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

• Label: 567.2.i
• Level: $567$
• Weight: $2$
• Character orbit: 567.i
• Rep. character: $\chi_{567}(215,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $60$
• Newform subspaces: $7$
• Sturm bound: $144$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.i (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(144\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(2\), \(11\), \(13\)

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

\( 60 q - 52 q^{4} + 7 q^{7} + O(q^{10}) \)

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.i.a	$567$	$2$	567.i	63.i	$6$	$2$	$1$	$4.528$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-5\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+2q^{4}+(-2-\zeta_{6})q^{7}+(8-4\zeta_{6})q^{13}+\cdots\)
567.2.i.b	$567$	$2$	567.i	63.i	$6$	$2$	$1$	$4.528$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+2q^{4}+(1+2\zeta_{6})q^{7}+(2-\zeta_{6})q^{13}+\cdots\)
567.2.i.c	$567$	$2$	567.i	63.i	$6$	$4$	$2$	$4.528$	\(\Q(\sqrt{-3}, \sqrt{-5})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{3}q^{2}-3q^{4}+(2+\beta _{2})q^{7}-\beta _{3}q^{8}+\cdots\)
567.2.i.d	$567$	$2$	567.i	63.i	$6$	$4$	$2$	$4.528$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{3}q^{2}+(\beta _{1}+\beta _{3})q^{5}+(-3+2\beta _{2}+\cdots)q^{7}+\cdots\)
567.2.i.e	$567$	$2$	567.i	63.i	$6$	$4$	$2$	$4.528$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{3}q^{2}+(-\beta _{1}-\beta _{3})q^{5}+(1-3\beta _{2}+\cdots)q^{7}+\cdots\)
567.2.i.f	$567$	$2$	567.i	63.i	$6$	$12$	$6$	$4.528$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{11}q^{2}+(-1+\beta _{7})q^{4}-\beta _{6}q^{5}+\cdots\)
567.2.i.g	$567$	$2$	567.i	63.i	$6$	$32$	$16$	$4.528$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$\mathrm{SU}(2)[C_{6}]$

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

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