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Properties

Label 3864.2.dz
Level $3864$
Weight $2$
Character orbit 3864.dz
Rep. character $\chi_{3864}(445,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $7680$
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.dz (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1288 \)
Character field: \(\Q(\zeta_{66})\)
Sturm bound: \(1536\)

Dimensions

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

Total New Old
Modular forms 15520 7680 7840
Cusp forms 15200 7680 7520
Eisenstein series 320 0 320

Trace form

\( 7680 q - 4 q^{2} + 4 q^{4} + 8 q^{8} - 384 q^{9} + O(q^{10}) \) \( 7680 q - 4 q^{2} + 4 q^{4} + 8 q^{8} - 384 q^{9} + 4 q^{16} + 4 q^{18} + 8 q^{23} - 384 q^{25} + 20 q^{26} + 52 q^{28} + 16 q^{30} + 16 q^{32} + 32 q^{34} - 36 q^{36} - 180 q^{38} + 12 q^{40} - 90 q^{42} + 130 q^{44} - 16 q^{46} + 32 q^{48} + 180 q^{50} + 144 q^{52} + 54 q^{56} - 38 q^{58} + 20 q^{60} - 144 q^{62} - 56 q^{64} - 20 q^{68} + 48 q^{70} + 32 q^{71} + 4 q^{72} + 46 q^{74} - 16 q^{79} - 162 q^{80} + 384 q^{81} + 24 q^{82} + 56 q^{84} + 32 q^{86} + 298 q^{88} + 332 q^{92} - 114 q^{94} - 20 q^{96} + 72 q^{98} + O(q^{100}) \)

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

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