Space of modular forms of level 44 and weight 1

• Label: 44.1
• Level: 44
• Weight: 1
• Dimension: 1
• Nonzero newspaces: 1
• Newform subspaces: 1
• Sturm bound: 120
• Trace bound: 0

Defining parameters

Level:	\( N \)	=	\( 44 = 2^{2} \cdot 11 \)
Weight:	\( k \)	=	\( 1 \)
Nonzero newspaces:			\( 1 \)
Newform subspaces:			\( 1 \)
Sturm bound:			\(120\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(44))\).

	Total	New	Old
Modular forms	26	9	17
Cusp forms	1	1	0
Eisenstein series	25	8	17

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^3 - q^5 + q^11 + q^15 - q^23 + q^27 - q^31 - q^33 - q^37 + 2 * q^47 + q^49 + 2 * q^53 - q^55 - q^59 - q^67 + q^69 - q^71 - q^81 - q^89 + q^93 - q^97

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(44))\)

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 available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
44.1.b	\(\chi_{44}(23, \cdot)\)	None	0	1
44.1.d	\(\chi_{44}(21, \cdot)\)	44.1.d.a	1	1
44.1.f	\(\chi_{44}(13, \cdot)\)	None	0	4
44.1.h	\(\chi_{44}(3, \cdot)\)	None	0	4