↑

Properties

Label 864.2.y
Level $864$
Weight $2$
Character orbit 864.y
Rep. character $\chi_{864}(97,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $216$
Newform subspaces $4$
Sturm bound $288$
Trace bound $11$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 864.y (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 27 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 4 \)
Sturm bound: \(288\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

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

Total New Old
Modular forms 912 216 696
Cusp forms 816 216 600
Eisenstein series 96 0 96

Trace form

\( 216 q + O(q^{10}) \) \( 216 q + 24 q^{29} - 36 q^{33} - 36 q^{41} + 24 q^{45} + 12 q^{57} + 48 q^{65} + 48 q^{69} + 48 q^{77} + 48 q^{81} - 12 q^{89} + 144 q^{93} + 36 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.y.a 864.y 27.e $48$ $6.899$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$
864.2.y.b 864.y 27.e $54$ $6.899$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$
864.2.y.c 864.y 27.e $54$ $6.899$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$
864.2.y.d 864.y 27.e $60$ $6.899$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$

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

\( S_{2}^{\mathrm{old}}(864, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)