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

• Label: 567.2.p
• Level: $567$
• Weight: $2$
• Character orbit: 567.p
• Rep. character: $\chi_{567}(80,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $56$
• Newform subspaces: $5$
• Sturm bound: $144$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.p (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(144\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	168	72	96
Cusp forms	120	56	64
Eisenstein series	48	16	32

Trace form

\( 56 q + 26 q^{4} + O(q^{10}) \)

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.p.a	$567$	$2$	567.p	21.g	$6$	$2$	$1$	$4.528$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(-3\)	\(0\)	\(-3\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+\zeta_{6})q^{2}+(1-\zeta_{6})q^{4}-3\zeta_{6}q^{5}+\cdots\)
567.2.p.b	$567$	$2$	567.p	21.g	$6$	$2$	$1$	$4.528$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(3\)	\(0\)	\(3\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2-\zeta_{6})q^{2}+(1-\zeta_{6})q^{4}+3\zeta_{6}q^{5}+\cdots\)
567.2.p.c	$567$	$2$	567.p	21.g	$6$	$10$	$5$	$4.528$	10.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{3}-\beta _{4}-\beta _{5}-\beta _{7}-\beta _{8})q^{2}+\cdots\)
567.2.p.d	$567$	$2$	567.p	21.g	$6$	$10$	$5$	$4.528$	10.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{4}+\beta _{7}+\beta _{8})q^{2}+(1+\beta _{2}+\beta _{5}+\cdots)q^{4}+\cdots\)
567.2.p.e	$567$	$2$	567.p	21.g	$6$	$32$	$16$	$4.528$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(567, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)