Properties

Label 3840.2.o
Level $3840$
Weight $2$
Character orbit 3840.o
Rep. character $\chi_{3840}(3839,\cdot)$
Character field $\Q$
Dimension $184$
Sturm bound $1536$

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Defining parameters

Level: \( N \) \(=\) \( 3840 = 2^{8} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3840.o (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 60 \)
Character field: \(\Q\)
Sturm bound: \(1536\)

Dimensions

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

Total New Old
Modular forms 816 200 616
Cusp forms 720 184 536
Eisenstein series 96 16 80

Trace form

\( 184 q + 8 q^{9} + O(q^{10}) \) \( 184 q + 8 q^{9} + 8 q^{25} + 120 q^{49} - 8 q^{81} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3840, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(960, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1920, [\chi])\)\(^{\oplus 2}\)