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Properties

Label 3864.2.do
Level $3864$
Weight $2$
Character orbit 3864.do
Rep. character $\chi_{3864}(365,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $5760$
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.do (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 552 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(1536\)

Dimensions

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

Total New Old
Modular forms 7760 5760 2000
Cusp forms 7600 5760 1840
Eisenstein series 160 0 160

Trace form

\( 5760 q + 8 q^{4} - 6 q^{6} + O(q^{10}) \) \( 5760 q + 8 q^{4} - 6 q^{6} - 6 q^{12} + 8 q^{16} - 6 q^{18} + 576 q^{25} - 32 q^{31} - 44 q^{34} - 6 q^{36} + 24 q^{39} + 308 q^{40} - 200 q^{46} + 58 q^{48} + 576 q^{49} - 68 q^{52} - 52 q^{54} - 68 q^{58} + 20 q^{64} + 80 q^{72} + 22 q^{78} + 36 q^{82} + 154 q^{84} + 24 q^{87} + 418 q^{90} - 92 q^{94} + 388 q^{96} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3864, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(552, [\chi])\)\(^{\oplus 2}\)