↑

Properties

Label 2790.2.j
Level $2790$
Weight $2$
Character orbit 2790.j
Rep. character $\chi_{2790}(931,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $240$
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.j (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
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 1168 240 928
Cusp forms 1136 240 896
Eisenstein series 32 0 32

Trace form

\( 240 q - 4 q^{2} - 4 q^{3} - 120 q^{4} - 4 q^{5} + 4 q^{6} + 8 q^{8} + 8 q^{9} + O(q^{10}) \) \( 240 q - 4 q^{2} - 4 q^{3} - 120 q^{4} - 4 q^{5} + 4 q^{6} + 8 q^{8} + 8 q^{9} + 12 q^{11} + 8 q^{12} + 4 q^{14} - 8 q^{15} - 120 q^{16} - 8 q^{17} + 8 q^{18} - 24 q^{19} - 4 q^{20} - 16 q^{21} + 12 q^{22} - 8 q^{24} - 120 q^{25} + 56 q^{27} + 12 q^{29} - 4 q^{30} - 4 q^{32} - 20 q^{33} + 12 q^{34} + 16 q^{35} - 4 q^{36} - 20 q^{38} - 48 q^{39} + 16 q^{41} - 24 q^{42} + 12 q^{43} - 24 q^{44} - 24 q^{46} - 24 q^{47} - 4 q^{48} - 108 q^{49} - 4 q^{50} + 4 q^{51} + 40 q^{54} + 4 q^{56} - 60 q^{57} + 28 q^{59} - 8 q^{60} + 12 q^{61} + 32 q^{62} - 8 q^{63} + 240 q^{64} + 8 q^{65} + 24 q^{66} + 12 q^{67} + 4 q^{68} + 76 q^{69} + 12 q^{70} - 48 q^{71} - 4 q^{72} - 24 q^{73} + 24 q^{74} - 4 q^{75} + 12 q^{76} - 80 q^{77} - 16 q^{78} + 24 q^{79} + 8 q^{80} - 24 q^{82} + 16 q^{83} + 20 q^{84} + 24 q^{85} - 4 q^{86} + 40 q^{87} + 12 q^{88} + 8 q^{89} - 48 q^{91} + 12 q^{94} + 8 q^{95} + 4 q^{96} + 12 q^{97} + 40 q^{98} - 24 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2790, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(279, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(558, [\chi])\)\(^{\oplus 2}\)