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Properties

Label 2340.2.dl
Level $2340$
Weight $2$
Character orbit 2340.dl
Rep. character $\chi_{2340}(961,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $112$
Sturm bound $1008$

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Defining parameters

Level: \( N \) \(=\) \( 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2340.dl (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 117 \)
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 1032 112 920
Cusp forms 984 112 872
Eisenstein series 48 0 48

Trace form

\( 112 q - 8 q^{9} + O(q^{10}) \) \( 112 q - 8 q^{9} + 2 q^{13} - 32 q^{17} + 56 q^{25} + 24 q^{27} - 20 q^{29} + 16 q^{35} - 16 q^{39} + 8 q^{43} + 52 q^{49} + 4 q^{51} + 80 q^{53} + 28 q^{61} - 2 q^{65} + 20 q^{69} + 16 q^{77} + 16 q^{79} + 16 q^{81} + 28 q^{87} - 24 q^{91} - 8 q^{95} + O(q^{100}) \)

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

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