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

• Label: 567.2.e
• Level: $567$
• Weight: $2$
• Character orbit: 567.e
• Rep. character: $\chi_{567}(163,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $56$
• Newform subspaces: $7$
• Sturm bound: $144$
• Trace bound: $2$

Defining parameters

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

\( 56 q - 22 q^{4} + 8 q^{7} + O(q^{10}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
567.2.e.a	$567$	$2$	567.e	7.c	$3$	$2$	$1$	$4.528$	\(\Q(\sqrt{-3}) \)	None					63.2.g.a	$2$	$1$	\(-1\)	\(0\)	\(1\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots\)
567.2.e.b	$567$	$2$	567.e	7.c	$3$	$2$	$1$	$4.528$	\(\Q(\sqrt{-3}) \)	None					63.2.g.a	$2$	$0$	\(1\)	\(0\)	\(-1\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots\)
567.2.e.c	$567$	$2$	567.e	7.c	$3$	$8$	$4$	$4.528$	8.0.1767277521.3	None		✓			567.2.e.c	$2$	$0$	\(-1\)	\(0\)	\(-2\)	\(1\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{2}-\beta _{6})q^{2}+(-\beta _{5}+\beta _{7})q^{4}+\cdots\)
567.2.e.d	$567$	$2$	567.e	7.c	$3$	$8$	$4$	$4.528$	8.0.1767277521.3	None		✓			567.2.e.c	$2$	$0$	\(1\)	\(0\)	\(2\)	\(1\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{2}+\beta _{6})q^{2}+(-\beta _{5}+\beta _{7})q^{4}+(1+\cdots)q^{5}+\cdots\)
567.2.e.e	$567$	$2$	567.e	7.c	$3$	$10$	$5$	$4.528$	10.0.\(\cdots\).1	None					63.2.g.b	$2$	$0$	\(-2\)	\(0\)	\(-4\)	\(5\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{2}+(-\beta _{3}+\beta _{6}+\beta _{7})q^{4}+(-1+\cdots)q^{5}+\cdots\)
567.2.e.f	$567$	$2$	567.e	7.c	$3$	$10$	$5$	$4.528$	10.0.\(\cdots\).1	None					63.2.g.b	$2$	$0$	\(2\)	\(0\)	\(4\)	\(5\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(-\beta _{3}+\beta _{6}+\beta _{7})q^{4}+(1+\cdots)q^{5}+\cdots\)
567.2.e.g	$567$	$2$	567.e	7.c	$3$	$16$	$8$	$4.528$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓	✓		567.2.e.g	$4$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$3^{5}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{2}+(-\beta _{5}-\beta _{7}-\beta _{8}-\beta _{12}+\cdots)q^{4}+\cdots\)

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

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