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Properties

Label 3840.2.cp
Level $3840$
Weight $2$
Character orbit 3840.cp
Rep. character $\chi_{3840}(239,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $1504$
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.cp (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 960 \)
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 1568 4704
Cusp forms 6016 1504 4512
Eisenstein series 256 64 192

Trace form

\( 1504 q - 16 q^{9} + O(q^{10}) \) \( 1504 q - 16 q^{9} + 8 q^{15} + 32 q^{19} - 16 q^{21} - 16 q^{25} + 64 q^{31} + 16 q^{39} - 8 q^{45} - 32 q^{49} + 16 q^{51} - 48 q^{55} - 32 q^{61} - 16 q^{69} + 8 q^{75} - 16 q^{81} - 16 q^{85} + 32 q^{91} + 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{2}^{\mathrm{old}}(3840, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(960, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1920, [\chi])\)\(^{\oplus 2}\)