Space of modular forms of level 8025 and weight 2

• Label: 8025.2
• Level: 8025
• Weight: 2
• Dimension: 1578102
• Nonzero newspaces: 24
• Sturm bound: 9158400

Defining parameters

Level:	\( N \)	=	\( 8025 = 3 \cdot 5^{2} \cdot 107 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(9158400\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8025))\).

	Total	New	Old
Modular forms	2301472	1586714	714758
Cusp forms	2277729	1578102	699627
Eisenstein series	23743	8612	15131

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8025))\)

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
8025.2.a	\(\chi_{8025}(1, \cdot)\)	8025.2.a.a	1	1
		8025.2.a.b	1
		8025.2.a.c	1
		8025.2.a.d	1
		8025.2.a.e	1
		8025.2.a.f	1
		8025.2.a.g	1
		8025.2.a.h	1
		8025.2.a.i	1
		8025.2.a.j	1
		8025.2.a.k	1
		8025.2.a.l	1
		8025.2.a.m	1
		8025.2.a.n	1
		8025.2.a.o	1
		8025.2.a.p	1
		8025.2.a.q	1
		8025.2.a.r	2
		8025.2.a.s	2
		8025.2.a.t	3
		8025.2.a.u	3
		8025.2.a.v	3
		8025.2.a.w	4
		8025.2.a.x	5
		8025.2.a.y	5
		8025.2.a.z	5
		8025.2.a.ba	6
		8025.2.a.bb	7
		8025.2.a.bc	10
		8025.2.a.bd	11
		8025.2.a.be	11
		8025.2.a.bf	12
		8025.2.a.bg	13
		8025.2.a.bh	13
		8025.2.a.bi	16
		8025.2.a.bj	16
		8025.2.a.bk	17
		8025.2.a.bl	17
		8025.2.a.bm	18
		8025.2.a.bn	18
		8025.2.a.bo	22
		8025.2.a.bp	22
		8025.2.a.bq	29
		8025.2.a.br	29
8025.2.b	\(\chi_{8025}(4174, \cdot)\)	n/a	316	1
8025.2.d	\(\chi_{8025}(8024, \cdot)\)	n/a	644	1
8025.2.g	\(\chi_{8025}(3851, \cdot)\)	n/a	678	1
8025.2.i	\(\chi_{8025}(857, \cdot)\)	n/a	1272	2
8025.2.k	\(\chi_{8025}(2032, \cdot)\)	n/a	648	2
8025.2.m	\(\chi_{8025}(1606, \cdot)\)	n/a	2112	4
8025.2.n	\(\chi_{8025}(641, \cdot)\)	n/a	4304	4
8025.2.r	\(\chi_{8025}(964, \cdot)\)	n/a	2128	4
8025.2.t	\(\chi_{8025}(1604, \cdot)\)	n/a	4304	4
8025.2.u	\(\chi_{8025}(427, \cdot)\)	n/a	4320	8
8025.2.w	\(\chi_{8025}(1178, \cdot)\)	n/a	8480	8
8025.2.y	\(\chi_{8025}(76, \cdot)\)	n/a	17784	52
8025.2.ba	\(\chi_{8025}(26, \cdot)\)	n/a	35256	52
8025.2.bd	\(\chi_{8025}(74, \cdot)\)	n/a	33488	52
8025.2.bf	\(\chi_{8025}(49, \cdot)\)	n/a	16848	52
8025.2.bh	\(\chi_{8025}(7, \cdot)\)	n/a	33696	104
8025.2.bj	\(\chi_{8025}(143, \cdot)\)	n/a	66976	104
8025.2.bk	\(\chi_{8025}(16, \cdot)\)	n/a	112320	208
8025.2.bl	\(\chi_{8025}(59, \cdot)\)	n/a	223808	208
8025.2.bn	\(\chi_{8025}(4, \cdot)\)	n/a	112320	208
8025.2.br	\(\chi_{8025}(71, \cdot)\)	n/a	223808	208
8025.2.bt	\(\chi_{8025}(23, \cdot)\)	n/a	447616	416
8025.2.bv	\(\chi_{8025}(22, \cdot)\)	n/a	224640	416

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8025))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8025)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(107))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(321))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(535))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1605))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2675))\)\(^{\oplus 2}\)