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Properties

Label 2475.2.bz
Level $2475$
Weight $2$
Character orbit 2475.bz
Rep. character $\chi_{2475}(809,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $480$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2475.bz (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 825 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2475, [\chi])\).

Total New Old
Modular forms 1472 480 992
Cusp forms 1408 480 928
Eisenstein series 64 0 64

Trace form

\( 480 q + 120 q^{4} + 20 q^{7} + O(q^{10}) \) \( 480 q + 120 q^{4} + 20 q^{7} + 40 q^{10} - 112 q^{16} + 20 q^{19} - 20 q^{22} - 32 q^{25} + 120 q^{28} + 24 q^{31} + 120 q^{43} - 40 q^{46} - 92 q^{49} - 40 q^{52} + 8 q^{55} + 32 q^{64} + 80 q^{67} - 48 q^{70} - 60 q^{85} + 40 q^{88} - 32 q^{91} - 40 q^{94} + 140 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2475, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2475, [\chi])\) into lower level spaces

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