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Properties

Label 520.4
Level 520
Weight 4
Dimension 12196
Nonzero newspaces 32
Sturm bound 64512
Trace bound 6

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Defining parameters

Level: \( N \) = \( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(64512\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(520))\).

Total New Old
Modular forms 24768 12460 12308
Cusp forms 23616 12196 11420
Eisenstein series 1152 264 888

Trace form

\( 12196 q - 24 q^{2} - 32 q^{3} - 64 q^{4} + 18 q^{5} + 56 q^{6} - 8 q^{7} + 144 q^{8} - 174 q^{9} + O(q^{10}) \) \( 12196 q - 24 q^{2} - 32 q^{3} - 64 q^{4} + 18 q^{5} + 56 q^{6} - 8 q^{7} + 144 q^{8} - 174 q^{9} - 140 q^{10} - 288 q^{11} - 456 q^{12} - 10 q^{13} - 240 q^{14} + 356 q^{15} + 232 q^{16} + 510 q^{17} + 944 q^{18} + 1016 q^{19} + 956 q^{20} + 128 q^{21} + 168 q^{22} - 1536 q^{23} - 520 q^{24} - 206 q^{25} + 128 q^{26} - 2744 q^{27} - 392 q^{28} - 1146 q^{29} + 380 q^{30} - 272 q^{31} - 744 q^{32} + 2352 q^{33} - 480 q^{34} + 1592 q^{35} - 2384 q^{36} + 1630 q^{37} - 2936 q^{38} - 1608 q^{39} - 6624 q^{40} - 354 q^{41} - 9448 q^{42} - 208 q^{43} - 1520 q^{44} - 209 q^{45} + 4424 q^{46} + 3184 q^{47} + 8184 q^{48} - 3582 q^{49} + 5072 q^{50} + 608 q^{51} + 11868 q^{52} + 1444 q^{53} + 17360 q^{54} + 3980 q^{55} + 10624 q^{56} + 5064 q^{57} + 3824 q^{58} + 2504 q^{59} + 3700 q^{60} + 422 q^{61} - 2528 q^{62} + 4776 q^{63} - 5224 q^{64} + 1535 q^{65} - 7568 q^{66} - 392 q^{67} + 2272 q^{68} - 3160 q^{69} - 3920 q^{70} - 6104 q^{71} - 10912 q^{72} - 7004 q^{73} - 7632 q^{74} - 11940 q^{75} - 7208 q^{76} - 8032 q^{77} - 5584 q^{78} - 14944 q^{79} - 10036 q^{80} - 7350 q^{81} - 11856 q^{82} - 14296 q^{83} - 8496 q^{84} - 5123 q^{85} - 200 q^{86} - 26504 q^{87} + 13984 q^{88} - 4076 q^{89} + 17208 q^{90} - 1960 q^{91} + 20928 q^{92} + 13768 q^{93} + 10968 q^{94} + 17220 q^{95} + 5512 q^{96} + 7644 q^{97} + 6368 q^{98} + 40992 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(520))\)

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
520.4.a \(\chi_{520}(1, \cdot)\) 520.4.a.a 1 1
520.4.a.b 1
520.4.a.c 2
520.4.a.d 3
520.4.a.e 3
520.4.a.f 4
520.4.a.g 4
520.4.a.h 4
520.4.a.i 4
520.4.a.j 4
520.4.a.k 6
520.4.d \(\chi_{520}(209, \cdot)\) 520.4.d.a 24 1
520.4.d.b 30
520.4.e \(\chi_{520}(181, \cdot)\) n/a 168 1
520.4.f \(\chi_{520}(129, \cdot)\) 520.4.f.a 2 1
520.4.f.b 2
520.4.f.c 30
520.4.f.d 30
520.4.g \(\chi_{520}(261, \cdot)\) n/a 144 1
520.4.j \(\chi_{520}(469, \cdot)\) n/a 216 1
520.4.k \(\chi_{520}(441, \cdot)\) 520.4.k.a 20 1
520.4.k.b 22
520.4.p \(\chi_{520}(389, \cdot)\) n/a 248 1
520.4.q \(\chi_{520}(81, \cdot)\) 520.4.q.a 2 2
520.4.q.b 20
520.4.q.c 20
520.4.q.d 20
520.4.q.e 22
520.4.s \(\chi_{520}(31, \cdot)\) None 0 2
520.4.t \(\chi_{520}(99, \cdot)\) n/a 496 2
520.4.w \(\chi_{520}(57, \cdot)\) n/a 126 2
520.4.y \(\chi_{520}(317, \cdot)\) n/a 496 2
520.4.bb \(\chi_{520}(183, \cdot)\) None 0 2
520.4.bc \(\chi_{520}(363, \cdot)\) n/a 496 2
520.4.bd \(\chi_{520}(103, \cdot)\) None 0 2
520.4.be \(\chi_{520}(27, \cdot)\) n/a 432 2
520.4.bh \(\chi_{520}(177, \cdot)\) n/a 126 2
520.4.bj \(\chi_{520}(213, \cdot)\) n/a 496 2
520.4.bm \(\chi_{520}(291, \cdot)\) n/a 336 2
520.4.bn \(\chi_{520}(239, \cdot)\) None 0 2
520.4.bp \(\chi_{520}(69, \cdot)\) n/a 496 2
520.4.bu \(\chi_{520}(121, \cdot)\) 520.4.bu.a 40 2
520.4.bu.b 44
520.4.bv \(\chi_{520}(29, \cdot)\) n/a 496 2
520.4.by \(\chi_{520}(61, \cdot)\) n/a 336 2
520.4.bz \(\chi_{520}(49, \cdot)\) n/a 128 2
520.4.ca \(\chi_{520}(101, \cdot)\) n/a 336 2
520.4.cb \(\chi_{520}(9, \cdot)\) n/a 124 2
520.4.cf \(\chi_{520}(119, \cdot)\) None 0 4
520.4.cg \(\chi_{520}(11, \cdot)\) n/a 672 4
520.4.cj \(\chi_{520}(37, \cdot)\) n/a 992 4
520.4.cl \(\chi_{520}(137, \cdot)\) n/a 252 4
520.4.cm \(\chi_{520}(3, \cdot)\) n/a 992 4
520.4.cn \(\chi_{520}(23, \cdot)\) None 0 4
520.4.cs \(\chi_{520}(43, \cdot)\) n/a 992 4
520.4.ct \(\chi_{520}(87, \cdot)\) None 0 4
520.4.cu \(\chi_{520}(197, \cdot)\) n/a 992 4
520.4.cw \(\chi_{520}(33, \cdot)\) n/a 252 4
520.4.cz \(\chi_{520}(19, \cdot)\) n/a 992 4
520.4.da \(\chi_{520}(71, \cdot)\) None 0 4

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(520))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(520)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(130))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(260))\)\(^{\oplus 2}\)