Space of modular forms of level 8993 and weight 2

• Label: 8993.2
• Level: 8993
• Weight: 2
• Dimension: 3305330
• Nonzero newspaces: 20
• Sturm bound: 13406976

Defining parameters

Level:	\( N \)	=	\( 8993 = 17 \cdot 23^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 20 \)
Sturm bound:			\(13406976\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8993))\).

	Total	New	Old
Modular forms	3363712	3326464	37248
Cusp forms	3339777	3305330	34447
Eisenstein series	23935	21134	2801

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8993))\)

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
8993.2.a	\(\chi_{8993}(1, \cdot)\)	8993.2.a.a	1	1
		8993.2.a.b	2
		8993.2.a.c	3
		8993.2.a.d	3
		8993.2.a.e	4
		8993.2.a.f	4
		8993.2.a.g	9
		8993.2.a.h	11
		8993.2.a.i	11
		8993.2.a.j	12
		8993.2.a.k	14
		8993.2.a.l	14
		8993.2.a.m	15
		8993.2.a.n	15
		8993.2.a.o	28
		8993.2.a.p	28
		8993.2.a.q	30
		8993.2.a.r	30
		8993.2.a.s	60
		8993.2.a.t	60
		8993.2.a.u	70
		8993.2.a.v	70
		8993.2.a.w	90
		8993.2.a.x	90
8993.2.b	\(\chi_{8993}(8465, \cdot)\)	n/a	736	1
8993.2.e	\(\chi_{8993}(3175, \cdot)\)	n/a	1472	2
8993.2.g	\(\chi_{8993}(2117, \cdot)\)	n/a	2948	4
8993.2.i	\(\chi_{8993}(647, \cdot)\)	n/a	6720	10
8993.2.k	\(\chi_{8993}(1057, \cdot)\)	n/a	5888	8
8993.2.n	\(\chi_{8993}(118, \cdot)\)	n/a	7360	10
8993.2.o	\(\chi_{8993}(392, \cdot)\)	n/a	16192	22
8993.2.q	\(\chi_{8993}(795, \cdot)\)	n/a	14720	20
8993.2.t	\(\chi_{8993}(254, \cdot)\)	n/a	18172	22
8993.2.v	\(\chi_{8993}(399, \cdot)\)	n/a	29440	40
8993.2.x	\(\chi_{8993}(47, \cdot)\)	n/a	36344	44
8993.2.y	\(\chi_{8993}(28, \cdot)\)	n/a	58880	80
8993.2.bb	\(\chi_{8993}(70, \cdot)\)	n/a	72688	88
8993.2.bc	\(\chi_{8993}(18, \cdot)\)	n/a	161920	220
8993.2.bd	\(\chi_{8993}(22, \cdot)\)	n/a	145376	176
8993.2.bf	\(\chi_{8993}(16, \cdot)\)	n/a	181720	220
8993.2.bi	\(\chi_{8993}(4, \cdot)\)	n/a	363440	440
8993.2.bk	\(\chi_{8993}(2, \cdot)\)	n/a	726880	880
8993.2.bn	\(\chi_{8993}(5, \cdot)\)	n/a	1453760	1760

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8993))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8993)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(391))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(529))\)\(^{\oplus 2}\)