Space of modular forms of level 567, weight 2, and Character 567.g

• Label: 567.2.g
• Level: $567$
• Weight: $2$
• Character orbit: 567.g
• Rep. character: $\chi_{567}(109,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $60$
• Newform subspaces: $12$
• Sturm bound: $144$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.g (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(144\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(2\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(567, [\chi])\).

	Total	New	Old
Modular forms	168	68	100
Cusp forms	120	60	60
Eisenstein series	48	8	40

Trace form

\( 60 q - 30 q^{4} - 3 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(567, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
567.2.g.a	$567$	$2$	567.g	63.g	$3$	$2$	$1$	$4.528$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(-2\)	\(0\)	\(-4\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-2q^{5}+\cdots\)
567.2.g.b	$567$	$2$	567.g	63.g	$3$	$2$	$1$	$4.528$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(0\)	\(-8\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-4q^{5}+(2+\cdots)q^{7}+\cdots\)
567.2.g.c	$567$	$2$	567.g	63.g	$3$	$2$	$1$	$4.528$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{U}(1)[D_{3}]$	\(q+2\zeta_{6}q^{4}+(-3+2\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{13}+\cdots\)
567.2.g.d	$567$	$2$	567.g	63.g	$3$	$2$	$1$	$4.528$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(5\)	$1$	$\mathrm{U}(1)[D_{3}]$	\(q+2\zeta_{6}q^{4}+(3-\zeta_{6})q^{7}+(7-7\zeta_{6})q^{13}+\cdots\)
567.2.g.e	$567$	$2$	567.g	63.g	$3$	$2$	$1$	$4.528$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(8\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+4q^{5}+(2-3\zeta_{6})q^{7}+\cdots\)
567.2.g.f	$567$	$2$	567.g	63.g	$3$	$2$	$1$	$4.528$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(2\)	\(0\)	\(4\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+2q^{5}+(-1+\cdots)q^{7}+\cdots\)
567.2.g.g	$567$	$2$	567.g	63.g	$3$	$4$	$2$	$4.528$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{2}+(-4+4\beta _{1})q^{4}+\beta _{3}q^{5}+\cdots\)
567.2.g.h	$567$	$2$	567.g	63.g	$3$	$6$	$3$	$4.528$	6.0.309123.1	None		$2$	$0$	\(-2\)	\(0\)	\(2\)	\(2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}-\beta _{4}+\beta _{5})q^{2}+(-2+\beta _{2}+\cdots)q^{4}+\cdots\)
567.2.g.i	$567$	$2$	567.g	63.g	$3$	$6$	$3$	$4.528$	6.0.309123.1	None		$2$	$0$	\(2\)	\(0\)	\(-2\)	\(2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{4}+\beta _{5})q^{2}+(-\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
567.2.g.j	$567$	$2$	567.g	63.g	$3$	$8$	$4$	$4.528$	8.0.1767277521.3	None		$2$	$0$	\(-1\)	\(0\)	\(4\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{2}-\beta _{6})q^{2}+(-\beta _{5}+\beta _{7})q^{4}+\cdots\)
567.2.g.k	$567$	$2$	567.g	63.g	$3$	$8$	$4$	$4.528$	8.0.1767277521.3	None		$2$	$0$	\(1\)	\(0\)	\(-4\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{2}+\beta _{6})q^{2}+(-\beta _{5}+\beta _{7})q^{4}+(-1+\cdots)q^{5}+\cdots\)
567.2.g.l	$567$	$2$	567.g	63.g	$3$	$16$	$8$	$4.528$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{5}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{2}+(-\beta _{5}-\beta _{7}-\beta _{8}-\beta _{12}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(567, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(567, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)