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Properties

Label 3864.2.ds
Level $3864$
Weight $2$
Character orbit 3864.ds
Rep. character $\chi_{3864}(25,\cdot)$
Character field $\Q(\zeta_{33})$
Dimension $1920$
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.ds (of order \(33\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 161 \)
Character field: \(\Q(\zeta_{33})\)
Sturm bound: \(1536\)

Dimensions

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

Total New Old
Modular forms 15680 1920 13760
Cusp forms 15040 1920 13120
Eisenstein series 640 0 640

Trace form

\( 1920 q + 96 q^{9} + O(q^{10}) \) \( 1920 q + 96 q^{9} - 8 q^{11} - 32 q^{19} + 12 q^{23} + 104 q^{25} + 8 q^{33} + 28 q^{35} - 44 q^{37} - 48 q^{41} + 104 q^{43} + 32 q^{49} - 36 q^{51} - 48 q^{55} + 72 q^{57} - 88 q^{59} + 24 q^{61} - 8 q^{67} + 8 q^{69} - 8 q^{73} - 16 q^{75} - 72 q^{77} + 96 q^{81} - 112 q^{83} + 264 q^{85} - 48 q^{89} + 32 q^{91} - 24 q^{93} + 216 q^{95} + 32 q^{97} + 16 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3864, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(322, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(483, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(644, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(966, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1288, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1932, [\chi])\)\(^{\oplus 2}\)