Space of modular forms of level 4205 and weight 2

• Label: 4205.2
• Level: 4205
• Weight: 2
• Dimension: 642587
• Nonzero newspaces: 24
• Sturm bound: 2825760

Defining parameters

Level:	$N$	=	$4205 = 5 \cdot 29^{2}$
Weight:	$k$	=	$2$
Nonzero newspaces:			$24$
Sturm bound:			$2825760$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_1(4205))$.

	Total	New	Old
Modular forms	711256	649477	61779
Cusp forms	701625	642587	59038
Eisenstein series	9631	6890	2741

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_1(4205))$

We only show spaces with even 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
4205.2.a	$\chi_{4205}(1, \cdot)$	4205.2.a.a	1	1
		4205.2.a.b	2
		4205.2.a.c	2
		4205.2.a.d	2
		4205.2.a.e	3
		4205.2.a.f	3
		4205.2.a.g	4
		4205.2.a.h	5
		4205.2.a.i	5
		4205.2.a.j	5
		4205.2.a.k	5
		4205.2.a.l	6
		4205.2.a.m	6
		4205.2.a.n	6
		4205.2.a.o	8
		4205.2.a.p	8
		4205.2.a.q	12
		4205.2.a.r	12
		4205.2.a.s	18
		4205.2.a.t	18
		4205.2.a.u	20
		4205.2.a.v	20
		4205.2.a.w	20
		4205.2.a.x	20
		4205.2.a.y	24
		4205.2.a.z	36
4205.2.b	$\chi_{4205}(2524, \cdot)$	n/a	378	1
4205.2.c	$\chi_{4205}(1681, \cdot)$	n/a	270	1
4205.2.d	$\chi_{4205}(4204, \cdot)$	n/a	380	1
4205.2.e	$\chi_{4205}(882, \cdot)$	n/a	758	2
4205.2.j	$\chi_{4205}(1723, \cdot)$	n/a	758	2
4205.2.k	$\chi_{4205}(571, \cdot)$	n/a	1620	6
4205.2.l	$\chi_{4205}(904, \cdot)$	n/a	2280	6
4205.2.m	$\chi_{4205}(196, \cdot)$	n/a	1620	6
4205.2.n	$\chi_{4205}(574, \cdot)$	n/a	2268	6
4205.2.o	$\chi_{4205}(137, \cdot)$	n/a	4548	12
4205.2.t	$\chi_{4205}(827, \cdot)$	n/a	4548	12
4205.2.u	$\chi_{4205}(146, \cdot)$	n/a	8120	28
4205.2.v	$\chi_{4205}(144, \cdot)$	n/a	12096	28
4205.2.w	$\chi_{4205}(86, \cdot)$	n/a	8120	28
4205.2.x	$\chi_{4205}(59, \cdot)$	n/a	12152	28
4205.2.y	$\chi_{4205}(17, \cdot)$	n/a	24248	56
4205.2.bd	$\chi_{4205}(12, \cdot)$	n/a	24248	56
4205.2.be	$\chi_{4205}(16, \cdot)$	n/a	48720	168
4205.2.bf	$\chi_{4205}(24, \cdot)$	n/a	72912	168
4205.2.bg	$\chi_{4205}(6, \cdot)$	n/a	48720	168
4205.2.bh	$\chi_{4205}(4, \cdot)$	n/a	72576	168
4205.2.bi	$\chi_{4205}(3, \cdot)$	n/a	145488	336
4205.2.bn	$\chi_{4205}(2, \cdot)$	n/a	145488	336

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_1(4205))$ into lower level spaces

$S_{2}^{\mathrm{old}}(\Gamma_1(4205)) \cong$ $S_{2}^{\mathrm{new}}(\Gamma_1(1))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(29))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(145))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(841))$$^{\oplus 2}$