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

• Label: 572.2.n
• Level: $572$
• Weight: $2$
• Character orbit: 572.n
• Rep. character: $\chi_{572}(53,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $48$
• Newform subspaces: $2$
• Sturm bound: $168$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.n (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 2 \)
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	360	48	312
Cusp forms	312	48	264
Eisenstein series	48	0	48

Trace form

\( 48 q + 2 q^{3} - 6 q^{5} + 14 q^{7} - 10 q^{9} + O(q^{10}) \)

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.n.a	$572$	$2$	572.n	11.c	$5$	$20$	$5$	$4.567$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(0\)	\(1\)	\(1\)	\(3\)	$5$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{5}q^{3}+(-\beta _{9}-\beta _{10})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
572.2.n.b	$572$	$2$	572.n	11.c	$5$	$28$	$7$	$4.567$		None		$2$	$0$	\(0\)	\(1\)	\(-7\)	\(11\)		$\mathrm{SU}(2)[C_{5}]$

Decomposition of \(S_{2}^{\mathrm{old}}(572, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(572, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(143, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(286, [\chi])\)\(^{\oplus 2}\)