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Properties

Label 3240.2.cu
Level $3240$
Weight $2$
Character orbit 3240.cu
Rep. character $\chi_{3240}(307,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $2544$
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.cu (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1080 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(1296\)

Dimensions

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

Total New Old
Modular forms 7920 2640 5280
Cusp forms 7632 2544 5088
Eisenstein series 288 96 192

Trace form

\( 2544 q + 12 q^{2} + 6 q^{8} + O(q^{10}) \) \( 2544 q + 12 q^{2} + 6 q^{8} - 6 q^{10} + 48 q^{11} - 24 q^{16} + 12 q^{17} + 12 q^{20} - 12 q^{22} - 24 q^{25} + 48 q^{26} - 24 q^{28} - 48 q^{32} + 12 q^{35} + 24 q^{38} - 12 q^{40} + 48 q^{41} - 24 q^{43} - 12 q^{46} + 12 q^{50} - 12 q^{52} - 144 q^{56} - 12 q^{58} + 6 q^{62} + 24 q^{65} - 24 q^{67} + 36 q^{68} - 12 q^{70} - 12 q^{73} - 72 q^{76} + 204 q^{80} - 24 q^{82} + 24 q^{83} - 84 q^{86} + 36 q^{88} - 24 q^{91} + 126 q^{92} - 24 q^{97} + 120 q^{98} + O(q^{100}) \)

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

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