Properties

Label 720.2.cx
Level $720$
Weight $2$
Character orbit 720.cx
Rep. character $\chi_{720}(223,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $144$
Newform subspaces $5$
Sturm bound $288$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 720.cx (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 180 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 5 \)
Sturm bound: \(288\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(720, [\chi])\).

Total New Old
Modular forms 624 144 480
Cusp forms 528 144 384
Eisenstein series 96 0 96

Trace form

\( 144 q + O(q^{10}) \) \( 144 q + 24 q^{21} + 48 q^{53} + 48 q^{57} - 48 q^{65} - 24 q^{81} + 48 q^{93} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(720, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
720.2.cx.a 720.cx 180.x $8$ $5.749$ 8.0.12960000.1 None \(0\) \(-2\) \(8\) \(-6\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-1+\beta _{4}+\beta _{6})q^{3}+(2-2\beta _{4}+\beta _{7})q^{5}+\cdots\)
720.2.cx.b 720.cx 180.x $8$ $5.749$ 8.0.12960000.1 None \(0\) \(2\) \(8\) \(6\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-\beta _{1}-\beta _{3})q^{3}+(-\beta _{1}+2\beta _{4})q^{5}+\cdots\)
720.2.cx.c 720.cx 180.x $40$ $5.749$ None \(0\) \(-4\) \(-8\) \(6\) $\mathrm{SU}(2)[C_{12}]$
720.2.cx.d 720.cx 180.x $40$ $5.749$ None \(0\) \(4\) \(-8\) \(-6\) $\mathrm{SU}(2)[C_{12}]$
720.2.cx.e 720.cx 180.x $48$ $5.749$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(720, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(720, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 3}\)