Space of modular forms of level 567, weight 2, and trivial character

• Label: 567.2.a
• Level: $567$
• Weight: $2$
• Character orbit: 567.a
• Rep. character: $\chi_{567}(1,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $9$
• Sturm bound: $144$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(144\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(567))\).

	Total	New	Old
Modular forms	84	24	60
Cusp forms	61	24	37
Eisenstein series	23	0	23

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)	\(7\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(18\)	\(5\)	\(13\)		\(13\)	\(5\)	\(8\)		\(5\)	\(0\)	\(5\)
\(+\)	\(-\)	\(-\)		\(24\)	\(9\)	\(15\)		\(18\)	\(9\)	\(9\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(-\)		\(24\)	\(7\)	\(17\)		\(18\)	\(7\)	\(11\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(+\)		\(18\)	\(3\)	\(15\)		\(12\)	\(3\)	\(9\)		\(6\)	\(0\)	\(6\)
Plus space		\(+\)		\(36\)	\(8\)	\(28\)		\(25\)	\(8\)	\(17\)		\(11\)	\(0\)	\(11\)
Minus space		\(-\)		\(48\)	\(16\)	\(32\)		\(36\)	\(16\)	\(20\)		\(12\)	\(0\)	\(12\)

Trace form

24 * q + 24 * q^4 + 12 * q^10 + 12 * q^13 + 36 * q^16 - 12 * q^19 + 24 * q^25 + 12 * q^28 - 12 * q^31 - 24 * q^34 + 24 * q^37 + 12 * q^40 - 12 * q^43 - 12 * q^46 + 24 * q^49 - 12 * q^55 - 12 * q^58 + 36 * q^61 - 12 * q^64 - 24 * q^73 - 60 * q^76 + 12 * q^79 - 24 * q^82 + 48 * q^85 - 48 * q^88 - 12 * q^91 - 84 * q^94

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(567))\) 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					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	7
567.2.a.a	$567$	$2$	567.a	1.a	$1$	$1$	$1$	$4.528$	\(\Q\)	None	✓	✓			567.2.a.a	$1$	$1$	\(-1\)	\(0\)	\(1\)	\(-1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+q^{5}-q^{7}+3q^{8}-q^{10}+\cdots\)
567.2.a.b	$567$	$2$	567.a	1.a	$1$	$1$	$1$	$4.528$	\(\Q\)	None	✓	✓			567.2.a.a	$1$	$1$	\(1\)	\(0\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-q^{5}-q^{7}-3q^{8}-q^{10}+\cdots\)
567.2.a.c	$567$	$2$	567.a	1.a	$1$	$3$	$3$	$4.528$	\(\Q(\zeta_{18})^+\)	None	✓		✓	✓	63.2.f.a	$1$	$1$	\(-3\)	\(0\)	\(-3\)	\(3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
567.2.a.d	$567$	$2$	567.a	1.a	$1$	$3$	$3$	$4.528$	3.3.321.1	None	✓		✓		63.2.f.b	$1$	$1$	\(-1\)	\(0\)	\(-5\)	\(-3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(-2-\beta _{2})q^{5}+\cdots\)
567.2.a.e	$567$	$2$	567.a	1.a	$1$	$3$	$3$	$4.528$	3.3.621.1	None	✓	✓			567.2.a.e	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+(-1-\beta _{2})q^{5}+\cdots\)
567.2.a.f	$567$	$2$	567.a	1.a	$1$	$3$	$3$	$4.528$	3.3.621.1	None	✓	✓			567.2.a.e	$1$	$0$	\(0\)	\(0\)	\(3\)	\(3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots\)
567.2.a.g	$567$	$2$	567.a	1.a	$1$	$3$	$3$	$4.528$	3.3.321.1	None	✓				63.2.f.b	$1$	$0$	\(1\)	\(0\)	\(5\)	\(-3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(2+\beta _{2})q^{5}+\cdots\)
567.2.a.h	$567$	$2$	567.a	1.a	$1$	$3$	$3$	$4.528$	\(\Q(\zeta_{18})^+\)	None	✓				63.2.f.a	$1$	$0$	\(3\)	\(0\)	\(3\)	\(3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
567.2.a.i	$567$	$2$	567.a	1.a	$1$	$4$	$4$	$4.528$	\(\Q(\sqrt{3}, \sqrt{7})\)	None	✓	✓	✓		567.2.a.i	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{2}-\beta _{2}q^{4}-2\beta _{1}q^{5}-q^{7}+(\beta _{1}+\cdots)q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(567))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(567)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(81))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(189))\)\(^{\oplus 2}\)