Space of modular forms of level 128, weight 2, and Character 128.e

• Label: 128.2.e
• Level: $128$
• Weight: $2$
• Character orbit: 128.e
• Rep. character: $\chi_{128}(33,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $32$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	128.e (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 16 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(32\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(128, [\chi])\).

	Total	New	Old
Modular forms	48	12	36
Cusp forms	16	4	12
Eisenstein series	32	8	24

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(128, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
128.2.e.a	$128$	$2$	128.e	16.e	$4$	$2$	$1$	$1.022$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+i)q^{3}+(1+i)q^{5}+2iq^{7}+\cdots\)
128.2.e.b	$128$	$2$	128.e	16.e	$4$	$2$	$1$	$1.022$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(2\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1-i)q^{3}+(1+i)q^{5}-2iq^{7}+iq^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(128, [\chi])\) into lower level spaces

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