Space of modular forms of level 128, weight 6, and trivial character

• Label: 128.6.a
• Level: $128$
• Weight: $6$
• Character orbit: 128.a
• Rep. character: $\chi_{128}(1,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $12$
• Sturm bound: $96$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	128.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(96\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(128))\).

	Total	New	Old
Modular forms	88	20	68
Cusp forms	72	20	52
Eisenstein series	16	0	16

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	Dim
\(+\)	\(9\)
\(-\)	\(11\)

Trace form

\( 20 q + 1620 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(128))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2
128.6.a.a	$128$	$6$	128.a	1.a	$1$	$1$	$1$	$20.529$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-6\)	\(-94\)	\(-244\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-6q^{3}-94q^{5}-244q^{7}-207q^{9}+\cdots\)
128.6.a.b	$128$	$6$	128.a	1.a	$1$	$1$	$1$	$20.529$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-6\)	\(94\)	\(244\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-6q^{3}+94q^{5}+244q^{7}-207q^{9}+\cdots\)
128.6.a.c	$128$	$6$	128.a	1.a	$1$	$1$	$1$	$20.529$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(6\)	\(-94\)	\(244\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+6q^{3}-94q^{5}+244q^{7}-207q^{9}+\cdots\)
128.6.a.d	$128$	$6$	128.a	1.a	$1$	$1$	$1$	$20.529$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(6\)	\(94\)	\(-244\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+6q^{3}+94q^{5}-244q^{7}-207q^{9}+\cdots\)
128.6.a.e	$128$	$6$	128.a	1.a	$1$	$2$	$2$	$20.529$	\(\Q(\sqrt{19}) \)	None	✓	$1$	$1$	\(0\)	\(-20\)	\(-44\)	\(136\)		$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-10+\beta )q^{3}+(-22+2\beta )q^{5}+(68+\cdots)q^{7}+\cdots\)
128.6.a.f	$128$	$6$	128.a	1.a	$1$	$2$	$2$	$20.529$	\(\Q(\sqrt{19}) \)	None	✓	$1$	$1$	\(0\)	\(-20\)	\(44\)	\(-136\)		$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-10+\beta )q^{3}+(22-2\beta )q^{5}+(-68+\cdots)q^{7}+\cdots\)
128.6.a.g	$128$	$6$	128.a	1.a	$1$	$2$	$2$	$20.529$	\(\Q(\sqrt{6}) \)	None	✓	$1$	$1$	\(0\)	\(-4\)	\(-100\)	\(184\)		$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(-2+\beta )q^{3}+(-50-2\beta )q^{5}+(92+\cdots)q^{7}+\cdots\)
128.6.a.h	$128$	$6$	128.a	1.a	$1$	$2$	$2$	$20.529$	\(\Q(\sqrt{6}) \)	None	✓	$1$	$0$	\(0\)	\(-4\)	\(100\)	\(-184\)		$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(-2+\beta )q^{3}+(50+2\beta )q^{5}+(-92+\cdots)q^{7}+\cdots\)
128.6.a.i	$128$	$6$	128.a	1.a	$1$	$2$	$2$	$20.529$	\(\Q(\sqrt{6}) \)	None	✓	$1$	$0$	\(0\)	\(4\)	\(-100\)	\(-184\)		$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(2+\beta )q^{3}+(-50+2\beta )q^{5}+(-92+\cdots)q^{7}+\cdots\)
128.6.a.j	$128$	$6$	128.a	1.a	$1$	$2$	$2$	$20.529$	\(\Q(\sqrt{6}) \)	None	✓	$1$	$0$	\(0\)	\(4\)	\(100\)	\(184\)		$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(2+\beta )q^{3}+(50-2\beta )q^{5}+(92+2\beta )q^{7}+\cdots\)
128.6.a.k	$128$	$6$	128.a	1.a	$1$	$2$	$2$	$20.529$	\(\Q(\sqrt{19}) \)	None	✓	$1$	$1$	\(0\)	\(20\)	\(-44\)	\(-136\)		$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(10+\beta )q^{3}+(-22-2\beta )q^{5}+(-68+\cdots)q^{7}+\cdots\)
128.6.a.l	$128$	$6$	128.a	1.a	$1$	$2$	$2$	$20.529$	\(\Q(\sqrt{19}) \)	None	✓	$1$	$0$	\(0\)	\(20\)	\(44\)	\(136\)		$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(10+\beta )q^{3}+(22+2\beta )q^{5}+(68+6\beta )q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(128))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(128)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 2}\)