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Properties

Label 3360.2.ey
Level $3360$
Weight $2$
Character orbit 3360.ey
Rep. character $\chi_{3360}(883,\cdot)$
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.ey (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

\( 1152 q - 32 q^{12} - 32 q^{19} - 32 q^{22} + 80 q^{32} - 16 q^{34} + 112 q^{38} + 80 q^{40} + 64 q^{43} + 1152 q^{49} + 32 q^{51} + 32 q^{52} + 64 q^{55} + 96 q^{56} - 64 q^{61} - 96 q^{64} + 112 q^{68}+ \cdots + 128 q^{94}+O(q^{100}) \) Copy content Toggle raw display

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

\( S_{2}^{\mathrm{old}}(3360, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1120, [\chi])\)\(^{\oplus 2}\)