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

• Label: 175.3.u
• Level: $175$
• Weight: $3$
• Character orbit: 175.u
• Rep. character: $\chi_{175}(19,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $304$
• 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.u (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 175 \)
Character field:			\(\Q(\zeta_{30})\)
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	336	336	0
Cusp forms	304	304	0
Eisenstein series	32	32	0

Trace form

\( 304 q - 5 q^{2} - 15 q^{3} - 75 q^{4} - 15 q^{5} + 10 q^{8} + 99 q^{9} + O(q^{10}) \)

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.u.a	$175$	$3$	175.u	175.u	$30$	$304$	$38$	$4.768$		None		$4$	$0$	\(-5\)	\(-15\)	\(-15\)	\(0\)		$\mathrm{SU}(2)[C_{30}]$