Properties

Label 3840.2.cg
Level $3840$
Weight $2$
Character orbit 3840.cg
Rep. character $\chi_{3840}(367,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $768$
Sturm bound $1536$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3840 = 2^{8} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3840.cg (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 320 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(1536\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3840, [\chi])\).

Total New Old
Modular forms 6272 768 5504
Cusp forms 6016 768 5248
Eisenstein series 256 0 256

Trace form

\( 768 q + O(q^{10}) \) \( 768 q - 32 q^{51} + 64 q^{69} - 128 q^{71} + 32 q^{79} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3840, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3840, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3840, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(960, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1280, [\chi])\)\(^{\oplus 2}\)