Space of modular forms of level 128, weight 12, and trivial character

• Label: 128.12.a
• Level: $128$
• Weight: $12$
• Character orbit: 128.a
• Rep. character: $\chi_{128}(1,\cdot)$
• Character field: $\Q$
• Dimension: $44$
• Newform subspaces: $8$
• Sturm bound: $192$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	128.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(192\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(128))\).

	Total	New	Old
Modular forms	184	44	140
Cusp forms	168	44	124
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
\(+\)	\(23\)
\(-\)	\(21\)

Trace form

44 * q + 2598156 * q^9 - 10558936 * q^17 + 498051892 * q^25 - 220346032 * q^33 - 75332936 * q^41 + 12483953868 * q^49 + 3136866608 * q^57 + 4481721008 * q^65 - 30994859864 * q^73 + 108991885788 * q^81 - 328754480024 * q^89 + 580166463656 * q^97

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(128))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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
128.12.a.a	$128$	$12$	128.a	1.a	$1$	$5$	$5$	$98.348$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	✓			128.12.a.a	$1$	$1$	\(0\)	\(-506\)	\(-4446\)	\(17860\)		$-$	$-$	$2^{29}\cdot 3$	$\mathrm{SU}(2)$	\(q+(-101+\beta _{1})q^{3}+(-888+5\beta _{1}+\cdots)q^{5}+\cdots\)
128.12.a.b	$128$	$12$	128.a	1.a	$1$	$5$	$5$	$98.348$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	✓			128.12.a.a	$1$	$1$	\(0\)	\(-506\)	\(4446\)	\(-17860\)		$-$	$-$	$2^{29}\cdot 3$	$\mathrm{SU}(2)$	\(q+(-101+\beta _{1})q^{3}+(888-5\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
128.12.a.c	$128$	$12$	128.a	1.a	$1$	$5$	$5$	$98.348$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	✓			128.12.a.a	$1$	$1$	\(0\)	\(506\)	\(-4446\)	\(-17860\)		$-$	$-$	$2^{29}\cdot 3$	$\mathrm{SU}(2)$	\(q+(101-\beta _{1})q^{3}+(-888+5\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
128.12.a.d	$128$	$12$	128.a	1.a	$1$	$5$	$5$	$98.348$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	✓			128.12.a.a	$1$	$0$	\(0\)	\(506\)	\(4446\)	\(17860\)		$+$	$+$	$2^{29}\cdot 3$	$\mathrm{SU}(2)$	\(q+(101-\beta _{1})q^{3}+(888-5\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
128.12.a.e	$128$	$12$	128.a	1.a	$1$	$6$	$6$	$98.348$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	✓			128.12.a.e	$1$	$0$	\(0\)	\(-20\)	\(-1804\)	\(49368\)		$+$	$+$	$2^{43}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+(-3-\beta _{1})q^{3}+(-299-4\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
128.12.a.f	$128$	$12$	128.a	1.a	$1$	$6$	$6$	$98.348$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	✓			128.12.a.e	$1$	$0$	\(0\)	\(-20\)	\(1804\)	\(-49368\)		$+$	$+$	$2^{43}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+(-3-\beta _{1})q^{3}+(299+4\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
128.12.a.g	$128$	$12$	128.a	1.a	$1$	$6$	$6$	$98.348$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	✓	✓		128.12.a.e	$1$	$1$	\(0\)	\(20\)	\(-1804\)	\(-49368\)		$-$	$-$	$2^{43}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+(3+\beta _{1})q^{3}+(-299-4\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
128.12.a.h	$128$	$12$	128.a	1.a	$1$	$6$	$6$	$98.348$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	✓			128.12.a.e	$1$	$0$	\(0\)	\(20\)	\(1804\)	\(49368\)		$+$	$+$	$2^{43}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+(3+\beta _{1})q^{3}+(299+4\beta _{1}-\beta _{2})q^{5}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(128))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_0(128)) \simeq \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 5}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 2}\)