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

• Label: 128.2.g
• Level: $128$
• Weight: $2$
• Character orbit: 128.g
• Rep. character: $\chi_{128}(17,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $32$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	128.g (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 32 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(32\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	80	20	60
Cusp forms	48	12	36
Eisenstein series	32	8	24

Trace form

\( 12 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + O(q^{10}) \)

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.g.a	$128$	$2$	128.g	32.g	$8$	$4$	$1$	$1.022$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(-\zeta_{8}-\zeta_{8}^{2})q^{3}+(-1-\zeta_{8}-2\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
128.2.g.b	$128$	$2$	128.g	32.g	$8$	$8$	$2$	$1.022$	8.0.18939904.2	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(8\)	$2^{3}$	$\mathrm{SU}(2)[C_{8}]$	\(q+(\beta _{2}+\beta _{6}-\beta _{7})q^{3}+(-\beta _{6}-\beta _{7})q^{5}+\cdots\)

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

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