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Properties

Label 3240.2.bp
Level $3240$
Weight $2$
Character orbit 3240.bp
Rep. character $\chi_{3240}(1027,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1136$
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.bp (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 360 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1296\)

Dimensions

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

Total New Old
Modular forms 2688 1168 1520
Cusp forms 2496 1136 1360
Eisenstein series 192 32 160

Trace form

\( 1136 q + O(q^{10}) \) \( 1136 q - 8 q^{10} + 8 q^{16} + 12 q^{22} + 8 q^{25} - 40 q^{28} + 4 q^{40} + 8 q^{43} + 104 q^{46} + 20 q^{52} + 12 q^{58} + 8 q^{67} + 24 q^{70} - 16 q^{73} + 36 q^{76} - 24 q^{82} + 156 q^{88} - 32 q^{91} + 8 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3240, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1080, [\chi])\)\(^{\oplus 2}\)