Space of modular forms of level 574, weight 2, and Character 574.e

• Label: 574.2.e
• Level: $574$
• Weight: $2$
• Character orbit: 574.e
• Rep. character: $\chi_{574}(165,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $56$
• Newform subspaces: $8$
• Sturm bound: $168$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 574 = 2 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	574.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(168\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(574, [\chi])\).

	Total	New	Old
Modular forms	176	56	120
Cusp forms	160	56	104
Eisenstein series	16	0	16

Trace form

\( 56 q - 28 q^{4} - 4 q^{5} - 8 q^{6} - 24 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(574, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
574.2.e.a	$574$	$2$	574.e	7.c	$3$	$2$	$1$	$4.583$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(-2\)	\(2\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
574.2.e.b	$574$	$2$	574.e	7.c	$3$	$2$	$1$	$4.583$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(1\)	\(1\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
574.2.e.c	$574$	$2$	574.e	7.c	$3$	$2$	$1$	$4.583$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(3\)	\(1\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
574.2.e.d	$574$	$2$	574.e	7.c	$3$	$4$	$2$	$4.583$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(2\)	\(-1\)	\(1\)	\(-10\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{1})q^{2}-\beta _{3}q^{3}-\beta _{1}q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)
574.2.e.e	$574$	$2$	574.e	7.c	$3$	$6$	$3$	$4.583$	6.0.309123.1	None		$2$	$0$	\(-3\)	\(3\)	\(-4\)	\(-4\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{4})q^{2}+\beta _{4}q^{3}-\beta _{4}q^{4}+(-1+\cdots)q^{5}+\cdots\)
574.2.e.f	$574$	$2$	574.e	7.c	$3$	$8$	$4$	$4.583$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(4\)	\(-4\)	\(-3\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{2}q^{2}+(-1+\beta _{2})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
574.2.e.g	$574$	$2$	574.e	7.c	$3$	$12$	$6$	$4.583$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(6\)	\(-1\)	\(0\)	\(-1\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{8}q^{2}+\beta _{2}q^{3}+(-1-\beta _{8})q^{4}+\beta _{10}q^{5}+\cdots\)
574.2.e.h	$574$	$2$	574.e	7.c	$3$	$20$	$10$	$4.583$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(-10\)	\(1\)	\(-2\)	\(1\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{10}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(-1-\beta _{10}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(574, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(574, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(287, [\chi])\)\(^{\oplus 2}\)