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

• Label: 175.2.t
• Level: $175$
• Weight: $2$
• Character orbit: 175.t
• Rep. character: $\chi_{175}(4,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $144$
• 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.t (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 175 \)
Character field:			\(\Q(\zeta_{30})\)
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	176	176	0
Cusp forms	144	144	0
Eisenstein series	32	32	0

Trace form

\( 144 q - 5 q^{2} - 5 q^{3} - 19 q^{4} - 3 q^{5} - 12 q^{6} - 50 q^{8} - 17 q^{9} + O(q^{10}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
175.2.t.a	$175$	$2$	175.t	175.t	$30$	$144$	$18$	$1.397$		None		✓	✓	✓	175.2.t.a	$4$	$0$	\(-5\)	\(-5\)	\(-3\)	\(0\)		$\mathrm{SU}(2)[C_{30}]$