Space of modular forms of level 75, weight 6, and Character 75.l

• Label: 75.6.l
• Level: $75$
• Weight: $6$
• Character orbit: 75.l
• Rep. character: $\chi_{75}(2,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $384$
• Newform subspaces: $1$
• Sturm bound: $60$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	75.l (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 75 \)
Character field:			\(\Q(\zeta_{20})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(60\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(75, [\chi])\).

	Total	New	Old
Modular forms	416	416	0
Cusp forms	384	384	0
Eisenstein series	32	32	0

Trace form

\( 384 q - 10 q^{3} - 20 q^{4} - 6 q^{6} + 60 q^{7} - 10 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(75, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
75.6.l.a	$75$	$6$	75.l	75.l	$20$	$384$	$48$	$12.029$		None		$4$	$0$	\(0\)	\(-10\)	\(0\)	\(60\)		$\mathrm{SU}(2)[C_{20}]$