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Properties

Label 495.4.l
Level $495$
Weight $4$
Character orbit 495.l
Rep. character $\chi_{495}(188,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $120$
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.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Sturm bound: \(288\)

Dimensions

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

Total New Old
Modular forms 448 120 328
Cusp forms 416 120 296
Eisenstein series 32 0 32

Trace form

\( 120 q + O(q^{10}) \) \( 120 q + 24 q^{13} - 1008 q^{16} + 1728 q^{28} + 1632 q^{31} - 792 q^{37} - 2544 q^{40} - 1920 q^{46} - 48 q^{52} + 5664 q^{58} + 192 q^{61} - 2016 q^{67} - 5664 q^{70} - 2808 q^{73} + 3552 q^{76} + 8496 q^{82} - 816 q^{85} + 1584 q^{88} - 9792 q^{91} + 2568 q^{97} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(495, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)