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Properties

Label 864.3.o
Level $864$
Weight $3$
Character orbit 864.o
Rep. character $\chi_{864}(127,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $48$
Newform subspaces $3$
Sturm bound $432$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 864.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 36 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(432\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(864, [\chi])\).

Total New Old
Modular forms 624 48 576
Cusp forms 528 48 480
Eisenstein series 96 0 96

Trace form

\( 48 q + O(q^{10}) \) \( 48 q + 48 q^{17} - 120 q^{25} + 48 q^{29} + 72 q^{41} + 168 q^{49} + 288 q^{53} - 96 q^{65} + 48 q^{73} + 96 q^{77} - 120 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(864, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
864.3.o.a 864.o 36.f $4$ $23.542$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(14\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(7-7\zeta_{12}^{2})q^{5}+(5\zeta_{12}-5\zeta_{12}^{3})q^{7}+\cdots\)
864.3.o.b 864.o 36.f $20$ $23.542$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(-14\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\beta _{2}-\beta _{3}+\beta _{6})q^{5}+(\beta _{10}-\beta _{12}+\cdots)q^{7}+\cdots\)
864.3.o.c 864.o 36.f $24$ $23.542$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(864, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(864, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)