Properties

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

Downloads

Learn more

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

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

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 the 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

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