Space of modular forms of level 128, weight 1, and Character 128.d

• Label: 128.1.d
• Level: $128$
• Weight: $1$
• Character orbit: 128.d
• Rep. character: $\chi_{128}(63,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $16$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	128.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(16\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(128, [\chi])\).

	Total	New	Old
Modular forms	9	1	8
Cusp forms	1	1	0
Eisenstein series	8	0	8

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	1	0	0	0

Trace form

\( q - q^{9} - 2 q^{17} + q^{25} + 2 q^{41} + q^{49} - 2 q^{73} + q^{81} - 2 q^{89} - 2 q^{97}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(128, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
128.1.d.a	$128$	$1$	128.d	8.d	$2$	$1$	$1$	$0.064$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{2}) \)	✓	✓	✓	✓	128.1.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-q^{9}-2q^{17}+q^{25}+2q^{41}+q^{49}+\cdots\)