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Properties

Label 3360.2.es
Level $3360$
Weight $2$
Character orbit 3360.es
Rep. character $\chi_{3360}(43,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $1152$
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.es (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 160 \)
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 1152 1952
Cusp forms 3040 1152 1888
Eisenstein series 64 0 64

Trace form

\( 1152 q + O(q^{10}) \) \( 1152 q - 32 q^{12} + 32 q^{19} - 32 q^{22} - 80 q^{32} + 16 q^{34} - 112 q^{38} + 80 q^{40} - 64 q^{43} - 1152 q^{49} + 32 q^{51} - 32 q^{52} - 64 q^{55} + 96 q^{56} - 64 q^{61} + 96 q^{64} + 112 q^{68} + 144 q^{76} - 48 q^{78} + 160 q^{80} + 160 q^{82} - 160 q^{83} + 128 q^{86} + 32 q^{88} + 32 q^{90} - 128 q^{94} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3360, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)