Space of modular forms of level 4026 and weight 2

• Label: 4026.2
• Level: 4026
• Weight: 2
• Dimension: 109677
• Nonzero newspaces: 84
• Sturm bound: 1785600

Defining parameters

Level:	\( N \)	=	\( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 84 \)
Sturm bound:			\(1785600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4026))\).

	Total	New	Old
Modular forms	451200	109677	341523
Cusp forms	441601	109677	331924
Eisenstein series	9599	0	9599

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4026))\)

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
4026.2.a	\(\chi_{4026}(1, \cdot)\)	4026.2.a.a	1	1
		4026.2.a.b	1
		4026.2.a.c	1
		4026.2.a.d	1
		4026.2.a.e	1
		4026.2.a.f	1
		4026.2.a.g	1
		4026.2.a.h	1
		4026.2.a.i	1
		4026.2.a.j	1
		4026.2.a.k	2
		4026.2.a.l	2
		4026.2.a.m	2
		4026.2.a.n	3
		4026.2.a.o	3
		4026.2.a.p	3
		4026.2.a.q	4
		4026.2.a.r	4
		4026.2.a.s	4
		4026.2.a.t	4
		4026.2.a.u	5
		4026.2.a.v	5
		4026.2.a.w	6
		4026.2.a.x	6
		4026.2.a.y	7
		4026.2.a.z	7
		4026.2.a.ba	7
		4026.2.a.bb	8
		4026.2.a.bc	9
4026.2.b	\(\chi_{4026}(2441, \cdot)\)	n/a	240	1
4026.2.d	\(\chi_{4026}(4025, \cdot)\)	n/a	248	1
4026.2.g	\(\chi_{4026}(1585, \cdot)\)	n/a	104	1
4026.2.i	\(\chi_{4026}(2575, \cdot)\)	n/a	208	2
4026.2.j	\(\chi_{4026}(1231, \cdot)\)	n/a	248	2
4026.2.m	\(\chi_{4026}(1475, \cdot)\)	n/a	408	2
4026.2.n	\(\chi_{4026}(619, \cdot)\)	n/a	496	4
4026.2.o	\(\chi_{4026}(949, \cdot)\)	n/a	496	4
4026.2.p	\(\chi_{4026}(367, \cdot)\)	n/a	480	4
4026.2.q	\(\chi_{4026}(1057, \cdot)\)	n/a	432	4
4026.2.r	\(\chi_{4026}(1351, \cdot)\)	n/a	496	4
4026.2.s	\(\chi_{4026}(1681, \cdot)\)	n/a	496	4
4026.2.u	\(\chi_{4026}(1783, \cdot)\)	n/a	200	2
4026.2.x	\(\chi_{4026}(197, \cdot)\)	n/a	496	2
4026.2.z	\(\chi_{4026}(989, \cdot)\)	n/a	496	2
4026.2.bb	\(\chi_{4026}(41, \cdot)\)	n/a	992	4
4026.2.bd	\(\chi_{4026}(569, \cdot)\)	n/a	992	4
4026.2.be	\(\chi_{4026}(895, \cdot)\)	n/a	496	4
4026.2.bl	\(\chi_{4026}(487, \cdot)\)	n/a	496	4
4026.2.bm	\(\chi_{4026}(235, \cdot)\)	n/a	496	4
4026.2.bn	\(\chi_{4026}(163, \cdot)\)	n/a	496	4
4026.2.br	\(\chi_{4026}(529, \cdot)\)	n/a	416	4
4026.2.bu	\(\chi_{4026}(497, \cdot)\)	n/a	992	4
4026.2.bv	\(\chi_{4026}(857, \cdot)\)	n/a	992	4
4026.2.bz	\(\chi_{4026}(1139, \cdot)\)	n/a	992	4
4026.2.ca	\(\chi_{4026}(1613, \cdot)\)	n/a	992	4
4026.2.cb	\(\chi_{4026}(365, \cdot)\)	n/a	992	4
4026.2.cd	\(\chi_{4026}(131, \cdot)\)	n/a	992	4
