Space of modular forms of level 573, weight 2, and trivial character

• Label: 573.2.a
• Level: $573$
• Weight: $2$
• Character orbit: 573.a
• Rep. character: $\chi_{573}(1,\cdot)$
• Character field: $\Q$
• Dimension: $31$
• Newform subspaces: $7$
• Sturm bound: $128$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 573 = 3 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	573.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(128\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(573))\).

	Total	New	Old
Modular forms	66	31	35
Cusp forms	63	31	32
Eisenstein series	3	0	3

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

\(3\)	\(191\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(6\)
\(+\)	\(-\)	$-$	\(10\)
\(-\)	\(+\)	$-$	\(9\)
\(-\)	\(-\)	$+$	\(6\)
Plus space		\(+\)	\(12\)
Minus space		\(-\)	\(19\)

Trace form

\( 31 q + q^{2} - q^{3} + 29 q^{4} - 2 q^{5} - 3 q^{6} + 9 q^{8} + 31 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(573))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	191
573.2.a.a	$573$	$2$	573.a	1.a	$1$	$1$	$1$	$4.575$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(1\)	\(-2\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+q^{3}+2q^{4}-2q^{5}-2q^{6}+\cdots\)
573.2.a.b	$573$	$2$	573.a	1.a	$1$	$1$	$1$	$4.575$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(1\)	\(2\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}+2q^{5}-q^{6}+2q^{7}+\cdots\)
573.2.a.c	$573$	$2$	573.a	1.a	$1$	$1$	$1$	$4.575$	\(\Q\)	None	✓	$1$	$0$	\(2\)	\(1\)	\(2\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+q^{3}+2q^{4}+2q^{5}+2q^{6}+\cdots\)
573.2.a.d	$573$	$2$	573.a	1.a	$1$	$5$	$5$	$4.575$	5.5.24217.1	None	✓	$1$	$1$	\(-3\)	\(5\)	\(-5\)	\(-5\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{2})q^{2}+q^{3}+(1+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
573.2.a.e	$573$	$2$	573.a	1.a	$1$	$6$	$6$	$4.575$	6.6.4125937.1	None	✓	$1$	$1$	\(-1\)	\(-6\)	\(1\)	\(-9\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{3}+\beta _{5})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
573.2.a.f	$573$	$2$	573.a	1.a	$1$	$7$	$7$	$4.575$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(3\)	\(7\)	\(-1\)	\(1\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}-\beta _{5}q^{5}+\cdots\)
573.2.a.g	$573$	$2$	573.a	1.a	$1$	$10$	$10$	$4.575$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$0$	\(3\)	\(-10\)	\(1\)	\(11\)		$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(2-\beta _{3})q^{4}+\beta _{9}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(573))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(573)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(191))\)\(^{\oplus 2}\)