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

• Label: 90.4.c
• Level: $90$
• Weight: $4$
• Character orbit: 90.c
• Rep. character: $\chi_{90}(19,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $3$
• Sturm bound: $72$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	90.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(72\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	62	8	54
Cusp forms	46	8	38
Eisenstein series	16	0	16

Trace form

\( 8 q - 32 q^{4} + 6 q^{5} + O(q^{10}) \)

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.c.a	$90$	$4$	90.c	5.b	$2$	$2$	$2$	$5.310$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}-4q^{4}+(-2+11i)q^{5}+2iq^{7}+\cdots\)
90.4.c.b	$90$	$4$	90.c	5.b	$2$	$2$	$2$	$5.310$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(10\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-4q^{4}+(5-5i)q^{5}-13iq^{7}+\cdots\)
90.4.c.c	$90$	$4$	90.c	5.b	$2$	$4$	$4$	$5.310$	\(\Q(i, \sqrt{31})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-4q^{4}-\beta _{1}q^{5}-\beta _{3}q^{7}+4\beta _{2}q^{8}+\cdots\)

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

\( S_{4}^{\mathrm{old}}(90, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 3}\)