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Properties

Label 3864.2.bp
Level $3864$
Weight $2$
Character orbit 3864.bp
Rep. character $\chi_{3864}(185,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $352$
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.bp (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1536\)

Dimensions

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

Total New Old
Modular forms 1568 352 1216
Cusp forms 1504 352 1152
Eisenstein series 64 0 64

Trace form

\( 352 q - 8 q^{7} + O(q^{10}) \) \( 352 q - 8 q^{7} + 12 q^{19} - 164 q^{25} + 96 q^{31} + 4 q^{37} + 24 q^{39} - 56 q^{43} + 48 q^{45} + 16 q^{49} - 12 q^{51} - 32 q^{57} + 52 q^{63} - 4 q^{67} - 36 q^{73} - 108 q^{75} - 56 q^{79} - 16 q^{81} + 16 q^{85} - 48 q^{87} - 84 q^{91} + 16 q^{93} - 112 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3864, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(483, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(966, [\chi])\)\(^{\oplus 3}\)