Space of modular forms of level 90, weight 11, and Character 90.b

• Label: 90.11.b
• Level: $90$
• Weight: $11$
• Character orbit: 90.b
• Rep. character: $\chi_{90}(89,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $1$
• Sturm bound: $198$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	90.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(198\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(90, [\chi])\).

	Total	New	Old
Modular forms	188	20	168
Cusp forms	172	20	152
Eisenstein series	16	0	16

Trace form

20 * q + 10240 * q^4 + 82240 * q^10 + 5242880 * q^16 - 6418080 * q^19 - 27678000 * q^25 + 103749680 * q^31 - 23308160 * q^34 + 42106880 * q^40 - 659422720 * q^46 - 41560140 * q^49 + 3032188480 * q^55 - 3937749800 * q^61 + 2684354560 * q^64 + 6173666560 * q^70 - 3286056960 * q^76 - 4433579280 * q^79 - 14179382060 * q^85 + 74924957760 * q^91 - 23966195200 * q^94

Decomposition of \(S_{11}^{\mathrm{new}}(90, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
90.11.b.a	$90$	$11$	90.b	15.d	$2$	$20$	$20$	$57.182$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓	✓	✓	90.11.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{64}\cdot 3^{52}\cdot 5^{20}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+2^{9}q^{4}+(8\beta _{1}+\beta _{4})q^{5}+\beta _{5}q^{7}+\cdots\)

Decomposition of \(S_{11}^{\mathrm{old}}(90, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(90, [\chi]) \simeq \) \(S_{11}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)