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

• Label: 1088.2.l
• Level: $1088$
• Weight: $2$
• Character orbit: 1088.l
• Rep. character: $\chi_{1088}(273,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $64$
• Newform subspaces: $3$
• Sturm bound: $288$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1088 = 2^{6} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1088.l (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 16 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(288\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	304	64	240
Cusp forms	272	64	208
Eisenstein series	32	0	32

Trace form

\( 64 q + O(q^{10}) \)

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.l.a	$1088$	$2$	1088.l	16.e	$4$	$2$	$1$	$8.688$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+i)q^{3}+(1+i)q^{5}-2iq^{7}+\cdots\)
1088.2.l.b	$1088$	$2$	1088.l	16.e	$4$	$30$	$15$	$8.688$		None		$2$	$0$	\(0\)	\(2\)	\(-2\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
1088.2.l.c	$1088$	$2$	1088.l	16.e	$4$	$32$	$16$	$8.688$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(1088, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)