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Properties

Label 490.6
Level 490
Weight 6
Dimension 10345
Nonzero newspaces 12
Sturm bound 84672
Trace bound 4

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Defining parameters

Level: \( N \) = \( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(84672\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(490))\).

Total New Old
Modular forms 35760 10345 25415
Cusp forms 34800 10345 24455
Eisenstein series 960 0 960

Trace form

\( 10345 q - 4 q^{2} + 76 q^{3} - 112 q^{4} + 217 q^{5} + 784 q^{6} + 464 q^{7} - 64 q^{8} - 4219 q^{9} + O(q^{10}) \) \( 10345 q - 4 q^{2} + 76 q^{3} - 112 q^{4} + 217 q^{5} + 784 q^{6} + 464 q^{7} - 64 q^{8} - 4219 q^{9} - 1668 q^{10} - 2516 q^{11} + 1216 q^{12} + 14714 q^{13} - 240 q^{14} - 4316 q^{15} - 768 q^{16} - 11994 q^{17} + 2060 q^{18} + 8492 q^{19} + 2640 q^{20} + 17580 q^{21} + 14640 q^{22} - 5304 q^{23} - 5376 q^{24} - 33179 q^{25} - 31928 q^{26} + 17848 q^{27} + 9344 q^{28} + 54102 q^{29} + 41712 q^{30} + 43504 q^{31} - 1024 q^{32} - 178176 q^{33} - 36680 q^{34} - 91590 q^{35} + 17040 q^{36} - 260790 q^{37} - 14048 q^{38} + 374996 q^{39} + 59200 q^{40} + 485746 q^{41} + 291888 q^{42} + 217844 q^{43} + 23168 q^{44} - 173445 q^{45} - 346000 q^{46} - 483528 q^{47} - 45056 q^{48} - 640540 q^{49} - 41012 q^{50} - 552280 q^{51} - 100128 q^{52} - 316878 q^{53} + 17808 q^{54} + 22306 q^{55} + 253440 q^{56} + 309320 q^{57} + 601896 q^{58} + 915052 q^{59} + 173856 q^{60} + 664906 q^{61} + 139312 q^{62} - 745944 q^{63} + 167936 q^{64} - 230078 q^{65} - 455360 q^{66} - 437788 q^{67} - 191904 q^{68} - 866000 q^{69} - 131208 q^{70} - 867000 q^{71} + 32960 q^{72} - 593410 q^{73} + 135368 q^{74} + 306188 q^{75} + 159680 q^{76} + 351384 q^{77} + 840640 q^{78} + 949520 q^{79} + 55552 q^{80} - 1029747 q^{81} - 525480 q^{82} + 444180 q^{83} - 139584 q^{84} - 290606 q^{85} - 1217136 q^{86} + 383736 q^{87} - 312576 q^{88} + 1258922 q^{89} + 1127724 q^{90} + 665428 q^{91} + 910464 q^{92} + 1497368 q^{93} + 1828928 q^{94} + 1173580 q^{95} + 102400 q^{96} - 1501138 q^{97} - 145536 q^{98} - 1723012 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(490))\)

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
490.6.a \(\chi_{490}(1, \cdot)\) 490.6.a.a 1 1
490.6.a.b 1
490.6.a.c 1
490.6.a.d 1
490.6.a.e 1
490.6.a.f 1
490.6.a.g 1
490.6.a.h 1
490.6.a.i 1
490.6.a.j 1
490.6.a.k 1
490.6.a.l 1
490.6.a.m 1
490.6.a.n 2
490.6.a.o 2
490.6.a.p 2
490.6.a.q 2
490.6.a.r 2
490.6.a.s 2
490.6.a.t 2
490.6.a.u 2
490.6.a.v 2
490.6.a.w 2
490.6.a.x 3
490.6.a.y 3
490.6.a.z 4
490.6.a.ba 4
490.6.a.bb 4
490.6.a.bc 4
490.6.a.bd 6
490.6.a.be 6
490.6.c \(\chi_{490}(99, \cdot)\) n/a 102 1
490.6.e \(\chi_{490}(361, \cdot)\) n/a 136 2
490.6.g \(\chi_{490}(97, \cdot)\) n/a 200 2
490.6.i \(\chi_{490}(79, \cdot)\) n/a 200 2
490.6.k \(\chi_{490}(71, \cdot)\) n/a 576 6
490.6.l \(\chi_{490}(117, \cdot)\) n/a 400 4
490.6.p \(\chi_{490}(29, \cdot)\) n/a 840 6
490.6.q \(\chi_{490}(11, \cdot)\) n/a 1104 12
490.6.s \(\chi_{490}(13, \cdot)\) n/a 1680 12
490.6.t \(\chi_{490}(9, \cdot)\) n/a 1680 12
490.6.w \(\chi_{490}(3, \cdot)\) n/a 3360 24

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(490))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(490)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(490))\)\(^{\oplus 1}\)