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Properties

Label 2340.2.dc
Level $2340$
Weight $2$
Character orbit 2340.dc
Rep. character $\chi_{2340}(1249,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $144$
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.dc (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
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 144 888
Cusp forms 984 144 840
Eisenstein series 48 0 48

Trace form

\( 144 q - 2 q^{5} - 8 q^{9} + O(q^{10}) \) \( 144 q - 2 q^{5} - 8 q^{9} - 8 q^{11} - 6 q^{15} - 16 q^{21} + 6 q^{25} + 4 q^{29} - 12 q^{31} + 36 q^{35} - 36 q^{41} + 8 q^{45} + 84 q^{49} - 60 q^{51} + 12 q^{55} + 52 q^{59} - 12 q^{61} + 24 q^{69} - 16 q^{71} - 26 q^{75} + 24 q^{79} - 16 q^{81} - 184 q^{89} - 40 q^{95} - 68 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2340, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(585, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1170, [\chi])\)\(^{\oplus 2}\)