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

• Label: 1088.2.b
• Level: $1088$
• Weight: $2$
• Character orbit: 1088.b
• Rep. character: $\chi_{1088}(577,\cdot)$
• Character field: $\Q$
• Dimension: $34$
• Newform subspaces: $13$
• Sturm bound: $288$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 1088 = 2^{6} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1088.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q\)
Newform subspaces:			\( 13 \)
Sturm bound:			\(288\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(3\), \(5\), \(19\), \(43\)

Dimensions

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

	Total	New	Old
Modular forms	156	38	118
Cusp forms	132	34	98
Eisenstein series	24	4	20

Trace form

\( 34 q - 34 q^{9} + 4 q^{13} + 2 q^{17} - 8 q^{21} - 22 q^{25} - 8 q^{33} - 26 q^{49} + 4 q^{53} + 24 q^{69} - 72 q^{77} + 42 q^{81} + 4 q^{89} - 8 q^{93}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1088.2.b.a	$1088$	$2$	1088.b	17.b	$2$	$2$	$2$	$8.688$	\(\Q(\sqrt{-2}) \)	None					34.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}+\beta q^{5}-5q^{9}-\beta q^{11}-2q^{13}+\cdots\)
1088.2.b.b	$1088$	$2$	1088.b	17.b	$2$	$2$	$2$	$8.688$	\(\Q(\sqrt{-2}) \)	None					34.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}-\beta q^{5}-5q^{9}-\beta q^{11}-2q^{13}+\cdots\)
1088.2.b.c	$1088$	$2$	1088.b	17.b	$2$	$2$	$2$	$8.688$	\(\Q(\sqrt{-1}) \)	None					136.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}-\beta q^{7}-q^{9}+\beta q^{11}+2 q^{13}+\cdots\)
1088.2.b.d	$1088$	$2$	1088.b	17.b	$2$	$2$	$2$	$8.688$	\(\Q(\sqrt{-1}) \)	None					136.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}-\beta q^{7}-q^{9}+\beta q^{11}+2 q^{13}+\cdots\)
1088.2.b.e	$1088$	$2$	1088.b	17.b	$2$	$2$	$2$	$8.688$	\(\Q(\sqrt{-2}) \)	None					68.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}+2\beta q^{5}+3\beta q^{7}+q^{9}-\beta q^{11}+\cdots\)
1088.2.b.f	$1088$	$2$	1088.b	17.b	$2$	$2$	$2$	$8.688$	\(\Q(\sqrt{-2}) \)	None					68.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}-2\beta q^{5}+3\beta q^{7}+q^{9}-\beta q^{11}+\cdots\)
1088.2.b.g	$1088$	$2$	1088.b	17.b	$2$	$2$	$2$	$8.688$	\(\Q(\sqrt{-2}) \)	None					136.2.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}+\beta q^{7}+3q^{9}+2\beta q^{11}-2q^{13}+\cdots\)
1088.2.b.h	$1088$	$2$	1088.b	17.b	$2$	$2$	$2$	$8.688$	\(\Q(\sqrt{-2}) \)	None					136.2.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{5}+\beta q^{7}+3q^{9}+2\beta q^{11}-2q^{13}+\cdots\)
1088.2.b.i	$1088$	$2$	1088.b	17.b	$2$	$2$	$2$	$8.688$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)					544.2.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta q^{5}+3 q^{9}+6 q^{13}+(\beta+1)q^{17}+\cdots\)
1088.2.b.j	$1088$	$2$	1088.b	17.b	$2$	$4$	$4$	$8.688$	\(\Q(\sqrt{-14 +2 \sqrt{17}})\)	\(\Q(\sqrt{-17}) \)					544.2.b.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{7}+(-4-\beta _{3})q^{9}+\cdots\)
1088.2.b.k	$1088$	$2$	1088.b	17.b	$2$	$4$	$4$	$8.688$	\(\Q(\sqrt{-14 +2 \sqrt{17}})\)	\(\Q(\sqrt{-17}) \)					544.2.b.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{3}+\beta _{1}q^{7}+(-2+\beta _{2})q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
1088.2.b.l	$1088$	$2$	1088.b	17.b	$2$	$4$	$4$	$8.688$	\(\Q(\sqrt{-2 + \sqrt{2}})\)	None					544.2.b.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{5}+\beta _{1}q^{7}+(-1+\cdots)q^{9}+\cdots\)
1088.2.b.m	$1088$	$2$	1088.b	17.b	$2$	$4$	$4$	$8.688$	\(\Q(\sqrt{-2 + \sqrt{2}})\)	None					544.2.b.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(-\beta _{1}-\beta _{2})q^{5}+\beta _{1}q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1088, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(136, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(272, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(544, [\chi])\)\(^{\oplus 2}\)