↑

Properties

Label 2340.2.fv
Level $2340$
Weight $2$
Character orbit 2340.fv
Rep. character $\chi_{2340}(41,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $224$
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.fv (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 117 \)
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 2064 224 1840
Cusp forms 1968 224 1744
Eisenstein series 96 0 96

Trace form

\( 224 q - 8 q^{7} + O(q^{10}) \) \( 224 q - 8 q^{7} - 12 q^{11} - 4 q^{15} - 8 q^{19} + 28 q^{21} + 24 q^{27} + 8 q^{31} - 28 q^{33} - 4 q^{37} - 16 q^{39} - 24 q^{41} - 16 q^{45} + 72 q^{47} - 12 q^{57} + 8 q^{63} + 28 q^{67} + 24 q^{71} + 28 q^{73} - 48 q^{77} - 12 q^{79} - 20 q^{81} - 36 q^{83} - 12 q^{85} + 64 q^{87} + 60 q^{89} - 8 q^{91} - 68 q^{93} - 4 q^{97} + 60 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2340, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(234, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(468, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(585, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1170, [\chi])\)\(^{\oplus 2}\)