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Properties

Label 456.6
Level 456
Weight 6
Dimension 12016
Nonzero newspaces 18
Sturm bound 69120
Trace bound 6

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Defining parameters

Level: \( N \) = \( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 18 \)
Sturm bound: \(69120\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(456))\).

Total New Old
Modular forms 29232 12152 17080
Cusp forms 28368 12016 16352
Eisenstein series 864 136 728

Trace form

\( 12016 q - 4 q^{2} + 4 q^{3} + 52 q^{4} - 196 q^{5} - 374 q^{6} + 308 q^{7} - 136 q^{8} + 1102 q^{9} + O(q^{10}) \) \( 12016 q - 4 q^{2} + 4 q^{3} + 52 q^{4} - 196 q^{5} - 374 q^{6} + 308 q^{7} - 136 q^{8} + 1102 q^{9} + 1364 q^{10} - 40 q^{11} + 958 q^{12} + 204 q^{13} - 7384 q^{14} - 1422 q^{15} - 5732 q^{16} + 1340 q^{17} - 446 q^{18} + 7692 q^{19} + 12752 q^{20} - 3888 q^{21} - 12772 q^{22} - 13152 q^{23} - 410 q^{24} + 2046 q^{25} + 13040 q^{26} + 32569 q^{27} + 33788 q^{28} - 1872 q^{29} - 11994 q^{30} - 80536 q^{31} + 8176 q^{32} - 38086 q^{33} - 50556 q^{34} + 6600 q^{35} - 19658 q^{36} + 52608 q^{37} + 4712 q^{38} + 114822 q^{39} + 47372 q^{40} + 50240 q^{41} - 3354 q^{42} - 80508 q^{43} - 13824 q^{44} - 151902 q^{45} + 119628 q^{46} - 205020 q^{47} + 118654 q^{48} - 33018 q^{49} - 14788 q^{50} + 158735 q^{51} - 71172 q^{52} + 129692 q^{53} - 98798 q^{54} + 229996 q^{55} - 21616 q^{56} + 21580 q^{57} - 155056 q^{58} - 102472 q^{59} - 787974 q^{60} - 299880 q^{61} - 225380 q^{62} + 9540 q^{63} + 921052 q^{64} + 389836 q^{65} + 959534 q^{66} + 849108 q^{67} + 1034004 q^{68} - 3600 q^{69} + 355228 q^{70} + 404980 q^{71} + 20554 q^{72} - 613150 q^{73} - 1083712 q^{74} - 725432 q^{75} - 1785876 q^{76} - 618108 q^{77} - 1050078 q^{78} - 1264552 q^{79} - 1070112 q^{80} - 102146 q^{81} + 1058736 q^{82} + 649756 q^{83} + 567750 q^{84} + 398136 q^{85} + 1506236 q^{86} + 853398 q^{87} + 1744988 q^{88} + 232208 q^{89} + 869850 q^{90} - 481620 q^{91} - 1400292 q^{92} - 275850 q^{93} - 1424076 q^{94} - 113144 q^{95} + 1556524 q^{96} + 227900 q^{97} + 919692 q^{98} + 729755 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(456))\)

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
456.6.a \(\chi_{456}(1, \cdot)\) 456.6.a.a 4 1
456.6.a.b 5
456.6.a.c 5
456.6.a.d 5
456.6.a.e 5
456.6.a.f 6
456.6.a.g 7
456.6.a.h 7
456.6.d \(\chi_{456}(191, \cdot)\) None 0 1
456.6.e \(\chi_{456}(379, \cdot)\) n/a 200 1
456.6.f \(\chi_{456}(113, \cdot)\) 456.6.f.a 50 1
456.6.f.b 50
456.6.g \(\chi_{456}(229, \cdot)\) n/a 180 1
456.6.j \(\chi_{456}(419, \cdot)\) n/a 360 1
456.6.k \(\chi_{456}(151, \cdot)\) None 0 1
456.6.p \(\chi_{456}(341, \cdot)\) n/a 396 1
456.6.q \(\chi_{456}(49, \cdot)\) 456.6.q.a 24 2
456.6.q.b 24
456.6.q.c 26
456.6.q.d 26
456.6.t \(\chi_{456}(31, \cdot)\) None 0 2
456.6.u \(\chi_{456}(11, \cdot)\) n/a 792 2
456.6.v \(\chi_{456}(221, \cdot)\) n/a 792 2
456.6.y \(\chi_{456}(259, \cdot)\) n/a 400 2
456.6.z \(\chi_{456}(239, \cdot)\) None 0 2
456.6.be \(\chi_{456}(277, \cdot)\) n/a 400 2
456.6.bf \(\chi_{456}(65, \cdot)\) n/a 200 2
456.6.bg \(\chi_{456}(25, \cdot)\) n/a 300 6
456.6.bj \(\chi_{456}(29, \cdot)\) n/a 2376 6
456.6.bk \(\chi_{456}(61, \cdot)\) n/a 1200 6
456.6.bm \(\chi_{456}(41, \cdot)\) n/a 600 6
456.6.bp \(\chi_{456}(67, \cdot)\) n/a 1200 6
456.6.br \(\chi_{456}(23, \cdot)\) None 0 6
456.6.bs \(\chi_{456}(79, \cdot)\) None 0 6
456.6.bu \(\chi_{456}(35, \cdot)\) n/a 2376 6

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(456))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(456)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(228))\)\(^{\oplus 2}\)