Space of modular forms of level 1089, weight 2, and Character 1089.d

• Label: 1089.2.d
• Level: $1089$
• Weight: $2$
• Character orbit: 1089.d
• Rep. character: $\chi_{1089}(1088,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $7$
• Sturm bound: $264$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 1089 = 3^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1089.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(264\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(2\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1089, [\chi])\).

	Total	New	Old
Modular forms	156	36	120
Cusp forms	108	36	72
Eisenstein series	48	0	48

Trace form

\( 36 q + 36 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1089, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1089.2.d.a	$1089$	$2$	1089.d	33.d	$2$	$2$	$2$	$8.696$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}-q^{4}-\beta q^{5}-2\beta q^{7}+3q^{8}+\cdots\)
1089.2.d.b	$1089$	$2$	1089.d	33.d	$2$	$2$	$2$	$8.696$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}-q^{4}+\beta q^{5}-2\beta q^{7}-3q^{8}+\cdots\)
1089.2.d.c	$1089$	$2$	1089.d	33.d	$2$	$4$	$4$	$8.696$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		$2$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{2})q^{2}+(2+2\beta _{2})q^{4}-2\beta _{1}q^{5}+\cdots\)
1089.2.d.d	$1089$	$2$	1089.d	33.d	$2$	$4$	$4$	$8.696$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+q^{4}+(-2\beta _{1}+\beta _{3})q^{5}+2\beta _{3}q^{7}+\cdots\)
1089.2.d.e	$1089$	$2$	1089.d	33.d	$2$	$4$	$4$	$8.696$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+q^{4}+(2\beta _{1}-\beta _{3})q^{5}+2\beta _{3}q^{7}+\cdots\)
1089.2.d.f	$1089$	$2$	1089.d	33.d	$2$	$4$	$4$	$8.696$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		$2$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{2})q^{2}+(2+2\beta _{2})q^{4}-2\beta _{1}q^{5}+\cdots\)
1089.2.d.g	$1089$	$2$	1089.d	33.d	$2$	$16$	$16$	$8.696$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{15}q^{2}+(1+\beta _{4})q^{4}+(-\beta _{2}+\beta _{5}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1089, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1089, [\chi]) \cong \)