↑

Properties

Label 2340.2.cm
Level $2340$
Weight $2$
Character orbit 2340.cm
Rep. character $\chi_{2340}(311,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $672$
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.cm (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 468 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1008\)

Dimensions

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

Total New Old
Modular forms 1024 672 352
Cusp forms 992 672 320
Eisenstein series 32 0 32

Trace form

\( 672 q + O(q^{10}) \) \( 672 q + 24 q^{12} - 336 q^{25} + 32 q^{30} - 68 q^{36} - 60 q^{38} - 20 q^{42} - 4 q^{48} - 336 q^{49} - 18 q^{52} - 72 q^{64} + 104 q^{66} - 156 q^{68} - 64 q^{69} + 168 q^{74} + 96 q^{77} - 30 q^{78} + 72 q^{82} + 36 q^{90} + 60 q^{92} - 36 q^{94} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2340, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(468, [\chi])\)\(^{\oplus 2}\)