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

• Label: 567.2.f
• Level: $567$
• Weight: $2$
• Character orbit: 567.f
• Rep. character: $\chi_{567}(190,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $48$
• Newform subspaces: $14$
• Sturm bound: $144$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.f (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 14 \)
Sturm bound:			\(144\)
Trace bound:			\(10\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

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

	Total	New	Old
Modular forms	168	48	120
Cusp forms	120	48	72
Eisenstein series	48	0	48

Trace form

\( 48 q - 24 q^{4} + O(q^{10}) \)

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.f.a	$567$	$2$	567.f	9.c	$3$	$2$	$1$	$4.528$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(-2\)	\(0\)	\(-1\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots\)
567.2.f.b	$567$	$2$	567.f	9.c	$3$	$2$	$1$	$4.528$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(0\)	\(-2\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-2\zeta_{6}q^{5}+\cdots\)
567.2.f.c	$567$	$2$	567.f	9.c	$3$	$2$	$1$	$4.528$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(0\)	\(1\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}+\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
567.2.f.d	$567$	$2$	567.f	9.c	$3$	$2$	$1$	$4.528$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-3\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{4}-3\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+\cdots\)
567.2.f.e	$567$	$2$	567.f	9.c	$3$	$2$	$1$	$4.528$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{4}+3\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+\cdots\)
567.2.f.f	$567$	$2$	567.f	9.c	$3$	$2$	$1$	$4.528$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(-1\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots\)
567.2.f.g	$567$	$2$	567.f	9.c	$3$	$2$	$1$	$4.528$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(2\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+2\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
567.2.f.h	$567$	$2$	567.f	9.c	$3$	$2$	$1$	$4.528$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(2\)	\(0\)	\(1\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
567.2.f.i	$567$	$2$	567.f	9.c	$3$	$4$	$2$	$4.528$	\(\Q(\sqrt{-3}, \sqrt{7})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+5\beta _{2}q^{4}+(\beta _{1}+\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots\)
567.2.f.j	$567$	$2$	567.f	9.c	$3$	$4$	$2$	$4.528$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{12}^{2}q^{2}+(-1+\zeta_{12})q^{4}+(-2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
567.2.f.k	$567$	$2$	567.f	9.c	$3$	$4$	$2$	$4.528$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{12}^{2}q^{2}+(-1+\zeta_{12})q^{4}+(\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
567.2.f.l	$567$	$2$	567.f	9.c	$3$	$6$	$3$	$4.528$	6.0.1156923.1	None		$2$	$0$	\(0\)	\(0\)	\(-3\)	\(-3\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{4}q^{2}+(-\beta _{1}+\beta _{2}-2\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
567.2.f.m	$567$	$2$	567.f	9.c	$3$	$6$	$3$	$4.528$	6.0.1156923.1	None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(-3\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{4}q^{2}+(-\beta _{1}+\beta _{2}-2\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
567.2.f.n	$567$	$2$	567.f	9.c	$3$	$8$	$4$	$4.528$	8.0.49787136.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{3}q^{2}+\beta _{4}q^{4}-2\beta _{7}q^{5}+(1-\beta _{5}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(567, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)