Space of modular forms of level 128 and weight 1

• Label: 128.1
• Level: 128
• Weight: 1
• Dimension: 1
• Nonzero newspaces: 1
• Newform subspaces: 1
• Sturm bound: 1024
• Trace bound: 0

Defining parameters

Level:	\( N \)	=	\( 128 = 2^{7} \)
Weight:	\( k \)	=	\( 1 \)
Nonzero newspaces:			\( 1 \)
Newform subspaces:			\( 1 \)
Sturm bound:			\(1024\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(128))\).

	Total	New	Old
Modular forms	81	25	56
Cusp forms	1	1	0
Eisenstein series	80	24	56

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	1	0	0	0

Trace form

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

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(128))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
128.1.c	\(\chi_{128}(127, \cdot)\)	None	0	1
128.1.d	\(\chi_{128}(63, \cdot)\)	128.1.d.a	1	1
128.1.f	\(\chi_{128}(31, \cdot)\)	None	0	2
128.1.h	\(\chi_{128}(15, \cdot)\)	None	0	4
128.1.j	\(\chi_{128}(7, \cdot)\)	None	0	8
128.1.l	\(\chi_{128}(3, \cdot)\)	None	0	16