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Properties

Label 3240.2.ch
Level $3240$
Weight $2$
Character orbit 3240.ch
Rep. character $\chi_{3240}(251,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $864$
Sturm bound $1296$

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Defining parameters

Level: \( N \) \(=\) \( 3240 = 2^{3} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3240.ch (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 216 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(1296\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3240, [\chi])\).

Total New Old
Modular forms 3960 864 3096
Cusp forms 3816 864 2952
Eisenstein series 144 0 144

Trace form

\( 864 q + O(q^{10}) \) \( 864 q + 30 q^{14} - 60 q^{38} + 24 q^{41} - 72 q^{44} - 54 q^{52} - 84 q^{56} + 54 q^{58} - 72 q^{59} + 198 q^{62} + 18 q^{68} + 84 q^{74} - 120 q^{83} + 54 q^{86} + 120 q^{92} + 54 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3240, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3240, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3240, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(648, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1080, [\chi])\)\(^{\oplus 2}\)