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Properties

Label 3360.2.hc
Level $3360$
Weight $2$
Character orbit 3360.hc
Rep. character $\chi_{3360}(47,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $736$
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.hc (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 840 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1536\)

Dimensions

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

Total New Old
Modular forms 3200 800 2400
Cusp forms 2944 736 2208
Eisenstein series 256 64 192

Trace form

\( 736 q + 12 q^{3} + O(q^{10}) \) \( 736 q + 12 q^{3} - 8 q^{25} - 12 q^{33} + 32 q^{43} + 8 q^{51} + 8 q^{57} + 8 q^{67} - 24 q^{73} + 12 q^{75} + 8 q^{81} + 32 q^{91} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{2}^{\mathrm{old}}(3360, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(840, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1680, [\chi])\)\(^{\oplus 2}\)