Space of modular forms of level 175, weight 3, and Character 175.w

• Label: 175.3.w
• Level: $175$
• Weight: $3$
• Character orbit: 175.w
• Rep. character: $\chi_{175}(2,\cdot)$
• Character field: $\Q(\zeta_{60})$
• Dimension: $608$
• Newform subspaces: $1$
• Sturm bound: $60$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	175.w (of order \(60\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 175 \)
Character field:			\(\Q(\zeta_{60})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(60\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(175, [\chi])\).

	Total	New	Old
Modular forms	672	672	0
Cusp forms	608	608	0
Eisenstein series	64	64	0

Trace form

\( 608 q - 8 q^{2} - 8 q^{3} - 10 q^{4} - 6 q^{5} - 24 q^{6} - 14 q^{7} - 4 q^{8} - 10 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(175, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
175.3.w.a	$175$	$3$	175.w	175.w	$60$	$608$	$38$	$4.768$		None		$4$	$0$	\(-8\)	\(-8\)	\(-6\)	\(-14\)		$\mathrm{SU}(2)[C_{60}]$