Space of modular forms of level 90, weight 4, and Character 90.l

• Label: 90.4.l
• Level: $90$
• Weight: $4$
• Character orbit: 90.l
• Rep. character: $\chi_{90}(23,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $72$
• Newform subspaces: $1$
• Sturm bound: $72$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	90.l (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 45 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(72\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(90, [\chi])\).

	Total	New	Old
Modular forms	232	72	160
Cusp forms	200	72	128
Eisenstein series	32	0	32

Trace form

\( 72 q - 8 q^{3} + 16 q^{6} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(90, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
90.4.l.a	$90$	$4$	90.l	45.l	$12$	$72$	$18$	$5.310$		None		$4$	$0$	\(0\)	\(-8\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{4}^{\mathrm{old}}(90, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(90, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)