↑

Properties

Label 2340.2.fr
Level $2340$
Weight $2$
Character orbit 2340.fr
Rep. character $\chi_{2340}(19,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $824$
Sturm bound $1008$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2340.fr (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 260 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1008\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2340, [\chi])\).

Total New Old
Modular forms 2080 856 1224
Cusp forms 1952 824 1128
Eisenstein series 128 32 96

Trace form

\( 824 q - 12 q^{4} + 6 q^{5} + O(q^{10}) \) \( 824 q - 12 q^{4} + 6 q^{5} - 6 q^{10} + 12 q^{16} + 22 q^{20} - 8 q^{26} + 8 q^{29} - 16 q^{34} + 48 q^{40} - 16 q^{41} + 16 q^{44} - 96 q^{46} - 24 q^{49} + 12 q^{50} + 120 q^{56} - 12 q^{61} + 28 q^{65} - 24 q^{70} + 4 q^{74} - 28 q^{76} + 88 q^{80} + 18 q^{85} + 52 q^{86} - 20 q^{89} - 20 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2340, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2340, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2340, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(780, [\chi])\)\(^{\oplus 2}\)