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

• Label: 128.5.f
• Level: $128$
• Weight: $5$
• Character orbit: 128.f
• Rep. character: $\chi_{128}(31,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $28$
• Newform subspaces: $2$
• Sturm bound: $80$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	128.f (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 16 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(80\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	144	36	108
Cusp forms	112	28	84
Eisenstein series	32	8	24

Trace form

\( 28 q + 4 q^{5} + O(q^{10}) \)

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.f.a	$128$	$5$	128.f	16.f	$4$	$14$	$7$	$13.231$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(0\)	\(-2\)	\(2\)	\(4\)	$2^{42}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{5}q^{3}+\beta _{8}q^{5}+\beta _{9}q^{7}+(-19\beta _{1}+\cdots)q^{9}+\cdots\)
128.5.f.b	$128$	$5$	128.f	16.f	$4$	$14$	$7$	$13.231$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(0\)	\(2\)	\(2\)	\(-4\)	$2^{42}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{2}q^{3}-\beta _{3}q^{5}-\beta _{9}q^{7}+(19\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)

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

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