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Properties

Label 3240.2.w
Level $3240$
Weight $2$
Character orbit 3240.w
Rep. character $\chi_{3240}(163,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $560$
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.w (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q(i)\)
Sturm bound: \(1296\)

Dimensions

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

Total New Old
Modular forms 1344 592 752
Cusp forms 1248 560 688
Eisenstein series 96 32 64

Trace form

\( 560 q - 8 q^{10} + 8 q^{16} - 12 q^{22} + 8 q^{25} + 8 q^{28} + 4 q^{40} + 8 q^{43} + 8 q^{46} - 28 q^{52} - 12 q^{58} + 8 q^{67} + 36 q^{70} - 16 q^{73} - 48 q^{76} - 72 q^{82} - 12 q^{88} - 32 q^{91}+ \cdots + 8 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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

\( S_{2}^{\mathrm{old}}(3240, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1080, [\chi])\)\(^{\oplus 2}\)