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Properties

Label 2340.2.gn
Level $2340$
Weight $2$
Character orbit 2340.gn
Rep. character $\chi_{2340}(677,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $288$
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.gn (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
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 288 1776
Cusp forms 1968 288 1680
Eisenstein series 96 0 96

Trace form

\( 288 q + 4 q^{3} + O(q^{10}) \) \( 288 q + 4 q^{3} - 20 q^{15} - 12 q^{25} + 40 q^{27} + 8 q^{33} - 24 q^{37} + 24 q^{41} - 20 q^{45} + 24 q^{47} + 96 q^{51} - 24 q^{55} - 8 q^{57} + 24 q^{61} + 24 q^{63} - 12 q^{67} - 32 q^{75} - 144 q^{77} - 80 q^{81} - 124 q^{87} - 52 q^{93} - 120 q^{95} - 12 q^{97} + O(q^{100}) \)

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

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