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Properties

Label 3240.2.de
Level $3240$
Weight $2$
Character orbit 3240.de
Rep. character $\chi_{3240}(59,\cdot)$
Character field $\Q(\zeta_{54})$
Dimension $11592$
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.de (of order \(54\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3240 \)
Character field: \(\Q(\zeta_{54})\)
Sturm bound: \(1296\)

Dimensions

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

Total New Old
Modular forms 11736 11736 0
Cusp forms 11592 11592 0
Eisenstein series 144 144 0

Trace form

\( 11592 q - 36 q^{4} - 36 q^{6} - 72 q^{9} + O(q^{10}) \) \( 11592 q - 36 q^{4} - 36 q^{6} - 72 q^{9} - 18 q^{10} - 72 q^{11} - 36 q^{14} - 36 q^{16} - 72 q^{19} - 18 q^{20} - 36 q^{24} - 36 q^{25} - 54 q^{26} - 18 q^{30} - 36 q^{34} - 36 q^{35} - 36 q^{36} - 18 q^{40} - 72 q^{41} - 108 q^{44} - 36 q^{46} - 72 q^{49} + 99 q^{50} - 72 q^{51} + 90 q^{54} + 90 q^{56} - 72 q^{59} - 135 q^{60} - 36 q^{64} - 36 q^{65} - 108 q^{66} - 18 q^{70} - 36 q^{74} - 36 q^{75} - 36 q^{76} - 72 q^{81} - 90 q^{84} - 36 q^{86} - 72 q^{89} + 45 q^{90} - 72 q^{91} - 36 q^{94} - 36 q^{96} - 72 q^{99} + O(q^{100}) \)

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.