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Properties

Label 2790.2.cx
Level $2790$
Weight $2$
Character orbit 2790.cx
Rep. character $\chi_{2790}(233,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $512$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 2790 = 2 \cdot 3^{2} \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2790.cx (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 465 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2790, [\chi])\).

Total New Old
Modular forms 4736 512 4224
Cusp forms 4480 512 3968
Eisenstein series 256 0 256

Trace form

\( 512 q + 24 q^{7} + O(q^{10}) \) \( 512 q + 24 q^{7} + 16 q^{10} + 128 q^{16} - 56 q^{22} + 32 q^{25} - 16 q^{28} - 16 q^{31} + 32 q^{37} + 48 q^{46} - 16 q^{55} - 16 q^{58} + 64 q^{61} - 48 q^{70} - 80 q^{73} - 96 q^{76} - 48 q^{85} + 144 q^{88} - 160 q^{91} + 80 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2790, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2790, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2790, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(465, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(930, [\chi])\)\(^{\oplus 2}\)