Space of modular forms of level 572, weight 2, and Character 572.b

• Label: 572.2.b
• Level: $572$
• Weight: $2$
• Character orbit: 572.b
• Rep. character: $\chi_{572}(571,\cdot)$
• Character field: $\Q$
• Dimension: $80$
• Newform subspaces: $3$
• Sturm bound: $168$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 572 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(168\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(572, [\chi])\).

	Total	New	Old
Modular forms	88	88	0
Cusp forms	80	80	0
Eisenstein series	8	8	0

Trace form

\( 80 q - 4 q^{4} - 80 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(572, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
572.2.b.a	$572$	$2$	572.b	572.b	$2$	$4$	$4$	$4.567$	\(\Q(\sqrt{-2}, \sqrt{-13})\)	\(\Q(\sqrt{-13}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{2}q^{2}-2q^{4}+\beta _{2}q^{7}+2\beta _{2}q^{8}+\cdots\)
572.2.b.b	$572$	$2$	572.b	572.b	$2$	$20$	$20$	$4.567$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	\(\Q(\sqrt{-143}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{14}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{14}q^{2}-\beta _{9}q^{3}+\beta _{12}q^{4}+(-\beta _{3}+\cdots)q^{6}+\cdots\)
572.2.b.c	$572$	$2$	572.b	572.b	$2$	$56$	$56$	$4.567$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$