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Properties

Label 2340.2.gs
Level $2340$
Weight $2$
Character orbit 2340.gs
Rep. character $\chi_{2340}(653,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $336$
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.gs (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 585 \)
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 336 1728
Cusp forms 1968 336 1632
Eisenstein series 96 0 96

Trace form

\( 336 q + O(q^{10}) \) \( 336 q - 24 q^{11} - 4 q^{21} - 12 q^{27} + 52 q^{33} + 36 q^{35} - 10 q^{45} + 30 q^{47} + 16 q^{51} - 12 q^{57} + 26 q^{63} + 24 q^{65} + 24 q^{71} - 34 q^{75} + 48 q^{77} - 28 q^{81} + 120 q^{83} + 24 q^{85} + 4 q^{87} + 12 q^{91} + 16 q^{93} + 96 q^{97} + O(q^{100}) \)

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

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