Space of modular forms of level 1088, weight 2, and Character 1088.c

• Label: 1088.2.c
• Level: $1088$
• Weight: $2$
• Character orbit: 1088.c
• Rep. character: $\chi_{1088}(545,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $5$
• Sturm bound: $288$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 1088 = 2^{6} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1088.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(288\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1088, [\chi])\).

	Total	New	Old
Modular forms	156	32	124
Cusp forms	132	32	100
Eisenstein series	24	0	24

Trace form

\( 32 q - 32 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1088, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1088.2.c.a	$1088$	$2$	1088.c	8.b	$2$	$2$	$2$	$8.688$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{5}-4q^{7}+3q^{9}+2iq^{11}+2iq^{13}+\cdots\)
1088.2.c.b	$1088$	$2$	1088.c	8.b	$2$	$2$	$2$	$8.688$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{5}+4q^{7}+3q^{9}+2iq^{11}-2iq^{13}+\cdots\)
1088.2.c.c	$1088$	$2$	1088.c	8.b	$2$	$4$	$4$	$8.688$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}q^{3}-\zeta_{8}^{2}q^{5}-\zeta_{8}^{3}q^{7}-q^{9}+\cdots\)
1088.2.c.d	$1088$	$2$	1088.c	8.b	$2$	$12$	$12$	$8.688$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{8}q^{3}-\beta _{6}q^{5}+\beta _{3}q^{7}+(-2-\beta _{5}+\cdots)q^{9}+\cdots\)
1088.2.c.e	$1088$	$2$	1088.c	8.b	$2$	$12$	$12$	$8.688$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{15}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{3}+\beta _{5}q^{5}+\beta _{3}q^{7}+(-1+\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1088, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1088, [\chi]) \cong \)