Space of modular forms of level 75, weight 9, and Character 75.h

• Label: 75.9.h
• Level: $75$
• Weight: $9$
• Character orbit: 75.h
• Rep. character: $\chi_{75}(14,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $312$
• Newform subspaces: $1$
• Sturm bound: $90$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	75.h (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 75 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(90\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(75, [\chi])\).

	Total	New	Old
Modular forms	328	328	0
Cusp forms	312	312	0
Eisenstein series	16	16	0

Trace form

\( 312 q - 5 q^{3} - 9734 q^{4} + 509 q^{6} + 7907 q^{9} + O(q^{10}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(75, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
75.9.h.a	$75$	$9$	75.h	75.h	$10$	$312$	$78$	$30.553$		None		$4$	$0$	\(0\)	\(-5\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$