Properties

Label 980.4
Level 980
Weight 4
Dimension 43157
Nonzero newspaces 24
Sturm bound 225792
Trace bound 5

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(225792\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(980))\).

Total New Old
Modular forms 85872 43741 42131
Cusp forms 83472 43157 40315
Eisenstein series 2400 584 1816

Trace form

\( 43157 q - 32 q^{2} - 20 q^{3} - 30 q^{4} - 51 q^{5} - 70 q^{6} + 48 q^{7} + 106 q^{8} - q^{9} + O(q^{10}) \) \( 43157 q - 32 q^{2} - 20 q^{3} - 30 q^{4} - 51 q^{5} - 70 q^{6} + 48 q^{7} + 106 q^{8} - q^{9} - 137 q^{10} - 356 q^{11} - 770 q^{12} - 508 q^{13} - 348 q^{14} - 212 q^{15} - 242 q^{16} + 88 q^{17} + 372 q^{18} + 1148 q^{19} + 277 q^{20} + 1080 q^{21} + 834 q^{22} + 384 q^{23} + 1374 q^{24} + 239 q^{25} + 1046 q^{26} - 1016 q^{27} + 1260 q^{28} - 4026 q^{29} + 521 q^{30} + 16 q^{31} + 2698 q^{32} - 436 q^{33} - 42 q^{34} - 726 q^{35} - 3290 q^{36} + 5392 q^{37} - 4898 q^{38} + 1676 q^{39} - 1299 q^{40} - 2414 q^{41} - 4038 q^{42} - 1564 q^{43} - 8346 q^{44} - 569 q^{45} - 6142 q^{46} - 1920 q^{47} - 2780 q^{48} - 7428 q^{49} - 198 q^{50} - 5176 q^{51} + 7290 q^{52} + 928 q^{53} + 13086 q^{54} - 3674 q^{55} + 1548 q^{56} - 316 q^{57} + 654 q^{58} + 4444 q^{59} + 2617 q^{60} + 7390 q^{61} + 5230 q^{62} + 9768 q^{63} + 4134 q^{64} + 5366 q^{65} - 2430 q^{66} + 8372 q^{67} - 9094 q^{68} + 14164 q^{69} + 5025 q^{70} + 9432 q^{71} - 3474 q^{72} + 10524 q^{73} + 5262 q^{74} + 7580 q^{75} + 8498 q^{76} - 5508 q^{77} + 9546 q^{78} - 8032 q^{79} - 5902 q^{80} - 36399 q^{81} - 19624 q^{82} - 21564 q^{83} - 31500 q^{84} - 14586 q^{85} - 3008 q^{86} - 3816 q^{87} + 2808 q^{88} - 4654 q^{89} + 8982 q^{90} + 8964 q^{91} + 4364 q^{92} + 16516 q^{93} + 4992 q^{94} + 9796 q^{95} + 21704 q^{96} + 6344 q^{97} + 37488 q^{98} + 7820 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(980))\)

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
980.4.a \(\chi_{980}(1, \cdot)\) 980.4.a.a 1 1
980.4.a.b 1
980.4.a.c 1
980.4.a.d 1
980.4.a.e 1
980.4.a.f 1
980.4.a.g 1
980.4.a.h 1
980.4.a.i 1
980.4.a.j 1
980.4.a.k 1
980.4.a.l 1
980.4.a.m 1
980.4.a.n 2
980.4.a.o 2
980.4.a.p 2
980.4.a.q 2
980.4.a.r 2
980.4.a.s 2
980.4.a.t 2
980.4.a.u 2
980.4.a.v 6
980.4.a.w 6
980.4.c \(\chi_{980}(979, \cdot)\) n/a 352 1
980.4.e \(\chi_{980}(589, \cdot)\) 980.4.e.a 2 1
980.4.e.b 2
980.4.e.c 2
980.4.e.d 4
980.4.e.e 4
980.4.e.f 4
980.4.e.g 12
980.4.e.h 12
980.4.e.i 20
980.4.g \(\chi_{980}(391, \cdot)\) n/a 240 1
980.4.i \(\chi_{980}(361, \cdot)\) 980.4.i.a 2 2
980.4.i.b 2
980.4.i.c 2
980.4.i.d 2
980.4.i.e 2
980.4.i.f 2
980.4.i.g 2
980.4.i.h 2
980.4.i.i 2
980.4.i.j 2
980.4.i.k 2
980.4.i.l 2
980.4.i.m 2
980.4.i.n 2
980.4.i.o 2
980.4.i.p 2
980.4.i.q 2
980.4.i.r 2
980.4.i.s 4
980.4.i.t 4
980.4.i.u 4
980.4.i.v 4
980.4.i.w 4
980.4.i.x 12
980.4.i.y 12
980.4.k \(\chi_{980}(687, \cdot)\) n/a 718 2
980.4.m \(\chi_{980}(97, \cdot)\) n/a 120 2
980.4.o \(\chi_{980}(31, \cdot)\) n/a 480 2
980.4.q \(\chi_{980}(569, \cdot)\) n/a 120 2
980.4.s \(\chi_{980}(19, \cdot)\) n/a 704 2
980.4.u \(\chi_{980}(141, \cdot)\) n/a 336 6
980.4.v \(\chi_{980}(117, \cdot)\) n/a 240 4
980.4.x \(\chi_{980}(67, \cdot)\) n/a 1408 4
980.4.bb \(\chi_{980}(111, \cdot)\) n/a 2016 6
980.4.bd \(\chi_{980}(29, \cdot)\) n/a 504 6
980.4.bf \(\chi_{980}(139, \cdot)\) n/a 3000 6
980.4.bg \(\chi_{980}(81, \cdot)\) n/a 672 12
980.4.bi \(\chi_{980}(13, \cdot)\) n/a 1008 12
980.4.bk \(\chi_{980}(43, \cdot)\) n/a 6000 12
980.4.bl \(\chi_{980}(59, \cdot)\) n/a 6000 12
980.4.bn \(\chi_{980}(9, \cdot)\) n/a 1008 12
980.4.bp \(\chi_{980}(131, \cdot)\) n/a 4032 12
980.4.bs \(\chi_{980}(23, \cdot)\) n/a 12000 24
980.4.bu \(\chi_{980}(17, \cdot)\) n/a 2016 24

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(980))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(980)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(490))\)\(^{\oplus 2}\)