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

• Label: 128.5.c
• Level: $128$
• Weight: $5$
• Character orbit: 128.c
• Rep. character: $\chi_{128}(127,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $80$
• Trace bound: $5$

Defining parameters

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

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.c.a	$128$	$5$	128.c	4.b	$2$	$8$	$8$	$13.231$	8.0.205520896.4	None		$2$	$0$	\(0\)	\(0\)	\(-48\)	\(0\)	$2^{39}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-6-\beta _{2})q^{5}+(-\beta _{1}-\beta _{4}+\cdots)q^{7}+\cdots\)
128.5.c.b	$128$	$5$	128.c	4.b	$2$	$8$	$8$	$13.231$	8.0.205520896.4	None		$2$	$0$	\(0\)	\(0\)	\(48\)	\(0\)	$2^{39}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(6+\beta _{2})q^{5}+(\beta _{1}+\beta _{4})q^{7}+\cdots\)

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

\( S_{5}^{\mathrm{old}}(128, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)