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Properties

Label 2340.2.el
Level $2340$
Weight $2$
Character orbit 2340.el
Rep. character $\chi_{2340}(37,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $140$
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.el (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
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 2112 140 1972
Cusp forms 1920 140 1780
Eisenstein series 192 0 192

Trace form

\( 140 q - 2 q^{5} + 8 q^{11} - 6 q^{13} - 4 q^{17} + 20 q^{19} - 4 q^{23} + 6 q^{25} - 24 q^{31} + 12 q^{35} + 12 q^{37} - 10 q^{41} - 8 q^{43} + 8 q^{47} - 66 q^{49} + 6 q^{53} - 16 q^{55} - 24 q^{59} + 4 q^{61}+ \cdots - 72 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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

\( S_{2}^{\mathrm{old}}(2340, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(585, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(780, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1170, [\chi])\)\(^{\oplus 2}\)