↑

Properties

Label 2730.2.fb
Level $2730$
Weight $2$
Character orbit 2730.fb
Rep. character $\chi_{2730}(661,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $304$
Sturm bound $1344$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2730 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2730.fb (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2730, [\chi])\).

Total New Old
Modular forms 2752 304 2448
Cusp forms 2624 304 2320
Eisenstein series 128 0 128

Trace form

\( 304 q - 8 q^{7} - 304 q^{9} + O(q^{10}) \) \( 304 q - 8 q^{7} - 304 q^{9} + 8 q^{11} - 8 q^{12} - 16 q^{14} + 152 q^{16} - 16 q^{19} + 16 q^{22} + 16 q^{29} + 8 q^{31} + 16 q^{35} + 40 q^{37} + 40 q^{39} - 24 q^{41} - 120 q^{43} - 16 q^{44} + 24 q^{46} - 8 q^{49} + 48 q^{51} - 8 q^{52} - 16 q^{53} + 48 q^{55} - 24 q^{56} - 40 q^{57} - 32 q^{58} + 8 q^{63} + 16 q^{65} - 96 q^{67} - 48 q^{68} - 48 q^{71} - 128 q^{73} - 8 q^{74} + 8 q^{75} - 16 q^{76} + 32 q^{78} + 16 q^{79} + 304 q^{81} + 96 q^{83} + 16 q^{84} + 32 q^{86} + 96 q^{89} + 96 q^{91} - 8 q^{93} + 96 q^{95} - 104 q^{97} + 64 q^{98} - 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2730, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(2730, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2730, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(455, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(546, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(910, [\chi])\)\(^{\oplus 2}\)