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

• Label: 90.11.d
• Level: $90$
• Weight: $11$
• Character orbit: 90.d
• Rep. character: $\chi_{90}(71,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $198$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	90.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(198\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	188	16	172
Cusp forms	172	16	156
Eisenstein series	16	0	16

Trace form

16 * q - 8192 * q^4 - 45760 * q^7 - 283360 * q^13 + 4194304 * q^16 - 4740736 * q^19 - 31250000 * q^25 + 23429120 * q^28 + 62933024 * q^31 + 148420608 * q^34 - 350417440 * q^37 - 113072320 * q^43 - 67731456 * q^46 + 1061323152 * q^49 + 145080320 * q^52 - 997500000 * q^55 - 1169940480 * q^58 + 2814812000 * q^61 - 2147483648 * q^64 - 530453440 * q^67 - 1773684640 * q^73 + 2427256832 * q^76 + 4938953504 * q^79 + 3715461120 * q^82 - 25400360672 * q^91 - 3907921920 * q^94 - 7741797280 * q^97

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.d.a	$90$	$11$	90.d	3.b	$2$	$8$	$8$	$57.182$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		✓			90.11.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-51392\)	$2^{14}\cdot 3^{8}\cdot 5^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q-2^{4}\beta _{1}q^{2}-2^{9}q^{4}-\beta _{5}q^{5}+(-6424+\cdots)q^{7}+\cdots\)
90.11.d.b	$90$	$11$	90.d	3.b	$2$	$8$	$8$	$57.182$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		✓			90.11.d.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(5632\)	$2^{14}\cdot 3^{8}\cdot 5^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q-2^{4}\beta _{2}q^{2}-2^{9}q^{4}-\beta _{6}q^{5}+(704+\cdots)q^{7}+\cdots\)

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

\( S_{11}^{\mathrm{old}}(90, [\chi]) \simeq \) \(S_{11}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)