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Properties

Label 2790.2.bi
Level $2790$
Weight $2$
Character orbit 2790.bi
Rep. character $\chi_{2790}(1489,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $360$
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.bi (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 1168 360 808
Cusp forms 1136 360 776
Eisenstein series 32 0 32

Trace form

\( 360 q + 180 q^{4} - 8 q^{6} + 12 q^{9} + O(q^{10}) \) \( 360 q + 180 q^{4} - 8 q^{6} + 12 q^{9} - 8 q^{11} + 20 q^{14} + 28 q^{15} - 180 q^{16} + 64 q^{21} - 4 q^{24} - 12 q^{29} - 8 q^{30} - 88 q^{35} - 64 q^{39} - 44 q^{41} - 16 q^{44} + 8 q^{45} + 24 q^{46} + 192 q^{49} - 8 q^{50} - 48 q^{51} - 28 q^{54} - 20 q^{56} + 32 q^{59} + 32 q^{60} - 12 q^{61} - 360 q^{64} - 8 q^{65} - 8 q^{66} + 20 q^{69} - 32 q^{71} + 60 q^{75} + 24 q^{79} - 36 q^{81} + 44 q^{84} + 24 q^{85} - 16 q^{86} + 72 q^{89} + 16 q^{90} + 48 q^{91} + 12 q^{94} + 60 q^{95} + 4 q^{96} - 16 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2790, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1395, [\chi])\)\(^{\oplus 2}\)