Space of modular forms of level 128, weight 2, and trivial character

• Label: 128.2.a
• Level: $128$
• Weight: $2$
• Character orbit: 128.a
• Rep. character: $\chi_{128}(1,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $4$
• Sturm bound: $32$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	128.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(32\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(128))\).

	Total	New	Old
Modular forms	24	4	20
Cusp forms	9	4	5
Eisenstein series	15	0	15

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
\(+\)	\(1\)
\(-\)	\(3\)

Trace form

\( 4 q + 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(128))\) 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
128.2.a.a	$128$	$2$	128.a	1.a	$1$	$1$	$1$	$1.022$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(-4\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-2q^{5}-4q^{7}+q^{9}+2q^{11}+\cdots\)
128.2.a.b	$128$	$2$	128.a	1.a	$1$	$1$	$1$	$1.022$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(4\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+2q^{5}+4q^{7}+q^{9}+2q^{11}+\cdots\)
128.2.a.c	$128$	$2$	128.a	1.a	$1$	$1$	$1$	$1.022$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(4\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-2q^{5}+4q^{7}+q^{9}-2q^{11}+\cdots\)
128.2.a.d	$128$	$2$	128.a	1.a	$1$	$1$	$1$	$1.022$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(2\)	\(2\)	\(-4\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+2q^{5}-4q^{7}+q^{9}-2q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(128))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(128)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 2}\)