Space of modular forms of level 8024 and weight 2

• Label: 8024.2
• Level: 8024
• Weight: 2
• Dimension: 1115626
• Nonzero newspaces: 30
• Sturm bound: 8017920

Defining parameters

Level:	\( N \)	=	\( 8024 = 2^{3} \cdot 17 \cdot 59 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 30 \)
Sturm bound:			\(8017920\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8024))\).

	Total	New	Old
Modular forms	2015616	1122466	893150
Cusp forms	1993345	1115626	877719
Eisenstein series	22271	6840	15431

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8024))\)

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
8024.2.a	\(\chi_{8024}(1, \cdot)\)	8024.2.a.a	1	1
		8024.2.a.b	1
		8024.2.a.c	1
		8024.2.a.d	1
		8024.2.a.e	1
		8024.2.a.f	1
		8024.2.a.g	1
		8024.2.a.h	1
		8024.2.a.i	1
		8024.2.a.j	1
		8024.2.a.k	1
		8024.2.a.l	1
		8024.2.a.m	1
		8024.2.a.n	1
		8024.2.a.o	1
		8024.2.a.p	2
		8024.2.a.q	2
		8024.2.a.r	2
		8024.2.a.s	3
		8024.2.a.t	3
		8024.2.a.u	3
		8024.2.a.v	18
		8024.2.a.w	20
		8024.2.a.x	22
		8024.2.a.y	23
		8024.2.a.z	24
		8024.2.a.ba	30
		8024.2.a.bb	32
		8024.2.a.bc	33
8024.2.b	\(\chi_{8024}(4249, \cdot)\)	n/a	262	1
8024.2.d	\(\chi_{8024}(4013, \cdot)\)	n/a	928	1
8024.2.g	\(\chi_{8024}(3775, \cdot)\)	None	0	1
8024.2.i	\(\chi_{8024}(4011, \cdot)\)	n/a	1076	1
8024.2.j	\(\chi_{8024}(7787, \cdot)\)	n/a	960	1
8024.2.l	\(\chi_{8024}(8023, \cdot)\)	None	0	1
8024.2.o	\(\chi_{8024}(237, \cdot)\)	n/a	1044	1
8024.2.r	\(\chi_{8024}(1653, \cdot)\)	n/a	2088	2
8024.2.t	\(\chi_{8024}(1415, \cdot)\)	None	0	2
8024.2.u	\(\chi_{8024}(5665, \cdot)\)	n/a	524	2
8024.2.w	\(\chi_{8024}(5427, \cdot)\)	n/a	2152	2
8024.2.z	\(\chi_{8024}(1889, \cdot)\)	n/a	1040	4
8024.2.bb	\(\chi_{8024}(1651, \cdot)\)	n/a	4304	4
8024.2.bc	\(\chi_{8024}(943, \cdot)\)	None	0	4
8024.2.be	\(\chi_{8024}(1181, \cdot)\)	n/a	4176	4
8024.2.bh	\(\chi_{8024}(1535, \cdot)\)	None	0	8
8024.2.bi	\(\chi_{8024}(827, \cdot)\)	n/a	8352	8
8024.2.bl	\(\chi_{8024}(589, \cdot)\)	n/a	8608	8
8024.2.bm	\(\chi_{8024}(1297, \cdot)\)	n/a	2160	8
8024.2.bo	\(\chi_{8024}(137, \cdot)\)	n/a	6720	28
8024.2.bq	\(\chi_{8024}(373, \cdot)\)	n/a	30128	28
8024.2.bt	\(\chi_{8024}(679, \cdot)\)	None	0	28
8024.2.bv	\(\chi_{8024}(443, \cdot)\)	n/a	26880	28
8024.2.bw	\(\chi_{8024}(67, \cdot)\)	n/a	30128	28
8024.2.by	\(\chi_{8024}(103, \cdot)\)	None	0	28
8024.2.cb	\(\chi_{8024}(205, \cdot)\)	n/a	26880	28
8024.2.cd	\(\chi_{8024}(169, \cdot)\)	n/a	7560	28
8024.2.cf	\(\chi_{8024}(115, \cdot)\)	n/a	60256	56
8024.2.ch	\(\chi_{8024}(81, \cdot)\)	n/a	15120	56
8024.2.ci	\(\chi_{8024}(47, \cdot)\)	None	0	56
8024.2.ck	\(\chi_{8024}(21, \cdot)\)	n/a	60256	56
8024.2.cn	\(\chi_{8024}(53, \cdot)\)	n/a	120512	112
8024.2.cp	\(\chi_{8024}(111, \cdot)\)	None	0	112
8024.2.cq	\(\chi_{8024}(43, \cdot)\)	n/a	120512	112
8024.2.cs	\(\chi_{8024}(9, \cdot)\)	n/a	30240	112
8024.2.cv	\(\chi_{8024}(65, \cdot)\)	n/a	60480	224
8024.2.cw	\(\chi_{8024}(37, \cdot)\)	n/a	241024	224
8024.2.cz	\(\chi_{8024}(3, \cdot)\)	n/a	241024	224
8024.2.da	\(\chi_{8024}(7, \cdot)\)	None	0	224

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8024))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8024)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(118))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(136))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(236))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(472))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1003))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2006))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4012))\)\(^{\oplus 2}\)