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Properties

Label 3360.2.fh
Level $3360$
Weight $2$
Character orbit 3360.fh
Rep. character $\chi_{3360}(491,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $1536$
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.fh (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 96 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(1536\)

Dimensions

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

Total New Old
Modular forms 3104 1536 1568
Cusp forms 3040 1536 1504
Eisenstein series 64 0 64

Trace form

\( 1536 q + O(q^{10}) \) \( 1536 q - 16 q^{10} - 64 q^{16} - 96 q^{27} + 48 q^{36} - 96 q^{39} + 128 q^{46} + 128 q^{52} + 288 q^{58} - 64 q^{61} - 64 q^{66} + 128 q^{67} + 112 q^{76} - 48 q^{78} + 64 q^{79} - 160 q^{88} - 16 q^{94} - 64 q^{96} + 128 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3360, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 2}\)