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

• Label: 1088.2.h
• Level: $1088$
• Weight: $2$
• Character orbit: 1088.h
• Rep. character: $\chi_{1088}(33,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• 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.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 136 \)
Character field:			\(\Q\)
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	156	36	120
Cusp forms	132	36	96
Eisenstein series	24	0	24

Trace form

\( 36 q + 36 q^{9} + O(q^{10}) \)

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.h.a	$1088$	$2$	1088.h	136.h	$2$	$4$	$4$	$8.688$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-2}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q-\zeta_{8}^{3}q^{3}+5q^{9}-\zeta_{8}^{3}q^{11}+(3+\zeta_{8}^{2}+\cdots)q^{17}+\cdots\)
1088.2.h.b	$1088$	$2$	1088.h	136.h	$2$	$8$	$8$	$8.688$	8.0.342102016.5	\(\Q(\sqrt{-34}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{13}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{2}q^{5}-\beta _{4}q^{7}-3q^{9}+\beta _{1}q^{17}+\cdots\)
1088.2.h.c	$1088$	$2$	1088.h	136.h	$2$	$24$	$24$	$8.688$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

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