Space of modular forms of level 3240 and weight 1

• Label: 3240.1
• Level: 3240
• Weight: 1
• Dimension: 108
• Nonzero newspaces: 7
• Newform subspaces: 35
• Sturm bound: 559872
• Trace bound: 19

Defining parameters

Level:	$N$	=	$3240 = 2^{3} \cdot 3^{4} \cdot 5$
Weight:	$k$	=	$1$
Nonzero newspaces:			$7$
Newform subspaces:			$35$
Sturm bound:			$559872$
Trace bound:			$19$

Dimensions

The following table gives the dimensions of various subspaces of $M_{1}(\Gamma_1(3240))$.

	Total	New	Old
Modular forms	5938	780	5158
Cusp forms	754	108	646
Eisenstein series	5184	672	4512

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

	$D_n$	$A_4$	$S_4$	$A_5$
Dimension	88	0	20	0

Trace form

$108 q - 4 q^{10} + 4 q^{16} + 8 q^{19} - 6 q^{25} + 16 q^{34} + 12 q^{37} + 10 q^{40} - 8 q^{46} + 4 q^{49} - 24 q^{55} + 12 q^{58} + 4 q^{61} + 24 q^{64} + 6 q^{70} - 32 q^{91} + 4 q^{94}+O(q^{100})$

Decomposition of $S_{1}^{\mathrm{new}}(\Gamma_1(3240))$

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
3240.1.c	$\chi_{3240}(809, \cdot)$	None	0	1
3240.1.e	$\chi_{3240}(2431, \cdot)$	None	0	1
3240.1.g	$\chi_{3240}(811, \cdot)$	None	0	1
3240.1.i	$\chi_{3240}(2429, \cdot)$	None	0	1
3240.1.j	$\chi_{3240}(3079, \cdot)$	None	0	1
3240.1.l	$\chi_{3240}(161, \cdot)$	None	0	1
3240.1.n	$\chi_{3240}(1781, \cdot)$	None	0	1
3240.1.p	$\chi_{3240}(1459, \cdot)$	3240.1.p.a	1	1
		3240.1.p.b	1
		3240.1.p.c	1
		3240.1.p.d	1
		3240.1.p.e	2
		3240.1.p.f	2
3240.1.r	$\chi_{3240}(323, \cdot)$	None	0	2
3240.1.u	$\chi_{3240}(973, \cdot)$	None	0	2
3240.1.v	$\chi_{3240}(1297, \cdot)$	3240.1.v.a	2	2
		3240.1.v.b	2
3240.1.y	$\chi_{3240}(647, \cdot)$	None	0	2
3240.1.z	$\chi_{3240}(379, \cdot)$	3240.1.z.a	2	2
		3240.1.z.b	2
		3240.1.z.c	2
		3240.1.z.d	2
		3240.1.z.e	2
		3240.1.z.f	2
		3240.1.z.g	2
		3240.1.z.h	2
		3240.1.z.i	2
		3240.1.z.j	2
		3240.1.z.k	4
		3240.1.z.l	4
3240.1.ba	$\chi_{3240}(701, \cdot)$	None	0	2
3240.1.bc	$\chi_{3240}(1241, \cdot)$	None	0	2
3240.1.be	$\chi_{3240}(919, \cdot)$	None	0	2
3240.1.bh	$\chi_{3240}(269, \cdot)$	3240.1.bh.a	2	2
		3240.1.bh.b	2
		3240.1.bh.c	2
		3240.1.bh.d	2
		3240.1.bh.e	4
		3240.1.bh.f	4
		3240.1.bh.g	4
		3240.1.bh.h	4
		3240.1.bh.i	4
3240.1.bj	$\chi_{3240}(1891, \cdot)$	None	0	2
3240.1.bl	$\chi_{3240}(271, \cdot)$	None	0	2
3240.1.bn	$\chi_{3240}(1889, \cdot)$	3240.1.bn.a	8	2
3240.1.bq	$\chi_{3240}(217, \cdot)$	3240.1.bq.a	4	4
		3240.1.bq.b	4
3240.1.br	$\chi_{3240}(863, \cdot)$	None	0	4
3240.1.bu	$\chi_{3240}(107, \cdot)$	None	0	4
3240.1.bv	$\chi_{3240}(757, \cdot)$	3240.1.bv.a	8	4
		3240.1.bv.b	8
		3240.1.bv.c	8
3240.1.by	$\chi_{3240}(91, \cdot)$	None	0	6
3240.1.bz	$\chi_{3240}(89, \cdot)$	None	0	6
3240.1.ca	$\chi_{3240}(629, \cdot)$	None	0	6
3240.1.cb	$\chi_{3240}(631, \cdot)$	None	0	6
3240.1.ce	$\chi_{3240}(521, \cdot)$	None	0	6
3240.1.cf	$\chi_{3240}(19, \cdot)$	None	0	6
3240.1.ck	$\chi_{3240}(199, \cdot)$	None	0	6
3240.1.cl	$\chi_{3240}(341, \cdot)$	None	0	6
3240.1.cn	$\chi_{3240}(143, \cdot)$	None	0	12
3240.1.co	$\chi_{3240}(37, \cdot)$	None	0	12
3240.1.cr	$\chi_{3240}(467, \cdot)$	None	0	12
3240.1.cs	$\chi_{3240}(73, \cdot)$	None	0	12
3240.1.cv	$\chi_{3240}(209, \cdot)$	None	0	18
3240.1.cw	$\chi_{3240}(101, \cdot)$	None	0	18
3240.1.cz	$\chi_{3240}(31, \cdot)$	None	0	18
3240.1.db	$\chi_{3240}(139, \cdot)$	None	0	18
3240.1.dd	$\chi_{3240}(79, \cdot)$	None	0	18
3240.1.df	$\chi_{3240}(211, \cdot)$	None	0	18
3240.1.dg	$\chi_{3240}(41, \cdot)$	None	0	18
3240.1.di	$\chi_{3240}(29, \cdot)$	None	0	18
3240.1.dl	$\chi_{3240}(83, \cdot)$	None	0	36
3240.1.dm	$\chi_{3240}(13, \cdot)$	None	0	36
3240.1.dp	$\chi_{3240}(23, \cdot)$	None	0	36
3240.1.dq	$\chi_{3240}(97, \cdot)$	None	0	36

