Space of modular forms of level 90, weight 3, and Character 90.k

• Label: 90.3.k
• Level: $90$
• Weight: $3$
• Character orbit: 90.k
• Rep. character: $\chi_{90}(7,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $48$
• Newform subspaces: $2$
• Sturm bound: $54$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	90.k (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 45 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(54\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(90, [\chi])\).

	Total	New	Old
Modular forms	160	48	112
Cusp forms	128	48	80
Eisenstein series	32	0	32

Trace form

\( 48 q + 4 q^{3} + 16 q^{6} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(90, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
90.3.k.a	$90$	$3$	90.k	45.k	$12$	$24$	$6$	$2.452$		None		$4$	$0$	\(-12\)	\(0\)	\(0\)	\(-6\)		$\mathrm{SU}(2)[C_{12}]$
90.3.k.b	$90$	$3$	90.k	45.k	$12$	$24$	$6$	$2.452$		None		$4$	$0$	\(12\)	\(4\)	\(0\)	\(6\)		$\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{3}^{\mathrm{old}}(90, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(90, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)