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Properties

Label 2475.4.da
Level $2475$
Weight $4$
Character orbit 2475.da
Rep. character $\chi_{2475}(323,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $2880$
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.da (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 825 \)
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 8704 2880 5824
Cusp forms 8576 2880 5696
Eisenstein series 128 0 128

Trace form

\( 2880 q - 48 q^{7} + O(q^{10}) \) \( 2880 q - 48 q^{7} - 144 q^{10} - 288 q^{13} - 46080 q^{16} - 1056 q^{22} + 288 q^{25} + 864 q^{28} + 1296 q^{37} - 2592 q^{40} + 192 q^{43} - 7080 q^{49} + 8352 q^{52} - 4128 q^{55} + 2064 q^{58} - 1728 q^{67} - 8784 q^{70} - 5136 q^{73} - 840 q^{79} - 9360 q^{82} + 4320 q^{85} + 10608 q^{88} - 5520 q^{94} - 8112 q^{97} + O(q^{100}) \)

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

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