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Properties

Label 3864.2.bo
Level $3864$
Weight $2$
Character orbit 3864.bo
Rep. character $\chi_{3864}(2161,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $192$
Sturm bound $1536$

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Defining parameters

Level: \( N \) \(=\) \( 3864 = 2^{3} \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3864.bo (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 161 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1536\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3864, [\chi])\).

Total New Old
Modular forms 1568 192 1376
Cusp forms 1504 192 1312
Eisenstein series 64 0 64

Trace form

\( 192 q + 96 q^{9} + O(q^{10}) \) \( 192 q + 96 q^{9} + 12 q^{23} - 88 q^{25} - 40 q^{35} - 64 q^{49} + 48 q^{59} + 24 q^{73} - 48 q^{75} - 72 q^{77} - 96 q^{81} + 32 q^{85} - 24 q^{93} + 48 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3864, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3864, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3864, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(322, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(483, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(966, [\chi])\)\(^{\oplus 3}\)