↑

Properties

Label 490.3
Level 490
Weight 3
Dimension 4138
Nonzero newspaces 12
Sturm bound 42336
Trace bound 4

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(42336\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(490))\).

Total New Old
Modular forms 14592 4138 10454
Cusp forms 13632 4138 9494
Eisenstein series 960 0 960

Trace form

\( 4138 q - 2 q^{2} - 28 q^{3} - 16 q^{4} - 12 q^{5} + 8 q^{6} + 16 q^{7} + 4 q^{8} + O(q^{10}) \) \( 4138 q - 2 q^{2} - 28 q^{3} - 16 q^{4} - 12 q^{5} + 8 q^{6} + 16 q^{7} + 4 q^{8} + 38 q^{10} + 56 q^{11} + 40 q^{12} + 6 q^{13} - 72 q^{14} - 52 q^{15} - 40 q^{16} - 106 q^{17} - 94 q^{18} + 24 q^{19} + 20 q^{20} + 108 q^{21} + 112 q^{22} + 116 q^{23} + 96 q^{24} + 290 q^{25} + 468 q^{26} + 968 q^{27} + 104 q^{28} + 672 q^{29} + 552 q^{30} + 224 q^{31} + 8 q^{32} - 88 q^{33} - 114 q^{35} - 196 q^{36} + 546 q^{37} + 368 q^{38} + 612 q^{39} + 220 q^{40} + 488 q^{41} + 576 q^{42} - 140 q^{43} - 656 q^{45} + 80 q^{46} + 204 q^{47} + 16 q^{48} - 376 q^{49} - 310 q^{50} - 848 q^{51} - 388 q^{52} - 1046 q^{53} - 1656 q^{54} - 798 q^{55} - 576 q^{56} - 232 q^{57} - 1504 q^{58} - 1200 q^{59} - 472 q^{60} - 1660 q^{61} - 1280 q^{62} - 1536 q^{63} + 128 q^{64} + 378 q^{65} - 640 q^{66} + 276 q^{67} + 212 q^{68} + 84 q^{70} - 344 q^{71} - 188 q^{72} + 410 q^{73} + 384 q^{74} - 488 q^{75} + 80 q^{76} - 324 q^{77} + 408 q^{78} - 1480 q^{79} + 48 q^{80} + 1174 q^{81} - 464 q^{82} + 1044 q^{83} + 24 q^{84} - 530 q^{85} + 1128 q^{86} + 4208 q^{87} + 640 q^{88} + 3432 q^{89} + 2678 q^{90} + 2304 q^{91} + 664 q^{92} + 4952 q^{93} + 1872 q^{94} + 3532 q^{95} + 160 q^{96} + 1890 q^{97} + 624 q^{98} + 1824 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(490))\)

We only show spaces with odd 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
490.3.b \(\chi_{490}(391, \cdot)\) 490.3.b.a 8 1
490.3.b.b 8
490.3.b.c 8
490.3.d \(\chi_{490}(489, \cdot)\) 490.3.d.a 16 1
490.3.d.b 24
490.3.f \(\chi_{490}(197, \cdot)\) 490.3.f.a 2 2
490.3.f.b 2
490.3.f.c 2
490.3.f.d 4
490.3.f.e 4
490.3.f.f 4
490.3.f.g 4
490.3.f.h 4
490.3.f.i 4
490.3.f.j 4
490.3.f.k 4
490.3.f.l 4
490.3.f.m 4
490.3.f.n 8
490.3.f.o 8
490.3.f.p 8
490.3.f.q 12
490.3.h \(\chi_{490}(19, \cdot)\) 490.3.h.a 16 2
490.3.h.b 16
490.3.h.c 48
490.3.j \(\chi_{490}(31, \cdot)\) 490.3.j.a 8 2
490.3.j.b 16
490.3.j.c 16
490.3.j.d 16
490.3.m \(\chi_{490}(67, \cdot)\) n/a 160 4
490.3.n \(\chi_{490}(69, \cdot)\) n/a 336 6
490.3.o \(\chi_{490}(41, \cdot)\) n/a 240 6
490.3.r \(\chi_{490}(43, \cdot)\) n/a 672 12
490.3.u \(\chi_{490}(61, \cdot)\) n/a 432 12
490.3.v \(\chi_{490}(59, \cdot)\) n/a 672 12
490.3.x \(\chi_{490}(23, \cdot)\) n/a 1344 24

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(490))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(490)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 2}\)