Space of modular forms of level 8019 and weight 2

• Label: 8019.2
• Level: 8019
• Weight: 2
• Dimension: 1829304
• Nonzero newspaces: 24
• Sturm bound: 9447840

Defining parameters

Level:	\( N \)	=	\( 8019 = 3^{6} \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(9447840\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8019))\).

	Total	New	Old
Modular forms	2374920	1840968	533952
Cusp forms	2349001	1829304	519697
Eisenstein series	25919	11664	14255

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8019))\)

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
8019.2.a	\(\chi_{8019}(1, \cdot)\)	8019.2.a.a	3	1
		8019.2.a.b	3
		8019.2.a.c	21
		8019.2.a.d	21
		8019.2.a.e	21
		8019.2.a.f	21
		8019.2.a.g	36
		8019.2.a.h	36
		8019.2.a.i	48
		8019.2.a.j	48
		8019.2.a.k	51
		8019.2.a.l	51
8019.2.d	\(\chi_{8019}(8018, \cdot)\)	n/a	420	1
8019.2.e	\(\chi_{8019}(2674, \cdot)\)	n/a	720	2
8019.2.f	\(\chi_{8019}(730, \cdot)\)	n/a	1680	4
8019.2.g	\(\chi_{8019}(2672, \cdot)\)	n/a	840	2
8019.2.j	\(\chi_{8019}(892, \cdot)\)	n/a	2160	6
8019.2.k	\(\chi_{8019}(728, \cdot)\)	n/a	1680	4
8019.2.n	\(\chi_{8019}(487, \cdot)\)	n/a	3360	8
8019.2.o	\(\chi_{8019}(890, \cdot)\)	n/a	2556	6
8019.2.r	\(\chi_{8019}(298, \cdot)\)	n/a	6480	18
8019.2.u	\(\chi_{8019}(1700, \cdot)\)	n/a	3360	8
8019.2.v	\(\chi_{8019}(82, \cdot)\)	n/a	10224	24
8019.2.y	\(\chi_{8019}(296, \cdot)\)	n/a	7632	18
8019.2.z	\(\chi_{8019}(100, \cdot)\)	n/a	14580	54
8019.2.bc	\(\chi_{8019}(161, \cdot)\)	n/a	10224	24
8019.2.bd	\(\chi_{8019}(136, \cdot)\)	n/a	30528	72
8019.2.bf	\(\chi_{8019}(98, \cdot)\)	n/a	17388	54
8019.2.bh	\(\chi_{8019}(34, \cdot)\)	n/a	131220	162
8019.2.bi	\(\chi_{8019}(107, \cdot)\)	n/a	30528	72
8019.2.bl	\(\chi_{8019}(37, \cdot)\)	n/a	69552	216
8019.2.bo	\(\chi_{8019}(32, \cdot)\)	n/a	157140	162
8019.2.bq	\(\chi_{8019}(8, \cdot)\)	n/a	69552	216
8019.2.bs	\(\chi_{8019}(4, \cdot)\)	n/a	628560	648
8019.2.bu	\(\chi_{8019}(2, \cdot)\)	n/a	628560	648

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8019))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8019)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(243))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(297))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(729))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(891))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2673))\)\(^{\oplus 2}\)