Space of modular forms of level 128, weight 4, and Character 128.b

• Label: 128.4.b
• Level: $128$
• Weight: $4$
• Character orbit: 128.b
• Rep. character: $\chi_{128}(65,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $5$
• Sturm bound: $64$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	128.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(64\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(128, [\chi])\).

	Total	New	Old
Modular forms	56	12	44
Cusp forms	40	12	28
Eisenstein series	16	0	16

Trace form

\( 12 q - 108 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(128, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
128.4.b.a	$128$	$4$	128.b	8.b	$2$	$2$	$2$	$7.552$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(-64\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{3}-3iq^{5}-2^{5}q^{7}-37q^{9}+\cdots\)
128.4.b.b	$128$	$4$	128.b	8.b	$2$	$2$	$2$	$7.552$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-2}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{3}+19q^{9}+5^{2}\beta q^{11}-90q^{17}+\cdots\)
128.4.b.c	$128$	$4$	128.b	8.b	$2$	$2$	$2$	$7.552$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+iq^{5}+3^{3}q^{9}+23iq^{13}+94q^{17}+\cdots\)
128.4.b.d	$128$	$4$	128.b	8.b	$2$	$2$	$2$	$7.552$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(64\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{3}+3iq^{5}+2^{5}q^{7}-37q^{9}+\cdots\)
128.4.b.e	$128$	$4$	128.b	8.b	$2$	$4$	$4$	$7.552$	\(\Q(\sqrt{2}, \sqrt{-5})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+\beta _{3}q^{5}+\beta _{2}q^{7}-13q^{9}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(128, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(128, [\chi]) \cong \)