Space of modular forms of level 1136, weight 1, and Character 1136.h

• Label: 1136.1.h
• Level: $1136$
• Weight: $1$
• Character orbit: 1136.h
• Rep. character: $\chi_{1136}(993,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $1$
• Sturm bound: $144$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1136 = 2^{4} \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1136.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 71 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(144\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1136, [\chi])\).

	Total	New	Old
Modular forms	24	4	20
Cusp forms	18	3	15
Eisenstein series	6	1	5

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	3	0	0	0

Trace form

\( 3 q + q^{3} - q^{5} + 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1136, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1136.1.h.a	$1136$	$1$	1136.h	71.b	$2$	$3$	$3$	$0.567$	\(\Q(\zeta_{14})^+\)	$D_{7}$	\(\Q(\sqrt{-71}) \)	None	✓	$2$	$0$	\(0\)	\(1\)	\(-1\)	\(0\)	$1$		\(q+\beta _{1}q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+(1+\beta _{2})q^{9}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1136, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1136, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(71, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(142, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(284, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(568, [\chi])\)\(^{\oplus 2}\)