Space of modular forms of level 128, weight 5, and Character 128.d

• Label: 128.5.d
• Level: $128$
• Weight: $5$
• Character orbit: 128.d
• Rep. character: $\chi_{128}(63,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $4$
• Sturm bound: $80$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	128.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(80\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(128, [\chi])\).

	Total	New	Old
Modular forms	72	16	56
Cusp forms	56	16	40
Eisenstein series	16	0	16

Trace form

\( 16 q + 432 q^{9} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(128, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
128.5.d.a	$128$	$5$	128.d	8.d	$2$	$2$	$2$	$13.231$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 3$	$\mathrm{U}(1)[D_{2}]$	\(q-iq^{5}-3^{4}q^{9}+5iq^{13}-322q^{17}+\cdots\)
128.5.d.b	$128$	$5$	128.d	8.d	$2$	$2$	$2$	$13.231$	\(\Q(\sqrt{2}) \)	\(\Q(\sqrt{-2}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{3}+47q^{9}+21\beta q^{11}+574q^{17}+\cdots\)
128.5.d.c	$128$	$5$	128.d	8.d	$2$	$4$	$4$	$13.231$	\(\Q(i, \sqrt{6})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}-\beta _{1}q^{5}+\beta _{3}q^{7}+15q^{9}+\cdots\)
128.5.d.d	$128$	$5$	128.d	8.d	$2$	$8$	$8$	$13.231$	8.0.1871773696.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{38}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}-\beta _{2}q^{5}-\beta _{3}q^{7}+(55-\beta _{6}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(128, [\chi])\) into lower level spaces

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