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Properties

Label 3864.2.dp
Level $3864$
Weight $2$
Character orbit 3864.dp
Rep. character $\chi_{3864}(85,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $2880$
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.dp (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 184 \)
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 2880 4880
Cusp forms 7600 2880 4720
Eisenstein series 160 0 160

Trace form

\( 2880 q - 4 q^{2} - 4 q^{4} - 8 q^{6} - 8 q^{7} - 4 q^{8} + 288 q^{9} + O(q^{10}) \) \( 2880 q - 4 q^{2} - 4 q^{4} - 8 q^{6} - 8 q^{7} - 4 q^{8} + 288 q^{9} + 8 q^{10} + 4 q^{14} + 16 q^{15} + 12 q^{16} + 4 q^{18} - 40 q^{20} - 40 q^{22} + 8 q^{23} + 8 q^{24} + 288 q^{25} + 40 q^{26} - 4 q^{28} - 32 q^{31} + 36 q^{32} - 44 q^{34} + 26 q^{36} + 76 q^{40} + 130 q^{44} - 176 q^{46} + 144 q^{48} - 288 q^{49} - 86 q^{50} + 32 q^{52} - 36 q^{54} + 28 q^{56} - 54 q^{58} + 36 q^{60} + 8 q^{62} + 8 q^{63} - 28 q^{64} - 32 q^{66} + 48 q^{68} - 16 q^{71} + 4 q^{72} - 66 q^{74} + 276 q^{76} + 96 q^{79} + 16 q^{80} - 288 q^{81} + 296 q^{82} + 400 q^{86} - 10 q^{88} - 8 q^{90} - 32 q^{92} + 104 q^{94} - 160 q^{95} - 48 q^{96} + 18 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3864, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(184, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(552, [\chi])\)\(^{\oplus 2}\)