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Properties

Label 483.8.y
Level $483$
Weight $8$
Character orbit 483.y
Rep. character $\chi_{483}(4,\cdot)$
Character field $\Q(\zeta_{33})$
Dimension $4480$
Sturm bound $512$

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Defining parameters

Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 483.y (of order \(33\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 161 \)
Character field: \(\Q(\zeta_{33})\)
Sturm bound: \(512\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(483, [\chi])\).

Total New Old
Modular forms 9040 4480 4560
Cusp forms 8880 4480 4400
Eisenstein series 160 0 160

Trace form

\( 4480 q + 28 q^{2} + 13972 q^{4} - 4 q^{5} + 788 q^{7} - 4872 q^{8} + 163296 q^{9} + O(q^{10}) \) \( 4480 q + 28 q^{2} + 13972 q^{4} - 4 q^{5} + 788 q^{7} - 4872 q^{8} + 163296 q^{9} - 8000 q^{10} + 4076 q^{11} + 17984 q^{14} + 1116612 q^{16} - 51064 q^{17} + 20412 q^{18} - 66968 q^{19} - 9216 q^{20} - 333424 q^{22} + 186388 q^{23} + 3319760 q^{25} + 499604 q^{26} + 2567396 q^{28} - 377320 q^{29} - 5616 q^{30} - 41108 q^{31} + 949488 q^{32} - 287496 q^{33} + 2421344 q^{34} + 3104260 q^{35} - 23290092 q^{36} + 1271724 q^{37} - 6229468 q^{38} + 959148 q^{40} - 2337856 q^{41} - 1742742 q^{42} - 280240 q^{43} + 12105214 q^{44} - 2916 q^{45} - 878748 q^{46} - 1004308 q^{47} - 1089504 q^{48} - 5283560 q^{49} + 21965180 q^{50} - 5135292 q^{51} - 26059032 q^{52} - 3558408 q^{53} - 9401696 q^{55} + 18380778 q^{56} - 21731976 q^{57} + 10781742 q^{58} - 4155404 q^{59} - 1934820 q^{60} - 26601284 q^{61} - 45427632 q^{62} + 574452 q^{63} - 111794872 q^{64} - 5061832 q^{65} - 4599936 q^{66} + 3902400 q^{67} - 2879844 q^{68} - 1037664 q^{69} + 22727080 q^{70} - 26693936 q^{71} + 1775844 q^{72} + 1665528 q^{73} - 48234922 q^{74} - 5660496 q^{75} + 18692096 q^{76} - 27352744 q^{77} + 11197440 q^{78} - 63132 q^{79} + 7865042 q^{80} + 119042784 q^{81} + 93857696 q^{82} + 15812080 q^{83} + 24168024 q^{84} - 143769888 q^{85} - 64109720 q^{86} + 3411396 q^{87} + 96724030 q^{88} - 35335744 q^{89} + 11664000 q^{90} + 34251896 q^{91} + 283177548 q^{92} + 12188232 q^{93} - 32380042 q^{94} + 75250786 q^{95} + 27050220 q^{96} - 26014032 q^{97} + 133807072 q^{98} + 55995948 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(483, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{8}^{\mathrm{old}}(483, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(483, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 2}\)