Space of modular forms of level 90, weight 6, and Character 90.i

• Label: 90.6.i
• Level: $90$
• Weight: $6$
• Character orbit: 90.i
• Rep. character: $\chi_{90}(49,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $60$
• Newform subspaces: $1$
• Sturm bound: $108$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	90.i (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 45 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(108\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(90, [\chi])\).

	Total	New	Old
Modular forms	188	60	128
Cusp forms	172	60	112
Eisenstein series	16	0	16

Trace form

\( 60 q + 480 q^{4} + 58 q^{5} - 80 q^{6} - 754 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(90, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
90.6.i.a	$90$	$6$	90.i	45.j	$6$	$60$	$30$	$14.435$		None		$4$	$0$	\(0\)	\(0\)	\(58\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{6}^{\mathrm{old}}(90, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(90, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)