# Properties

 Label 825.4 Level 825 Weight 4 Dimension 48572 Nonzero newspaces 42 Sturm bound 192000 Trace bound 10

## Defining parameters

 Level: $$N$$ = $$825 = 3 \cdot 5^{2} \cdot 11$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$42$$ Sturm bound: $$192000$$ Trace bound: $$10$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(825))$$.

Total New Old
Modular forms 73120 49312 23808
Cusp forms 70880 48572 22308
Eisenstein series 2240 740 1500

## Trace form

 $$48572 q + 16 q^{2} - 69 q^{3} - 186 q^{4} + 12 q^{5} - 19 q^{6} - 150 q^{7} - 224 q^{8} - 197 q^{9} + O(q^{10})$$ $$48572 q + 16 q^{2} - 69 q^{3} - 186 q^{4} + 12 q^{5} - 19 q^{6} - 150 q^{7} - 224 q^{8} - 197 q^{9} - 312 q^{10} - 212 q^{11} + 162 q^{12} + 526 q^{13} + 1446 q^{14} + 288 q^{15} + 814 q^{16} - 820 q^{17} - 1081 q^{18} - 2044 q^{19} - 312 q^{20} - 2356 q^{21} - 970 q^{22} + 228 q^{23} + 653 q^{24} + 2932 q^{25} + 2638 q^{26} + 2793 q^{27} + 6624 q^{28} + 4172 q^{29} + 1692 q^{30} + 2330 q^{31} - 2236 q^{32} + 766 q^{33} - 7212 q^{34} - 4480 q^{35} - 2657 q^{36} - 7310 q^{37} - 12178 q^{38} - 8491 q^{39} - 11184 q^{40} - 5516 q^{41} - 10888 q^{42} - 9792 q^{43} - 14574 q^{44} + 4752 q^{45} + 2760 q^{46} + 6148 q^{47} + 10990 q^{48} + 16910 q^{49} + 21888 q^{50} + 9390 q^{51} + 43976 q^{52} + 19908 q^{53} + 10376 q^{54} + 9996 q^{55} + 35320 q^{56} + 11344 q^{57} + 18884 q^{58} + 2564 q^{59} + 3612 q^{60} + 2686 q^{61} - 18032 q^{62} + 3373 q^{63} - 31554 q^{64} - 9164 q^{65} - 4678 q^{66} - 20864 q^{67} - 35472 q^{68} - 14794 q^{69} - 18120 q^{70} - 892 q^{71} - 27686 q^{72} - 6550 q^{73} - 11554 q^{74} - 18872 q^{75} - 22016 q^{76} - 4356 q^{77} - 24220 q^{78} - 9770 q^{79} + 2008 q^{80} - 7353 q^{81} - 30322 q^{82} - 29928 q^{83} - 22916 q^{84} - 25236 q^{85} - 8344 q^{86} - 9204 q^{87} - 14942 q^{88} - 10304 q^{89} + 7128 q^{90} - 20210 q^{91} - 46326 q^{92} - 6239 q^{93} - 2576 q^{94} + 15728 q^{95} + 3460 q^{96} + 45336 q^{97} + 40756 q^{98} + 6421 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(825))$$

