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Properties

Label 3360.2.ij
Level $3360$
Weight $2$
Character orbit 3360.ij
Rep. character $\chi_{3360}(19,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $3072$
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.ij (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1120 \)
Character field: \(\Q(\zeta_{24})\)
Sturm bound: \(1536\)

Dimensions

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

Total New Old
Modular forms 6208 3072 3136
Cusp forms 6080 3072 3008
Eisenstein series 128 0 128

Trace form

\( 3072 q + O(q^{10}) \) \( 3072 q - 64 q^{14} + 48 q^{35} - 48 q^{50} + 192 q^{59} + 48 q^{60} - 144 q^{66} - 72 q^{70} + 128 q^{71} + 272 q^{74} + 72 q^{80} + 240 q^{96} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3360, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1120, [\chi])\)\(^{\oplus 2}\)