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