Space of modular forms of level 108 and weight 1

• Label: 108.1
• Level: 108
• Weight: 1
• Dimension: 1
• Nonzero newspaces: 1
• Newform subspaces: 1
• Sturm bound: 648
• Trace bound: 0

Defining parameters

Level:	\( N \)	=	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	=	\( 1 \)
Nonzero newspaces:			\( 1 \)
Newform subspaces:			\( 1 \)
Sturm bound:			\(648\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(108))\).

	Total	New	Old
Modular forms	76	17	59
Cusp forms	1	1	0
Eisenstein series	75	16	59

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

\( q - q^{7} - q^{13} - q^{19} + q^{25} + 2 q^{31} - q^{37} + 2 q^{43} - q^{61} - q^{67} - q^{73} - q^{79} + q^{91} - q^{97}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(108))\)

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
108.1.c	\(\chi_{108}(53, \cdot)\)	108.1.c.a	1	1
108.1.d	\(\chi_{108}(55, \cdot)\)	None	0	1
108.1.f	\(\chi_{108}(19, \cdot)\)	None	0	2
108.1.g	\(\chi_{108}(17, \cdot)\)	None	0	2
108.1.j	\(\chi_{108}(7, \cdot)\)	None	0	6
108.1.k	\(\chi_{108}(5, \cdot)\)	None	0	6