Space of modular forms of level 9802 and weight 2

• Label: 9802.2
• Level: 9802
• Weight: 2
• Dimension: 979655
• Nonzero newspaces: 48
• Sturm bound: 11924640

Defining parameters

Level:	\( N \)	=	\( 9802 = 2 \cdot 13^{2} \cdot 29 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 48 \)
Sturm bound:			\(11924640\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9802))\).

	Total	New	Old
Modular forms	2993928	979655	2014273
Cusp forms	2968393	979655	1988738
Eisenstein series	25535	0	25535

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9802))\)

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
9802.2.a	\(\chi_{9802}(1, \cdot)\)	9802.2.a.a	1	1
		9802.2.a.b	1
		9802.2.a.c	1
		9802.2.a.d	1
		9802.2.a.e	1
		9802.2.a.f	1
		9802.2.a.g	1
		9802.2.a.h	1
		9802.2.a.i	2
		9802.2.a.j	2
		9802.2.a.k	2
		9802.2.a.l	2
		9802.2.a.m	2
		9802.2.a.n	2
		9802.2.a.o	3
		9802.2.a.p	3
		9802.2.a.q	3
		9802.2.a.r	3
		9802.2.a.s	4
		9802.2.a.t	4
		9802.2.a.u	4
		9802.2.a.v	4
		9802.2.a.w	5
		9802.2.a.x	5
		9802.2.a.y	5
		9802.2.a.z	6
		9802.2.a.ba	7
		9802.2.a.bb	7
		9802.2.a.bc	9
		9802.2.a.bd	9
		9802.2.a.be	10
		9802.2.a.bf	10
		9802.2.a.bg	10
		9802.2.a.bh	10
		9802.2.a.bi	10
		9802.2.a.bj	10
		9802.2.a.bk	18
		9802.2.a.bl	18
		9802.2.a.bm	18
		9802.2.a.bn	18
		9802.2.a.bo	20
		9802.2.a.bp	20
		9802.2.a.bq	21
		9802.2.a.br	21
		9802.2.a.bs	24
		9802.2.a.bt	24
9802.2.b	\(\chi_{9802}(9801, \cdot)\)	n/a	384	1
9802.2.c	\(\chi_{9802}(2029, \cdot)\)	n/a	388	1
9802.2.d	\(\chi_{9802}(7773, \cdot)\)	n/a	362	1
9802.2.e	\(\chi_{9802}(5047, \cdot)\)	n/a	716	2
9802.2.h	\(\chi_{9802}(4831, \cdot)\)	n/a	770	2
9802.2.i	\(\chi_{9802}(99, \cdot)\)	n/a	770	2
9802.2.l	\(\chi_{9802}(1161, \cdot)\)	n/a	716	2
9802.2.m	\(\chi_{9802}(3189, \cdot)\)	n/a	768	2
9802.2.n	\(\chi_{9802}(7075, \cdot)\)	n/a	772	2
9802.2.o	\(\chi_{9802}(339, \cdot)\)	n/a	2322	6
9802.2.r	\(\chi_{9802}(249, \cdot)\)	n/a	1540	4
9802.2.s	\(\chi_{9802}(2685, \cdot)\)	n/a	1540	4
9802.2.v	\(\chi_{9802}(755, \cdot)\)	n/a	5064	12
9802.2.w	\(\chi_{9802}(1689, \cdot)\)	n/a	2316	6
9802.2.x	\(\chi_{9802}(1691, \cdot)\)	n/a	2328	6
9802.2.y	\(\chi_{9802}(2703, \cdot)\)	n/a	2304	6
9802.2.z	\(\chi_{9802}(315, \cdot)\)	n/a	4608	12
9802.2.ba	\(\chi_{9802}(233, \cdot)\)	n/a	5064	12
9802.2.bb	\(\chi_{9802}(521, \cdot)\)	n/a	5448	12
9802.2.bc	\(\chi_{9802}(753, \cdot)\)	n/a	5472	12
9802.2.bf	\(\chi_{9802}(2127, \cdot)\)	n/a	4620	12
9802.2.bg	\(\chi_{9802}(437, \cdot)\)	n/a	4620	12
9802.2.bj	\(\chi_{9802}(523, \cdot)\)	n/a	10224	24
9802.2.bk	\(\chi_{9802}(991, \cdot)\)	n/a	4632	12
9802.2.bl	\(\chi_{9802}(361, \cdot)\)	n/a	4608	12
9802.2.bm	\(\chi_{9802}(23, \cdot)\)	n/a	4632	12
9802.2.bp	\(\chi_{9802}(655, \cdot)\)	n/a	10920	24
9802.2.bq	\(\chi_{9802}(307, \cdot)\)	n/a	10920	24
9802.2.bt	\(\chi_{9802}(289, \cdot)\)	n/a	10896	24
9802.2.bu	\(\chi_{9802}(173, \cdot)\)	n/a	10944	24
9802.2.bv	\(\chi_{9802}(407, \cdot)\)	n/a	10224	24
9802.2.by	\(\chi_{9802}(89, \cdot)\)	n/a	9240	24
9802.2.bz	\(\chi_{9802}(19, \cdot)\)	n/a	9240	24
9802.2.cc	\(\chi_{9802}(53, \cdot)\)	n/a	32832	72
9802.2.cf	\(\chi_{9802}(41, \cdot)\)	n/a	21840	48
9802.2.cg	\(\chi_{9802}(215, \cdot)\)	n/a	21840	48
9802.2.cj	\(\chi_{9802}(51, \cdot)\)	n/a	32832	72
9802.2.ck	\(\chi_{9802}(183, \cdot)\)	n/a	32688	72
9802.2.cl	\(\chi_{9802}(25, \cdot)\)	n/a	32688	72
9802.2.cm	\(\chi_{9802}(81, \cdot)\)	n/a	65664	144
9802.2.cp	\(\chi_{9802}(21, \cdot)\)	n/a	65520	144
9802.2.cq	\(\chi_{9802}(31, \cdot)\)	n/a	65520	144
9802.2.ct	\(\chi_{9802}(49, \cdot)\)	n/a	65376	144
9802.2.cu	\(\chi_{9802}(121, \cdot)\)	n/a	65664	144
9802.2.cv	\(\chi_{9802}(9, \cdot)\)	n/a	65376	144
9802.2.cy	\(\chi_{9802}(37, \cdot)\)	n/a	131040	288
9802.2.cz	\(\chi_{9802}(11, \cdot)\)	n/a	131040	288

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9802))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9802)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(338))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(377))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(754))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4901))\)\(^{\oplus 2}\)