Properties

Label 864.2.r
Level $864$
Weight $2$
Character orbit 864.r
Rep. character $\chi_{864}(145,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $20$
Newform subspaces $2$
Sturm bound $288$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 864.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 72 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(864, [\chi])\).

Total New Old
Modular forms 336 28 308
Cusp forms 240 20 220
Eisenstein series 96 8 88

Trace form

\( 20 q + 2 q^{7} + O(q^{10}) \) \( 20 q + 2 q^{7} + 8 q^{17} - 14 q^{23} + 2 q^{31} - 2 q^{41} + 18 q^{47} + 28 q^{55} + 22 q^{65} + 48 q^{71} - 8 q^{73} + 2 q^{79} - 8 q^{89} + 40 q^{95} - 2 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(864, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
864.2.r.a 864.r 72.n $4$ $6.899$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{6}]$ \(q+2\zeta_{12}q^{5}+4\zeta_{12}^{2}q^{7}+(3\zeta_{12}-3\zeta_{12}^{3})q^{11}+\cdots\)
864.2.r.b 864.r 72.n $16$ $6.899$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{4}-\beta _{5}-\beta _{11})q^{5}+(-1+\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(864, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(864, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)