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

• Label: 90.6.c
• Level: $90$
• Weight: $6$
• Character orbit: 90.c
• Rep. character: $\chi_{90}(19,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $4$
• Sturm bound: $108$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	90.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(108\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	98	12	86
Cusp forms	82	12	70
Eisenstein series	16	0	16

Trace form

\( 12 q - 192 q^{4} - 6 q^{5} + O(q^{10}) \)

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.c.a	$90$	$6$	90.c	5.b	$2$	$2$	$2$	$14.435$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-110\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}-2^{4}q^{4}+(-55+5i)q^{5}+\cdots\)
90.6.c.b	$90$	$6$	90.c	5.b	$2$	$2$	$2$	$14.435$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(110\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}-2^{4}q^{4}+(55+5i)q^{5}+2iq^{7}+\cdots\)
90.6.c.c	$90$	$6$	90.c	5.b	$2$	$4$	$4$	$14.435$	\(\Q(i, \sqrt{1249})\)	None		$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$2^{3}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-2^{4}q^{4}+(-1-\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
90.6.c.d	$90$	$6$	90.c	5.b	$2$	$4$	$4$	$14.435$	\(\Q(i, \sqrt{19})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta _{2}q^{2}-2^{4}q^{4}+(5\beta _{1}-15\beta _{2})q^{5}+\cdots\)

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

\( S_{6}^{\mathrm{old}}(90, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 3}\)