Space of modular forms of level 8410 and weight 2

• Label: 8410.2
• Level: 8410
• Weight: 2
• Dimension: 646029
• Nonzero newspaces: 24
• Sturm bound: 8477280

Defining parameters

Level:	\( N \)	=	\( 8410 = 2 \cdot 5 \cdot 29^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(8477280\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8410))\).

	Total	New	Old
Modular forms	2128952	646029	1482923
Cusp forms	2109689	646029	1463660
Eisenstein series	19263	0	19263

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8410))\)

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
8410.2.a	\(\chi_{8410}(1, \cdot)\)	8410.2.a.a	1	1
		8410.2.a.b	1
		8410.2.a.c	1
		8410.2.a.d	1
		8410.2.a.e	1
		8410.2.a.f	1
		8410.2.a.g	1
		8410.2.a.h	1
		8410.2.a.i	1
		8410.2.a.j	1
		8410.2.a.k	1
		8410.2.a.l	1
		8410.2.a.m	1
		8410.2.a.n	2
		8410.2.a.o	2
		8410.2.a.p	2
		8410.2.a.q	2
		8410.2.a.r	2
		8410.2.a.s	2
		8410.2.a.t	2
		8410.2.a.u	2
		8410.2.a.v	3
		8410.2.a.w	3
		8410.2.a.x	3
		8410.2.a.y	3
		8410.2.a.z	4
		8410.2.a.ba	4
		8410.2.a.bb	4
		8410.2.a.bc	4
		8410.2.a.bd	6
		8410.2.a.be	6
		8410.2.a.bf	6
		8410.2.a.bg	6
		8410.2.a.bh	6
		8410.2.a.bi	6
		8410.2.a.bj	6
		8410.2.a.bk	6
		8410.2.a.bl	6
		8410.2.a.bm	6
		8410.2.a.bn	8
		8410.2.a.bo	8
		8410.2.a.bp	8
		8410.2.a.bq	8
		8410.2.a.br	9
		8410.2.a.bs	9
		8410.2.a.bt	9
		8410.2.a.bu	9
		8410.2.a.bv	12
		8410.2.a.bw	12
		8410.2.a.bx	12
		8410.2.a.by	12
		8410.2.a.bz	18
		8410.2.a.ca	18
8410.2.b	\(\chi_{8410}(6729, \cdot)\)	n/a	406	1
8410.2.c	\(\chi_{8410}(1681, \cdot)\)	n/a	270	1
8410.2.d	\(\chi_{8410}(8409, \cdot)\)	n/a	404	1
8410.2.e	\(\chi_{8410}(1723, \cdot)\)	n/a	810	2
8410.2.j	\(\chi_{8410}(3323, \cdot)\)	n/a	810	2
8410.2.k	\(\chi_{8410}(571, \cdot)\)	n/a	1620	6
8410.2.l	\(\chi_{8410}(1949, \cdot)\)	n/a	2424	6
8410.2.m	\(\chi_{8410}(651, \cdot)\)	n/a	1620	6
8410.2.n	\(\chi_{8410}(1619, \cdot)\)	n/a	2436	6
8410.2.o	\(\chi_{8410}(827, \cdot)\)	n/a	4860	12
8410.2.t	\(\chi_{8410}(137, \cdot)\)	n/a	4860	12
8410.2.u	\(\chi_{8410}(291, \cdot)\)	n/a	8120	28
8410.2.v	\(\chi_{8410}(289, \cdot)\)	n/a	12208	28
8410.2.w	\(\chi_{8410}(231, \cdot)\)	n/a	8120	28
8410.2.x	\(\chi_{8410}(59, \cdot)\)	n/a	12152	28
8410.2.y	\(\chi_{8410}(133, \cdot)\)	n/a	24360	56
8410.2.bd	\(\chi_{8410}(17, \cdot)\)	n/a	24360	56
8410.2.be	\(\chi_{8410}(81, \cdot)\)	n/a	48720	168
8410.2.bf	\(\chi_{8410}(49, \cdot)\)	n/a	72912	168
8410.2.bg	\(\chi_{8410}(51, \cdot)\)	n/a	48720	168
8410.2.bh	\(\chi_{8410}(9, \cdot)\)	n/a	73248	168
8410.2.bi	\(\chi_{8410}(73, \cdot)\)	n/a	146160	336
8410.2.bn	\(\chi_{8410}(3, \cdot)\)	n/a	146160	336

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8410))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8410)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(145))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(290))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(841))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1682))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4205))\)\(^{\oplus 2}\)