↑

Properties

Label 495.6
Level 495
Weight 6
Dimension 30582
Nonzero newspaces 24
Sturm bound 103680
Trace bound 5

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(103680\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(495))\).

Total New Old
Modular forms 43840 31070 12770
Cusp forms 42560 30582 11978
Eisenstein series 1280 488 792

Trace form

\( 30582 q + 10 q^{2} - 72 q^{3} - 98 q^{4} + 237 q^{5} + 596 q^{6} - 1044 q^{7} - 4286 q^{8} - 1928 q^{9} + O(q^{10}) \) \( 30582 q + 10 q^{2} - 72 q^{3} - 98 q^{4} + 237 q^{5} + 596 q^{6} - 1044 q^{7} - 4286 q^{8} - 1928 q^{9} + 5698 q^{10} + 3988 q^{11} + 10320 q^{12} - 3972 q^{13} - 9336 q^{14} - 8492 q^{15} - 23430 q^{16} - 16856 q^{17} - 23592 q^{18} + 18804 q^{19} + 33880 q^{20} + 30432 q^{21} + 39672 q^{22} + 11242 q^{23} + 23684 q^{24} + 37783 q^{25} - 27796 q^{26} - 20580 q^{27} - 78432 q^{28} - 41844 q^{29} - 54076 q^{30} - 57698 q^{31} - 146244 q^{32} - 81028 q^{33} - 22656 q^{34} - 972 q^{35} - 77644 q^{36} + 107862 q^{37} + 215948 q^{38} + 84924 q^{39} + 85270 q^{40} + 149576 q^{41} + 205784 q^{42} - 34908 q^{43} + 13660 q^{44} + 134542 q^{45} + 41412 q^{46} + 47748 q^{47} - 184540 q^{48} + 60646 q^{49} - 4660 q^{50} - 219852 q^{51} - 469116 q^{52} - 261276 q^{53} + 97572 q^{54} + 37769 q^{55} + 473488 q^{56} + 50576 q^{57} - 56232 q^{58} - 218798 q^{59} - 286584 q^{60} - 42016 q^{61} + 14948 q^{62} + 72496 q^{63} - 358554 q^{64} + 259258 q^{65} - 915960 q^{66} - 471062 q^{67} - 711288 q^{68} - 313448 q^{69} + 206102 q^{70} + 349202 q^{71} + 1300856 q^{72} + 463472 q^{73} + 957164 q^{74} - 610288 q^{75} - 96124 q^{76} + 789600 q^{77} - 142832 q^{78} + 103100 q^{79} - 523534 q^{80} + 1184480 q^{81} - 2867742 q^{82} + 224840 q^{83} - 25900 q^{84} + 600498 q^{85} - 113470 q^{86} - 1458136 q^{87} + 631532 q^{88} - 1420766 q^{89} + 477084 q^{90} - 16480 q^{91} + 1712528 q^{92} + 2046352 q^{93} + 1851072 q^{94} + 2634978 q^{95} + 5067788 q^{96} + 939938 q^{97} + 885764 q^{98} + 1984812 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(495))\)

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
495.6.a \(\chi_{495}(1, \cdot)\) 495.6.a.a 3 1
495.6.a.b 3
495.6.a.c 3
495.6.a.d 3
495.6.a.e 3
495.6.a.f 3
495.6.a.g 4
495.6.a.h 5
495.6.a.i 5
495.6.a.j 5
495.6.a.k 6
495.6.a.l 6
495.6.a.m 6
495.6.a.n 7
495.6.a.o 10
495.6.a.p 10
495.6.c \(\chi_{495}(199, \cdot)\) n/a 124 1
495.6.d \(\chi_{495}(494, \cdot)\) n/a 120 1
495.6.f \(\chi_{495}(296, \cdot)\) 495.6.f.a 80 1
495.6.i \(\chi_{495}(166, \cdot)\) n/a 400 2
495.6.k \(\chi_{495}(208, \cdot)\) n/a 296 2
495.6.l \(\chi_{495}(188, \cdot)\) n/a 200 2
495.6.n \(\chi_{495}(91, \cdot)\) n/a 400 4
495.6.p \(\chi_{495}(131, \cdot)\) n/a 480 2
495.6.r \(\chi_{495}(164, \cdot)\) n/a 712 2
495.6.u \(\chi_{495}(34, \cdot)\) n/a 600 2
495.6.x \(\chi_{495}(116, \cdot)\) n/a 320 4
495.6.z \(\chi_{495}(134, \cdot)\) n/a 480 4
495.6.ba \(\chi_{495}(64, \cdot)\) n/a 592 4
495.6.bc \(\chi_{495}(23, \cdot)\) n/a 1200 4
495.6.bf \(\chi_{495}(43, \cdot)\) n/a 1424 4
495.6.bg \(\chi_{495}(16, \cdot)\) n/a 1920 8
495.6.bi \(\chi_{495}(53, \cdot)\) n/a 960 8
495.6.bj \(\chi_{495}(28, \cdot)\) n/a 1184 8
495.6.bl \(\chi_{495}(4, \cdot)\) n/a 2848 8
495.6.bo \(\chi_{495}(29, \cdot)\) n/a 2848 8
495.6.bq \(\chi_{495}(41, \cdot)\) n/a 1920 8
495.6.bs \(\chi_{495}(7, \cdot)\) n/a 5696 16
495.6.bv \(\chi_{495}(38, \cdot)\) n/a 5696 16

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(495))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(495)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 2}\)