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Properties

Label 2790.2.cn
Level $2790$
Weight $2$
Character orbit 2790.cn
Rep. character $\chi_{2790}(377,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $256$
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.cn (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 465 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 2368 256 2112
Cusp forms 2240 256 1984
Eisenstein series 128 0 128

Trace form

\( 256 q + 8 q^{7} + O(q^{10}) \) \( 256 q + 8 q^{7} + 16 q^{10} - 256 q^{16} + 8 q^{22} - 16 q^{25} + 8 q^{28} - 64 q^{31} + 32 q^{37} - 32 q^{46} + 8 q^{55} - 16 q^{58} + 64 q^{61} - 48 q^{70} - 16 q^{73} - 32 q^{76} - 128 q^{85} + 8 q^{88} - 208 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2790, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(465, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(930, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1395, [\chi])\)\(^{\oplus 2}\)