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
825.4.a $$\chi_{825}(1, \cdot)$$ 825.4.a.a 1 1
825.4.a.b 1
825.4.a.c 1
825.4.a.d 1
825.4.a.e 1
825.4.a.f 1
825.4.a.g 1
825.4.a.h 1
825.4.a.i 1
825.4.a.j 1
825.4.a.k 2
825.4.a.l 2
825.4.a.m 2
825.4.a.n 3
825.4.a.o 3
825.4.a.p 3
825.4.a.q 3
825.4.a.r 3
825.4.a.s 3
825.4.a.t 4
825.4.a.u 4
825.4.a.v 4
825.4.a.w 5
825.4.a.x 5
825.4.a.y 5
825.4.a.z 5
825.4.a.ba 7
825.4.a.bb 7
825.4.a.bc 7
825.4.a.bd 7
825.4.c $$\chi_{825}(199, \cdot)$$ 825.4.c.a 2 1
825.4.c.b 2
825.4.c.c 2
825.4.c.d 2
825.4.c.e 2
825.4.c.f 2
825.4.c.g 2
825.4.c.h 4
825.4.c.i 4
825.4.c.j 4
825.4.c.k 6
825.4.c.l 6
825.4.c.m 6
825.4.c.n 6
825.4.c.o 6
825.4.c.p 8
825.4.c.q 8
825.4.c.r 10
825.4.c.s 10
825.4.d $$\chi_{825}(824, \cdot)$$ n/a 212 1
825.4.f $$\chi_{825}(626, \cdot)$$ n/a 222 1
825.4.j $$\chi_{825}(43, \cdot)$$ n/a 216 2
825.4.k $$\chi_{825}(518, \cdot)$$ n/a 360 2
825.4.m $$\chi_{825}(16, \cdot)$$ n/a 720 4
825.4.n $$\chi_{825}(301, \cdot)$$ n/a 456 4
825.4.o $$\chi_{825}(421, \cdot)$$ n/a 720 4
825.4.p $$\chi_{825}(181, \cdot)$$ n/a 720 4
825.4.q $$\chi_{825}(166, \cdot)$$ n/a 608 4
825.4.r $$\chi_{825}(31, \cdot)$$ n/a 720 4
825.4.s $$\chi_{825}(479, \cdot)$$ n/a 1424 4
825.4.v $$\chi_{825}(379, \cdot)$$ n/a 720 4
825.4.x $$\chi_{825}(131, \cdot)$$ n/a 1424 4
825.4.bd $$\chi_{825}(281, \cdot)$$ n/a 1424 4
825.4.bf $$\chi_{825}(266, \cdot)$$ n/a 1424 4
825.4.bi $$\chi_{825}(101, \cdot)$$ n/a 888 4
825.4.bj $$\chi_{825}(116, \cdot)$$ n/a 1424 4
825.4.bl $$\chi_{825}(34, \cdot)$$ n/a 592 4
825.4.bo $$\chi_{825}(134, \cdot)$$ n/a 1424 4
825.4.br $$\chi_{825}(29, \cdot)$$ n/a 1424 4
825.4.bs $$\chi_{825}(74, \cdot)$$ n/a 848 4
825.4.bu $$\chi_{825}(239, \cdot)$$ n/a 1424 4
825.4.bv $$\chi_{825}(229, \cdot)$$ n/a 720 4
825.4.bx $$\chi_{825}(49, \cdot)$$ n/a 432 4
825.4.by $$\chi_{825}(4, \cdot)$$ n/a 720 4
825.4.cb $$\chi_{825}(169, \cdot)$$ n/a 720 4
825.4.ce $$\chi_{825}(164, \cdot)$$ n/a 1424 4
825.4.cg $$\chi_{825}(41, \cdot)$$ n/a 1424 4
825.4.ci $$\chi_{825}(113, \cdot)$$ n/a 2848 8
825.4.cl $$\chi_{825}(28, \cdot)$$ n/a 1440 8
825.4.cm $$\chi_{825}(13, \cdot)$$ n/a 1440 8
825.4.cs $$\chi_{825}(23, \cdot)$$ n/a 2400 8
825.4.ct $$\chi_{825}(218, \cdot)$$ n/a 1696 8
825.4.cu $$\chi_{825}(53, \cdot)$$ n/a 2848 8
825.4.cv $$\chi_{825}(38, \cdot)$$ n/a 2848 8
825.4.cw $$\chi_{825}(7, \cdot)$$ n/a 864 8
825.4.cx $$\chi_{825}(52, \cdot)$$ n/a 1440 8
825.4.cy $$\chi_{825}(172, \cdot)$$ n/a 1440 8
825.4.cz $$\chi_{825}(142, \cdot)$$ n/a 1440 8
825.4.df $$\chi_{825}(47, \cdot)$$ n/a 2848 8

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(825))$$ into lower level spaces

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