↑

Properties

Label 310.8
Level 310
Weight 8
Dimension 6150
Nonzero newspaces 12
Sturm bound 46080
Trace bound 4

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 310 = 2 \cdot 5 \cdot 31 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(46080\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(310))\).

Total New Old
Modular forms 20400 6150 14250
Cusp forms 19920 6150 13770
Eisenstein series 480 0 480

Trace form

\( 6150 q - 16 q^{2} - 56 q^{3} + 384 q^{4} - 370 q^{5} - 2240 q^{6} - 208 q^{7} - 1024 q^{8} + 16382 q^{9} + O(q^{10}) \) \( 6150 q - 16 q^{2} - 56 q^{3} + 384 q^{4} - 370 q^{5} - 2240 q^{6} - 208 q^{7} - 1024 q^{8} + 16382 q^{9} - 720 q^{10} - 25320 q^{11} - 3584 q^{12} + 17204 q^{13} + 11392 q^{14} + 62920 q^{15} - 40960 q^{16} - 40548 q^{17} + 22448 q^{18} - 218200 q^{19} - 8320 q^{20} - 829940 q^{21} + 874848 q^{22} + 1050564 q^{23} + 86016 q^{24} - 515950 q^{25} - 838400 q^{26} - 1504820 q^{27} + 411648 q^{28} + 1536300 q^{29} + 743520 q^{30} + 3375720 q^{31} - 65536 q^{32} - 939672 q^{33} - 2797408 q^{34} - 2300060 q^{35} - 4421760 q^{36} - 4762768 q^{37} + 260320 q^{38} + 7684244 q^{39} - 209920 q^{40} + 3066720 q^{41} - 4932512 q^{42} - 8040396 q^{43} + 2938368 q^{44} + 6109590 q^{45} - 1139840 q^{46} - 851328 q^{47} - 229376 q^{48} + 4836498 q^{49} - 4973200 q^{50} + 20111660 q^{51} + 1101056 q^{52} - 9390576 q^{53} + 11840640 q^{54} - 8296900 q^{55} - 942080 q^{56} - 12960460 q^{57} - 3704160 q^{58} + 2909580 q^{59} - 4922880 q^{60} + 49571560 q^{61} + 641024 q^{62} + 38635904 q^{63} + 1572864 q^{64} - 8040770 q^{65} - 2497280 q^{66} - 12207748 q^{67} - 2595072 q^{68} - 71766716 q^{69} - 5567360 q^{70} + 2069400 q^{71} + 1436672 q^{72} + 29656424 q^{73} + 4578592 q^{74} + 10948640 q^{75} - 3813120 q^{76} + 88723704 q^{77} + 142898656 q^{78} + 61162980 q^{79} + 7208960 q^{80} - 51076650 q^{81} - 55322592 q^{82} - 245564076 q^{83} - 87593472 q^{84} - 61947340 q^{85} - 104300480 q^{86} - 65907840 q^{87} + 10862592 q^{88} + 158745360 q^{89} + 131477520 q^{90} + 174235820 q^{91} + 9225216 q^{92} + 363648544 q^{93} + 37225792 q^{94} + 22681240 q^{95} - 9175040 q^{96} - 44410728 q^{97} - 183156048 q^{98} - 228330436 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(310))\)

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
310.8.a \(\chi_{310}(1, \cdot)\) 310.8.a.a 6 1
310.8.a.b 8
310.8.a.c 8
310.8.a.d 9
310.8.a.e 9
310.8.a.f 10
310.8.a.g 10
310.8.a.h 10
310.8.b \(\chi_{310}(249, \cdot)\) n/a 104 1
310.8.e \(\chi_{310}(191, \cdot)\) n/a 152 2
310.8.f \(\chi_{310}(123, \cdot)\) n/a 224 2
310.8.h \(\chi_{310}(101, \cdot)\) n/a 288 4
310.8.k \(\chi_{310}(129, \cdot)\) n/a 224 2
310.8.n \(\chi_{310}(39, \cdot)\) n/a 448 4
310.8.p \(\chi_{310}(37, \cdot)\) n/a 448 4
310.8.q \(\chi_{310}(41, \cdot)\) n/a 608 8
310.8.s \(\chi_{310}(23, \cdot)\) n/a 896 8
310.8.t \(\chi_{310}(9, \cdot)\) n/a 896 8
310.8.w \(\chi_{310}(3, \cdot)\) n/a 1792 16

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(310))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(310)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(155))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(310))\)\(^{\oplus 1}\)