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Properties

Label 3360.2.en
Level $3360$
Weight $2$
Character orbit 3360.en
Rep. character $\chi_{3360}(421,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $768$
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.en (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
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 768 2336
Cusp forms 3040 768 2272
Eisenstein series 64 0 64

Trace form

\( 768 q + O(q^{10}) \) \( 768 q - 16 q^{10} - 16 q^{16} - 16 q^{18} + 16 q^{22} - 32 q^{23} - 16 q^{24} + 160 q^{32} + 160 q^{34} - 32 q^{43} + 16 q^{44} - 128 q^{46} + 32 q^{51} - 128 q^{52} - 64 q^{53} + 16 q^{54} + 16 q^{56} - 64 q^{61} + 192 q^{62} + 32 q^{63} + 32 q^{67} + 192 q^{68} - 64 q^{69} + 16 q^{74} - 112 q^{76} - 64 q^{77} - 128 q^{86} + 160 q^{88} - 16 q^{92} + 16 q^{94} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3360, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1120, [\chi])\)\(^{\oplus 2}\)