Space of modular forms of level 1088, weight 1, and Character 1088.n

• Label: 1088.1.n
• Level: $1088$
• Weight: $1$
• Character orbit: 1088.n
• Rep. character: $\chi_{1088}(735,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $144$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1088 = 2^{6} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1088.n (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 136 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(144\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1088, [\chi])\).

	Total	New	Old
Modular forms	40	4	36
Cusp forms	16	4	12
Eisenstein series	24	0	24

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

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

Decomposition of \(S_{1}^{\mathrm{new}}(1088, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1088.1.n.a	$1088$	$1$	1088.n	136.j	$4$	$2$	$1$	$0.543$	\(\Q(\sqrt{-1}) \)	$D_{4}$	None	\(\Q(\sqrt{2}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$		\(q+(-1+i)q^{7}+iq^{9}+iq^{17}+(-1+\cdots)q^{23}+\cdots\)
1088.1.n.b	$1088$	$1$	1088.n	136.j	$4$	$2$	$1$	$0.543$	\(\Q(\sqrt{-1}) \)	$D_{4}$	None	\(\Q(\sqrt{2}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$		\(q+(1-i)q^{7}+iq^{9}+iq^{17}+(1-i+\cdots)q^{23}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1088, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1088, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(136, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(272, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(544, [\chi])\)\(^{\oplus 2}\)