↑

Properties

Label 2790.2.bx
Level $2790$
Weight $2$
Character orbit 2790.bx
Rep. character $\chi_{2790}(109,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $320$
Sturm bound $1152$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2790 = 2 \cdot 3^{2} \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2790.bx (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 155 \)
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 320 2048
Cusp forms 2240 320 1920
Eisenstein series 128 0 128

Trace form

\( 320 q + 80 q^{4} - 4 q^{5} + O(q^{10}) \) \( 320 q + 80 q^{4} - 4 q^{5} + 4 q^{10} - 4 q^{11} - 80 q^{16} - 16 q^{19} + 4 q^{20} + 48 q^{26} - 16 q^{29} - 44 q^{31} + 4 q^{34} + 16 q^{35} + 6 q^{40} + 44 q^{41} + 4 q^{44} - 20 q^{46} + 40 q^{49} + 20 q^{50} + 32 q^{59} - 32 q^{61} + 80 q^{64} - 92 q^{65} - 4 q^{70} + 60 q^{71} + 4 q^{74} - 24 q^{76} + 36 q^{79} + 6 q^{80} + 64 q^{85} - 64 q^{86} + 28 q^{89} - 84 q^{91} + 46 q^{95} + O(q^{100}) \)

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

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