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Properties

Label 495.4.bi
Level $495$
Weight $4$
Character orbit 495.bi
Rep. character $\chi_{495}(53,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $576$
Sturm bound $288$

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Defining parameters

Level: \( N \) \(=\) \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 495.bi (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 165 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(288\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(495, [\chi])\).

Total New Old
Modular forms 1792 576 1216
Cusp forms 1664 576 1088
Eisenstein series 128 0 128

Trace form

\( 576 q - 48 q^{7} + O(q^{10}) \) \( 576 q - 48 q^{7} - 384 q^{10} + 192 q^{13} + 2304 q^{16} - 1056 q^{22} - 432 q^{25} + 864 q^{28} + 864 q^{31} - 864 q^{37} - 2592 q^{40} - 6048 q^{43} - 864 q^{46} - 1008 q^{52} + 5832 q^{55} + 3744 q^{58} + 576 q^{61} + 8832 q^{67} + 1296 q^{70} + 9624 q^{73} - 2592 q^{76} - 9360 q^{82} + 4320 q^{85} - 16512 q^{88} + 288 q^{91} - 8112 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(495, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(495, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(495, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)