Space of modular forms of level 8046 and weight 2

• Label: 8046.2
• Level: 8046
• Weight: 2
• Dimension: 473556
• Nonzero newspaces: 18
• Sturm bound: 7192800

Defining parameters

Level:	\( N \)	=	\( 8046 = 2 \cdot 3^{3} \cdot 149 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 18 \)
Sturm bound:			\(7192800\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8046))\).

	Total	New	Old
Modular forms	1807080	473556	1333524
Cusp forms	1789321	473556	1315765
Eisenstein series	17759	0	17759

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8046))\)

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
8046.2.a	\(\chi_{8046}(1, \cdot)\)	8046.2.a.a	1	1
		8046.2.a.b	1
		8046.2.a.c	2
		8046.2.a.d	2
		8046.2.a.e	8
		8046.2.a.f	8
		8046.2.a.g	9
		8046.2.a.h	9
		8046.2.a.i	12
		8046.2.a.j	12
		8046.2.a.k	12
		8046.2.a.l	12
		8046.2.a.m	12
		8046.2.a.n	12
		8046.2.a.o	12
		8046.2.a.p	12
		8046.2.a.q	14
		8046.2.a.r	14
		8046.2.a.s	16
		8046.2.a.t	16
8046.2.d	\(\chi_{8046}(595, \cdot)\)	n/a	200	1
8046.2.e	\(\chi_{8046}(2683, \cdot)\)	n/a	296	2
8046.2.f	\(\chi_{8046}(701, \cdot)\)	n/a	400	2
8046.2.h	\(\chi_{8046}(3277, \cdot)\)	n/a	300	2
8046.2.k	\(\chi_{8046}(895, \cdot)\)	n/a	2664	6
8046.2.m	\(\chi_{8046}(1385, \cdot)\)	n/a	600	4
8046.2.n	\(\chi_{8046}(1489, \cdot)\)	n/a	2700	6
8046.2.r	\(\chi_{8046}(491, \cdot)\)	n/a	5400	12
8046.2.s	\(\chi_{8046}(379, \cdot)\)	n/a	7200	36
8046.2.t	\(\chi_{8046}(217, \cdot)\)	n/a	7200	36
8046.2.w	\(\chi_{8046}(19, \cdot)\)	n/a	10800	72
8046.2.y	\(\chi_{8046}(161, \cdot)\)	n/a	14400	72
8046.2.bb	\(\chi_{8046}(235, \cdot)\)	n/a	10800	72
8046.2.bc	\(\chi_{8046}(25, \cdot)\)	n/a	97200	216
8046.2.bd	\(\chi_{8046}(71, \cdot)\)	n/a	21600	144
8046.2.bh	\(\chi_{8046}(7, \cdot)\)	n/a	97200	216
8046.2.bi	\(\chi_{8046}(11, \cdot)\)	n/a	194400	432

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8046))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8046)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(149))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(298))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(447))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(894))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1341))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2682))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4023))\)\(^{\oplus 2}\)