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Properties

Label 2790.2.ec
Level $2790$
Weight $2$
Character orbit 2790.ec
Rep. character $\chi_{2790}(107,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $1024$
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.ec (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 465 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 9472 1024 8448
Cusp forms 8960 1024 7936
Eisenstein series 512 0 512

Trace form

\( 1024 q - 48 q^{7} + O(q^{10}) \) \( 1024 q - 48 q^{7} - 16 q^{10} + 256 q^{16} - 88 q^{22} + 16 q^{25} - 8 q^{28} + 64 q^{31} - 32 q^{37} - 48 q^{46} - 8 q^{55} + 16 q^{58} - 64 q^{61} + 48 q^{70} + 176 q^{73} + 192 q^{76} + 48 q^{85} + 72 q^{88} + 160 q^{91} + 208 q^{97} + O(q^{100}) \)

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

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