Space of modular forms of level 570, weight 2, and Character 570.s

• Label: 570.2.s
• Level: $570$
• Weight: $2$
• Character orbit: 570.s
• Rep. character: $\chi_{570}(221,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $48$
• Newform subspaces: $2$
• Sturm bound: $240$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.s (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(240\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(570, [\chi])\).

	Total	New	Old
Modular forms	256	48	208
Cusp forms	224	48	176
Eisenstein series	32	0	32

Trace form

\( 48 q + 6 q^{3} - 24 q^{4} + 2 q^{6} - 24 q^{7} - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(570, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
570.2.s.a	$570$	$2$	570.s	57.f	$6$	$24$	$12$	$4.551$		None		$2$	$0$	\(-12\)	\(4\)	\(0\)	\(-12\)		$\mathrm{SU}(2)[C_{6}]$
570.2.s.b	$570$	$2$	570.s	57.f	$6$	$24$	$12$	$4.551$		None		$2$	$0$	\(12\)	\(2\)	\(0\)	\(-12\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(570, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(570, [\chi]) \cong \)