↑

Properties

Label 3864.2.dd
Level $3864$
Weight $2$
Character orbit 3864.dd
Rep. character $\chi_{3864}(181,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $3840$
Sturm bound $1536$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3864 = 2^{3} \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3864.dd (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1288 \)
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 3840 3920
Cusp forms 7600 3840 3760
Eisenstein series 160 0 160

Trace form

\( 3840 q - 4 q^{2} - 4 q^{4} - 4 q^{8} - 384 q^{9} + O(q^{10}) \) \( 3840 q - 4 q^{2} - 4 q^{4} - 4 q^{8} - 384 q^{9} - 4 q^{16} - 4 q^{18} - 8 q^{23} + 384 q^{25} - 44 q^{32} + 18 q^{36} + 110 q^{42} + 154 q^{44} - 16 q^{46} - 54 q^{50} - 110 q^{56} + 10 q^{58} - 28 q^{64} + 72 q^{70} + 16 q^{71} - 4 q^{72} - 22 q^{74} - 384 q^{81} - 330 q^{88} + 292 q^{92} + 44 q^{98} + O(q^{100}) \)

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

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