Decomposition of $S_{1}^{\mathrm{old}}(\Gamma_1(3240))$ into lower level spaces

$S_{1}^{\mathrm{old}}(\Gamma_1(3240)) \cong$ $S_{1}^{\mathrm{new}}(\Gamma_1(1))$$^{\oplus 40}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(2))$$^{\oplus 30}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(3))$$^{\oplus 32}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(4))$$^{\oplus 20}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(5))$$^{\oplus 20}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(6))$$^{\oplus 24}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(8))$$^{\oplus 10}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(9))$$^{\oplus 24}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(10))$$^{\oplus 15}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(12))$$^{\oplus 16}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(15))$$^{\oplus 16}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(18))$$^{\oplus 18}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(20))$$^{\oplus 10}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(24))$$^{\oplus 8}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(27))$$^{\oplus 16}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(30))$$^{\oplus 12}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(36))$$^{\oplus 12}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(40))$$^{\oplus 5}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(45))$$^{\oplus 12}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(54))$$^{\oplus 12}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(60))$$^{\oplus 8}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(72))$$^{\oplus 6}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(81))$$^{\oplus 8}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(90))$$^{\oplus 9}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(108))$$^{\oplus 8}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(120))$$^{\oplus 4}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(135))$$^{\oplus 8}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(162))$$^{\oplus 6}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(180))$$^{\oplus 6}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(216))$$^{\oplus 4}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(270))$$^{\oplus 6}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(324))$$^{\oplus 4}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(360))$$^{\oplus 3}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(405))$$^{\oplus 4}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(540))$$^{\oplus 4}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(648))$$^{\oplus 2}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(810))$$^{\oplus 3}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(1080))$$^{\oplus 2}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(1620))$$^{\oplus 2}$