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

• Label: 574.2.m
• Level: $574$
• Weight: $2$
• Character orbit: 574.m
• Rep. character: $\chi_{574}(27,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $112$
• Newform subspaces: $2$
• Sturm bound: $168$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 574 = 2 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	574.m (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 287 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(168\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	352	112	240
Cusp forms	320	112	208
Eisenstein series	32	0	32

Trace form

\( 112 q - 16 q^{9} + O(q^{10}) \)

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.m.a	$574$	$2$	574.m	287.l	$8$	$56$	$14$	$4.583$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$\mathrm{SU}(2)[C_{8}]$
574.2.m.b	$574$	$2$	574.m	287.l	$8$	$56$	$14$	$4.583$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$\mathrm{SU}(2)[C_{8}]$

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

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