(75))$$$$^{\oplus 2}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(165))$$$$^{\oplus 2}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(275))$$$$^{\oplus 2}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(825))$$$$^{\oplus 1}$$