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Properties

Label 3864.2.br
Level $3864$
Weight $2$
Character orbit 3864.br
Rep. character $\chi_{3864}(1747,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $768$
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.br (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1288 \)
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 1552 768 784
Cusp forms 1520 768 752
Eisenstein series 32 0 32

Trace form

\( 768 q + 4 q^{2} - 4 q^{4} - 8 q^{8} - 384 q^{9} + O(q^{10}) \) \( 768 q + 4 q^{2} - 4 q^{4} - 8 q^{8} - 384 q^{9} - 4 q^{16} + 4 q^{18} - 384 q^{25} - 20 q^{26} + 24 q^{32} + 8 q^{36} - 8 q^{46} + 32 q^{48} + 16 q^{50} - 76 q^{52} + 16 q^{58} - 144 q^{62} + 56 q^{64} - 48 q^{70} + 4 q^{72} - 384 q^{81} - 16 q^{82} - 56 q^{92} + 12 q^{94} + 20 q^{96} + 72 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3864, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1288, [\chi])\)\(^{\oplus 2}\)