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Properties

Label 2475.2.dx
Level $2475$
Weight $2$
Character orbit 2475.dx
Rep. character $\chi_{2475}(278,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $960$
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.dx (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 825 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 2944 960 1984
Cusp forms 2816 960 1856
Eisenstein series 128 0 128

Trace form

\( 960 q - 24 q^{7} + O(q^{10}) \) \( 960 q - 24 q^{7} - 64 q^{10} - 16 q^{13} + 240 q^{16} - 8 q^{22} - 32 q^{25} - 72 q^{28} + 48 q^{37} + 128 q^{40} - 56 q^{43} + 120 q^{49} + 96 q^{52} + 152 q^{55} + 208 q^{58} + 160 q^{64} - 64 q^{67} + 16 q^{70} - 32 q^{73} - 80 q^{82} - 24 q^{88} + 144 q^{97} + O(q^{100}) \)

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

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