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Properties

Label 3864.2.ep
Level $3864$
Weight $2$
Character orbit 3864.ep
Rep. character $\chi_{3864}(257,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $3840$
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.ep (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 483 \)
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 15680 3840 11840
Cusp forms 15040 3840 11200
Eisenstein series 640 0 640

Trace form

\( 3840 q - 4 q^{9} + O(q^{10}) \) \( 3840 q - 4 q^{9} - 16 q^{15} - 28 q^{21} + 200 q^{25} + 24 q^{33} + 44 q^{37} + 20 q^{39} - 72 q^{43} + 36 q^{45} - 92 q^{49} + 48 q^{57} - 72 q^{61} + 12 q^{63} - 24 q^{67} - 24 q^{73} + 88 q^{81} - 48 q^{85} + 486 q^{87} - 48 q^{91} - 48 q^{93} - 324 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3864, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(483, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(966, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1932, [\chi])\)\(^{\oplus 2}\)