Space of modular forms of level 1089, weight 3, and Character 1089.b

• Label: 1089.3.b
• Level: $1089$
• Weight: $3$
• Character orbit: 1089.b
• Rep. character: $\chi_{1089}(485,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $10$
• Sturm bound: $396$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1089 = 3^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1089.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(396\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(2\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1089, [\chi])\).

	Total	New	Old
Modular forms	288	72	216
Cusp forms	240	72	168
Eisenstein series	48	0	48

Trace form

\( 72 q - 144 q^{4} - 16 q^{7} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1089, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1089.3.b.a	$1089$	$3$	1089.b	3.b	$2$	$2$	$2$	$29.673$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+2q^{4}-4\beta q^{5}-q^{7}+6\beta q^{8}+\cdots\)
1089.3.b.b	$1089$	$3$	1089.b	3.b	$2$	$2$	$2$	$29.673$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+2q^{4}+4\beta q^{5}+q^{7}+6\beta q^{8}+\cdots\)
1089.3.b.c	$1089$	$3$	1089.b	3.b	$2$	$4$	$4$	$29.673$	\(\Q(\sqrt{-2}, \sqrt{15})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-20\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-4+\beta _{3})q^{4}+(-\beta _{1}+2\beta _{2}+\cdots)q^{5}+\cdots\)
1089.3.b.d	$1089$	$3$	1089.b	3.b	$2$	$4$	$4$	$29.673$	\(\Q(\sqrt{-2}, \sqrt{15})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(20\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-4+\beta _{3})q^{4}+(\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots\)
1089.3.b.e	$1089$	$3$	1089.b	3.b	$2$	$4$	$4$	$29.673$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}-2q^{4}+2\beta _{3}q^{5}-7\beta _{2}q^{7}+\cdots\)
1089.3.b.f	$1089$	$3$	1089.b	3.b	$2$	$8$	$8$	$29.673$	8.0.\(\cdots\).10	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-4-\beta _{2})q^{4}+(-\beta _{6}-\beta _{7})q^{5}+\cdots\)
1089.3.b.g	$1089$	$3$	1089.b	3.b	$2$	$8$	$8$	$29.673$	8.0.\(\cdots\).6	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-16\)	$2^{6}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+(-2-\beta _{3})q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
1089.3.b.h	$1089$	$3$	1089.b	3.b	$2$	$8$	$8$	$29.673$	8.0.3317760000.7	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{7}q^{2}+\beta _{3}q^{4}-\beta _{1}q^{5}+(\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots\)
1089.3.b.i	$1089$	$3$	1089.b	3.b	$2$	$16$	$16$	$29.673$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{2}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+\beta _{13}q^{5}+\cdots\)
1089.3.b.j	$1089$	$3$	1089.b	3.b	$2$	$16$	$16$	$29.673$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{2}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}-\beta _{13}q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(1089, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1089, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(363, [\chi])\)\(^{\oplus 2}\)