Space of modular forms of level 128, weight 3, and Character 128.d

• Label: 128.3.d
• Level: $128$
• Weight: $3$
• Character orbit: 128.d
• Rep. character: $\chi_{128}(63,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $3$
• Sturm bound: $48$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	128.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(48\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(128, [\chi])\).

	Total	New	Old
Modular forms	40	8	32
Cusp forms	24	8	16
Eisenstein series	16	0	16

Trace form

\( 8 q + 24 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(128, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
128.3.d.a	$128$	$3$	128.d	8.d	$2$	$2$	$2$	$3.488$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{U}(1)[D_{2}]$	\(q+iq^{5}-9q^{9}+3iq^{13}+30q^{17}+\cdots\)
128.3.d.b	$128$	$3$	128.d	8.d	$2$	$2$	$2$	$3.488$	\(\Q(\sqrt{2}) \)	\(\Q(\sqrt{-2}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{3}+23q^{9}-3\beta q^{11}-2q^{17}+\cdots\)
128.3.d.c	$128$	$3$	128.d	8.d	$2$	$4$	$4$	$3.488$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}^{2}q^{3}+\zeta_{8}q^{5}+\zeta_{8}^{3}q^{7}-q^{9}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(128, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(128, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)