↑

Properties

Label 2790.2.q
Level $2790$
Weight $2$
Character orbit 2790.q
Rep. character $\chi_{2790}(721,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $224$
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.q (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 31 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 2368 224 2144
Cusp forms 2240 224 2016
Eisenstein series 128 0 128

Trace form

\( 224 q - 56 q^{4} + O(q^{10}) \) \( 224 q - 56 q^{4} - 12 q^{11} - 8 q^{13} - 12 q^{14} - 56 q^{16} - 12 q^{17} + 12 q^{22} - 28 q^{23} + 224 q^{25} - 48 q^{26} - 4 q^{29} + 20 q^{31} + 12 q^{34} - 12 q^{35} - 48 q^{37} - 16 q^{38} - 48 q^{41} - 4 q^{43} + 8 q^{44} + 4 q^{46} + 16 q^{47} - 96 q^{49} - 8 q^{52} + 24 q^{53} + 12 q^{55} + 8 q^{56} + 20 q^{58} - 24 q^{59} + 80 q^{61} + 60 q^{62} - 56 q^{64} - 8 q^{65} - 32 q^{67} + 48 q^{68} - 52 q^{71} + 28 q^{73} - 12 q^{74} + 16 q^{77} + 44 q^{79} + 40 q^{82} + 52 q^{83} - 8 q^{85} + 52 q^{86} - 8 q^{88} + 48 q^{89} + 96 q^{91} - 8 q^{92} + 48 q^{94} - 8 q^{95} + 56 q^{97} + 64 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2790, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(62, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(93, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(186, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(310, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(465, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(930, [\chi])\)\(^{\oplus 2}\)