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

• Label: 570.2.c
• Level: $570$
• Weight: $2$
• Character orbit: 570.c
• Rep. character: $\chi_{570}(569,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $6$
• Sturm bound: $240$
• Trace bound: $15$

Defining parameters

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 285 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(240\)
Trace bound:			\(15\)
Distinguishing \(T_p\):			\(7\), \(11\), \(29\), \(37\)

Dimensions

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

	Total	New	Old
Modular forms	128	40	88
Cusp forms	112	40	72
Eisenstein series	16	0	16

Trace form

\( 40 q - 40 q^{4} + O(q^{10}) \)

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.c.a	$570$	$2$	570.c	285.b	$2$	$4$	$4$	$4.551$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}^{2}q^{2}+(\zeta_{8}+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-q^{4}+\cdots\)
570.2.c.b	$570$	$2$	570.c	285.b	$2$	$4$	$4$	$4.551$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}^{2}q^{2}+(\zeta_{8}+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-q^{4}+\cdots\)
570.2.c.c	$570$	$2$	570.c	285.b	$2$	$8$	$8$	$4.551$	8.0.1499238400.2	None		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{2}+(-1-\beta _{3}+\beta _{4}+\beta _{6}+\beta _{7})q^{3}+\cdots\)
570.2.c.d	$570$	$2$	570.c	285.b	$2$	$8$	$8$	$4.551$	\(\Q(\zeta_{24})\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{24}q^{2}-\zeta_{24}^{4}q^{3}-q^{4}+(-\zeta_{24}^{2}+\cdots)q^{5}+\cdots\)
570.2.c.e	$570$	$2$	570.c	285.b	$2$	$8$	$8$	$4.551$	\(\Q(\zeta_{24})\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{24}q^{2}+(-\zeta_{24}-\zeta_{24}^{6})q^{3}-q^{4}+\cdots\)
570.2.c.f	$570$	$2$	570.c	285.b	$2$	$8$	$8$	$4.551$	8.0.1499238400.2	None		$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{2}+(-\beta _{3}+\beta _{4}+\beta _{6}+\beta _{7})q^{3}+\cdots\)

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

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