Space of modular forms of level 55 and weight 1

• Label: 55.1
• Level: 55
• Weight: 1
• Dimension: 1
• Nonzero newspaces: 1
• Newform subspaces: 1
• Sturm bound: 240
• Trace bound: 0

Defining parameters

Level:	\( N \)	=	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	=	\( 1 \)
Nonzero newspaces:			\( 1 \)
Newform subspaces:			\( 1 \)
Sturm bound:			\(240\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(55))\).

	Total	New	Old
Modular forms	41	27	14
Cusp forms	1	1	0
Eisenstein series	40	26	14

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

\( q - q^{4} - q^{5} + q^{9} - q^{11} + q^{16} + q^{20} + q^{25} - 2 q^{31} - q^{36} + q^{44} - q^{45} - q^{49} + q^{55} + 2 q^{59} - q^{64} + 2 q^{71} - q^{80} + q^{81} - 2 q^{89} - q^{99}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(55))\)

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
55.1.c	\(\chi_{55}(21, \cdot)\)	None	0	1
55.1.d	\(\chi_{55}(54, \cdot)\)	55.1.d.a	1	1
55.1.f	\(\chi_{55}(12, \cdot)\)	None	0	2
55.1.h	\(\chi_{55}(19, \cdot)\)	None	0	4
55.1.i	\(\chi_{55}(6, \cdot)\)	None	0	4
55.1.k	\(\chi_{55}(3, \cdot)\)	None	0	8