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Properties

Label 2790.2.i
Level $2790$
Weight $2$
Character orbit 2790.i
Rep. character $\chi_{2790}(811,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $104$
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.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 31 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 1184 104 1080
Cusp forms 1120 104 1016
Eisenstein series 64 0 64

Trace form

\( 104 q + 104 q^{4} - 4 q^{7} + O(q^{10}) \) \( 104 q + 104 q^{4} - 4 q^{7} - 4 q^{11} + 20 q^{13} - 4 q^{14} + 104 q^{16} - 4 q^{17} + 8 q^{19} - 56 q^{23} - 52 q^{25} + 4 q^{26} - 4 q^{28} - 8 q^{29} + 28 q^{31} + 4 q^{34} - 16 q^{35} + 28 q^{37} - 12 q^{38} + 4 q^{41} - 24 q^{43} - 4 q^{44} - 40 q^{46} - 8 q^{47} - 44 q^{49} + 20 q^{52} - 24 q^{53} + 4 q^{55} - 4 q^{56} + 16 q^{58} - 8 q^{59} + 56 q^{61} - 12 q^{62} + 104 q^{64} - 8 q^{65} - 20 q^{67} - 4 q^{68} - 8 q^{71} - 20 q^{73} + 20 q^{74} + 8 q^{76} + 120 q^{77} + 4 q^{79} + 8 q^{83} + 16 q^{86} + 40 q^{89} + 88 q^{91} - 56 q^{92} - 16 q^{94} + 16 q^{95} + 104 q^{97} + 8 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2790, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(62, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(93, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(186, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(279, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(558, [\chi])\)\(^{\oplus 2}\)