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Properties

Label 483.8.e
Level $483$
Weight $8$
Character orbit 483.e
Rep. character $\chi_{483}(344,\cdot)$
Character field $\Q$
Dimension $336$
Sturm bound $512$

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Defining parameters

Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 483.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 69 \)
Character field: \(\Q\)
Sturm bound: \(512\)

Dimensions

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

Total New Old
Modular forms 452 336 116
Cusp forms 444 336 108
Eisenstein series 8 0 8

Trace form

\( 336 q - 52 q^{3} - 21400 q^{4} - 174 q^{6} - 4316 q^{9} + O(q^{10}) \) \( 336 q - 52 q^{3} - 21400 q^{4} - 174 q^{6} - 4316 q^{9} + 1294 q^{12} + 9976 q^{13} + 1379064 q^{16} + 3478 q^{18} + 22272 q^{24} + 4978984 q^{25} + 912368 q^{27} + 1476952 q^{31} + 1287422 q^{36} - 1885680 q^{39} + 3481952 q^{46} + 5639746 q^{48} - 39530064 q^{49} + 5713036 q^{52} - 8795836 q^{54} + 7855680 q^{55} - 4958156 q^{58} - 89261476 q^{64} - 12418792 q^{69} - 3973312 q^{70} + 22523640 q^{72} + 2654920 q^{73} - 7655792 q^{75} + 47044302 q^{78} - 27083116 q^{81} + 2564260 q^{82} + 14565272 q^{85} + 10188164 q^{87} + 39583892 q^{93} - 32801652 q^{94} - 11876334 q^{96} + O(q^{100}) \)

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

\( S_{8}^{\mathrm{old}}(483, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 2}\)