Properties

Label 3360.2.v
Level $3360$
Weight $2$
Character orbit 3360.v
Rep. character $\chi_{3360}(1919,\cdot)$
Character field $\Q$
Dimension $144$
Sturm bound $1536$

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Defining parameters

Level: \( N \) \(=\) \( 3360 = 2^{5} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3360.v (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 60 \)
Character field: \(\Q\)
Sturm bound: \(1536\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3360, [\chi])\).

Total New Old
Modular forms 800 144 656
Cusp forms 736 144 592
Eisenstein series 64 0 64

Trace form

\( 144 q + O(q^{10}) \) \( 144 q + 48 q^{45} + 144 q^{49} - 64 q^{61} + 96 q^{69} - 32 q^{81} + 48 q^{85} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3360, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3360, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3360, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1680, [\chi])\)\(^{\oplus 2}\)