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Properties

Label 2790.2.dh
Level $2790$
Weight $2$
Character orbit 2790.dh
Rep. character $\chi_{2790}(19,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $640$
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.dh (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 155 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 4736 640 4096
Cusp forms 4480 640 3840
Eisenstein series 256 0 256

Trace form

\( 640 q + 160 q^{4} - 2 q^{5} + O(q^{10}) \) \( 640 q + 160 q^{4} - 2 q^{5} - 4 q^{10} + 4 q^{11} - 160 q^{16} - 8 q^{19} + 2 q^{20} - 6 q^{25} - 48 q^{26} + 16 q^{29} + 56 q^{31} + 44 q^{34} + 8 q^{35} - 6 q^{40} - 20 q^{41} - 4 q^{44} + 44 q^{46} - 52 q^{49} - 20 q^{50} + 48 q^{55} - 32 q^{59} - 112 q^{61} + 160 q^{64} + 116 q^{65} - 32 q^{70} - 108 q^{71} - 28 q^{74} + 48 q^{76} - 24 q^{79} + 18 q^{80} - 16 q^{85} + 88 q^{86} + 44 q^{89} + 108 q^{91} + 50 q^{95} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2790, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(310, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(465, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(930, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1395, [\chi])\)\(^{\oplus 2}\)