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Properties

Label 3240.2.cj
Level $3240$
Weight $2$
Character orbit 3240.cj
Rep. character $\chi_{3240}(469,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $1272$
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.cj (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1080 \)
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 1320 2640
Cusp forms 3816 1272 2544
Eisenstein series 144 48 96

Trace form

\( 1272 q - 12 q^{4} + O(q^{10}) \) \( 1272 q - 12 q^{4} - 3 q^{10} + 12 q^{14} - 12 q^{16} + 27 q^{20} - 12 q^{25} + 24 q^{26} - 24 q^{31} - 24 q^{34} + 9 q^{40} + 24 q^{41} + 30 q^{44} - 6 q^{46} - 24 q^{49} - 72 q^{50} - 24 q^{55} - 30 q^{56} - 6 q^{64} + 12 q^{65} - 21 q^{70} - 156 q^{71} + 42 q^{74} - 36 q^{76} - 24 q^{79} - 78 q^{80} + 126 q^{86} + 12 q^{89} - 12 q^{94} + 42 q^{95} + O(q^{100}) \)

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

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