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Properties

Label 2475.4.dl
Level $2475$
Weight $4$
Character orbit 2475.dl
Rep. character $\chi_{2475}(368,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1728$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2475.dl (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 165 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2475, [\chi])\).

Total New Old
Modular forms 8832 1728 7104
Cusp forms 8448 1728 6720
Eisenstein series 384 0 384

Trace form

\( 1728 q + 48 q^{7} + O(q^{10}) \) \( 1728 q + 48 q^{7} - 192 q^{13} + 6912 q^{16} + 1056 q^{22} - 864 q^{28} - 1728 q^{31} + 864 q^{37} + 6048 q^{43} + 1728 q^{46} + 1008 q^{52} - 3744 q^{58} - 1152 q^{61} - 8832 q^{67} - 9624 q^{73} + 5184 q^{76} + 9360 q^{82} + 16512 q^{88} - 576 q^{91} + 8112 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(2475, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(2475, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2475, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(495, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(825, [\chi])\)\(^{\oplus 2}\)