Space of modular forms of level 175, weight 2, and Character 175.x

• Label: 175.2.x
• Level: $175$
• Weight: $2$
• Character orbit: 175.x
• Rep. character: $\chi_{175}(3,\cdot)$
• Character field: $\Q(\zeta_{60})$
• Dimension: $288$
• Newform subspaces: $1$
• Sturm bound: $40$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 175 \)
Character field:			\(\Q(\zeta_{60})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(40\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(175, [\chi])\).

	Total	New	Old
Modular forms	352	352	0
Cusp forms	288	288	0
Eisenstein series	64	64	0

Trace form

\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(175, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
175.2.x.a	$175$	$2$	175.x	175.x	$60$	$288$	$18$	$1.397$		None		$4$	$0$	\(-8\)	\(-24\)	\(-30\)	\(-10\)		$\mathrm{SU}(2)[C_{60}]$