Space of modular forms of level 3136, weight 1, and Character 3136.h

• Label: 3136.1.h
• Level: $3136$
• Weight: $1$
• Character orbit: 3136.h
• Rep. character: $\chi_{3136}(97,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $448$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 3136 = 2^{6} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3136.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 56 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(448\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3136, [\chi])\).

	Total	New	Old
Modular forms	68	8	60
Cusp forms	20	8	12
Eisenstein series	48	0	48

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	8	0	0	0

Trace form

\( 8 q + 8 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3136, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3136.1.h.a	$3136$	$1$	3136.h	56.h	$2$	$8$	$8$	$1.565$	\(\Q(\zeta_{16})\)	$D_{8}$	\(\Q(\sqrt{-2}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$		\(q+(\zeta_{16}^{3}-\zeta_{16}^{5})q^{3}+(1-\zeta_{16}^{2}+\zeta_{16}^{6}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3136, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3136, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 6}\)