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Properties

Label 2340.2.cd
Level $2340$
Weight $2$
Character orbit 2340.cd
Rep. character $\chi_{2340}(589,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $168$
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.cd (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 585 \)
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 168 864
Cusp forms 984 168 816
Eisenstein series 48 0 48

Trace form

\( 168 q - 2 q^{9} + O(q^{10}) \) \( 168 q - 2 q^{9} - 6 q^{21} - 56 q^{29} + q^{35} + 38 q^{39} - 12 q^{41} + 15 q^{45} - 84 q^{49} - 14 q^{51} - 11 q^{65} + 40 q^{69} + 12 q^{71} + 32 q^{75} - 6 q^{79} + 46 q^{81} - 30 q^{89} + 6 q^{91} + 48 q^{95} - 12 q^{99} + O(q^{100}) \)

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

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