Space of modular forms of level 135 and weight 1

• Label: 135.1
• Level: 135
• Weight: 1
• Dimension: 2
• Nonzero newspaces: 1
• Newform subspaces: 2
• Sturm bound: 1296
• Trace bound: 0

Defining parameters

Level:	$N$	=	$135 = 3^{3} \cdot 5$
Weight:	$k$	=	$1$
Nonzero newspaces:			$1$
Newform subspaces:			$2$
Sturm bound:			$1296$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{1}(\Gamma_1(135))$.

	Total	New	Old
Modular forms	122	50	72
Cusp forms	2	2	0
Eisenstein series	120	48	72

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

	$D_n$	$A_4$	$S_4$	$A_5$
Dimension	2	0	0	0

Trace form

$2 q - 2 q^{10} - 2 q^{16} - 2 q^{19} + 2 q^{25} - 2 q^{31} + 2 q^{34} + 2 q^{40} + 2 q^{46} + 2 q^{49} - 2 q^{61} + 2 q^{64} - 2 q^{79} - 2 q^{85} - 4 q^{94}+O(q^{100})$

Decomposition of $S_{1}^{\mathrm{new}}(\Gamma_1(135))$

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
135.1.c	$\chi_{135}(26, \cdot)$	None	0	1
135.1.d	$\chi_{135}(134, \cdot)$	135.1.d.a	1	1
		135.1.d.b	1
135.1.g	$\chi_{135}(28, \cdot)$	None	0	2
135.1.h	$\chi_{135}(44, \cdot)$	None	0	2
135.1.i	$\chi_{135}(71, \cdot)$	None	0	2
135.1.l	$\chi_{135}(37, \cdot)$	None	0	4
135.1.n	$\chi_{135}(14, \cdot)$	None	0	6
135.1.o	$\chi_{135}(11, \cdot)$	None	0	6
135.1.r	$\chi_{135}(7, \cdot)$	None	0	12