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Properties

Label 2790.2.bt
Level $2790$
Weight $2$
Character orbit 2790.bt
Rep. character $\chi_{2790}(1331,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $192$
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.bt (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 93 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 2368 192 2176
Cusp forms 2240 192 2048
Eisenstein series 128 0 128

Trace form

\( 192 q + 48 q^{4} - 16 q^{7} + O(q^{10}) \) \( 192 q + 48 q^{4} - 16 q^{7} - 48 q^{16} + 16 q^{19} - 192 q^{25} - 24 q^{28} - 64 q^{31} - 40 q^{34} - 120 q^{43} + 40 q^{46} - 96 q^{49} + 40 q^{55} - 80 q^{58} + 48 q^{64} + 16 q^{67} + 80 q^{73} + 24 q^{76} + 80 q^{79} + 48 q^{82} + 120 q^{91} + 80 q^{94} + 168 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2790, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(93, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(186, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(279, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(465, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(558, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(930, [\chi])\)\(^{\oplus 2}\)