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 - 12 * q^10 + 4 * q^13 + 2 * q^16 - 8 * q^19 - 10 * q^25 - 28 * q^28 + 10 * q^31 - 2 * q^37 - 12 * q^40 + 16 * q^43 + 12 * q^46 + 8 * q^49 - 14 * q^52 - 108 * q^55 + 18 * q^58 + 4 * q^61 - 88 * q^64 + 16 * q^67 - 54 * q^70 + 4 * q^73 + 112 * q^76 + 28 * q^79 + 72 * q^82 + 36 * q^85 + 30 * q^88 + 46 * q^91 - 30 * q^94 + 4 * q^97

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}$