4026.2.ch	\(\chi_{4026}(611, \cdot)\)	n/a	960	4
4026.2.ci	\(\chi_{4026}(95, \cdot)\)	n/a	992	4
4026.2.cj	\(\chi_{4026}(1559, \cdot)\)	n/a	992	4
4026.2.cm	\(\chi_{4026}(149, \cdot)\)	n/a	992	4
4026.2.co	\(\chi_{4026}(1699, \cdot)\)	n/a	496	4
4026.2.cq	\(\chi_{4026}(947, \cdot)\)	n/a	832	4
4026.2.ct	\(\chi_{4026}(703, \cdot)\)	n/a	496	4
4026.2.cu	\(\chi_{4026}(25, \cdot)\)	n/a	992	8
4026.2.cv	\(\chi_{4026}(361, \cdot)\)	n/a	992	8
4026.2.cw	\(\chi_{4026}(199, \cdot)\)	n/a	832	8
4026.2.cx	\(\chi_{4026}(301, \cdot)\)	n/a	992	8
4026.2.cy	\(\chi_{4026}(757, \cdot)\)	n/a	992	8
4026.2.cz	\(\chi_{4026}(169, \cdot)\)	n/a	992	8
4026.2.db	\(\chi_{4026}(85, \cdot)\)	n/a	992	8
4026.2.dd	\(\chi_{4026}(1379, \cdot)\)	n/a	1984	8
4026.2.de	\(\chi_{4026}(191, \cdot)\)	n/a	1984	8
4026.2.df	\(\chi_{4026}(389, \cdot)\)	n/a	1984	8
4026.2.dg	\(\chi_{4026}(377, \cdot)\)	n/a	1984	8
4026.2.dl	\(\chi_{4026}(23, \cdot)\)	n/a	1632	8
4026.2.dm	\(\chi_{4026}(175, \cdot)\)	n/a	992	8
4026.2.dr	\(\chi_{4026}(211, \cdot)\)	n/a	992	8
4026.2.ds	\(\chi_{4026}(877, \cdot)\)	n/a	992	8
4026.2.dt	\(\chi_{4026}(721, \cdot)\)	n/a	992	8
4026.2.du	\(\chi_{4026}(145, \cdot)\)	n/a	992	8
4026.2.dw	\(\chi_{4026}(53, \cdot)\)	n/a	1984	8
4026.2.dz	\(\chi_{4026}(229, \cdot)\)	n/a	992	8
4026.2.eb	\(\chi_{4026}(431, \cdot)\)	n/a	1984	8
4026.2.ee	\(\chi_{4026}(413, \cdot)\)	n/a	1984	8
4026.2.ef	\(\chi_{4026}(503, \cdot)\)	n/a	1984	8
4026.2.eg	\(\chi_{4026}(83, \cdot)\)	n/a	1984	8
4026.2.ek	\(\chi_{4026}(1781, \cdot)\)	n/a	1984	8
4026.2.em	\(\chi_{4026}(167, \cdot)\)	n/a	1984	8
4026.2.en	\(\chi_{4026}(107, \cdot)\)	n/a	1984	8
4026.2.eo	\(\chi_{4026}(563, \cdot)\)	n/a	1984	8
4026.2.es	\(\chi_{4026}(65, \cdot)\)	n/a	1984	8
4026.2.et	\(\chi_{4026}(1601, \cdot)\)	n/a	1984	8
4026.2.ew	\(\chi_{4026}(463, \cdot)\)	n/a	800	8
4026.2.fa	\(\chi_{4026}(685, \cdot)\)	n/a	992	8
4026.2.fb	\(\chi_{4026}(97, \cdot)\)	n/a	992	8
4026.2.fc	\(\chi_{4026}(1147, \cdot)\)	n/a	992	8
4026.2.fj	\(\chi_{4026}(49, \cdot)\)	n/a	992	8
4026.2.fk	\(\chi_{4026}(545, \cdot)\)	n/a	1984	8
4026.2.fm	\(\chi_{4026}(161, \cdot)\)	n/a	1984	8
4026.2.fp	\(\chi_{4026}(59, \cdot)\)	n/a	3968	16
4026.2.fr	\(\chi_{4026}(7, \cdot)\)	n/a	1984	16
4026.2.fs	\(\chi_{4026}(151, \cdot)\)	n/a	1984	16
4026.2.ft	\(\chi_{4026}(349, \cdot)\)	n/a	1984	16
4026.2.fu	\(\chi_{4026}(139, \cdot)\)	n/a	1984	16
4026.2.fz	\(\chi_{4026}(43, \cdot)\)	n/a	1984	16
4026.2.ga	\(\chi_{4026}(287, \cdot)\)	n/a	3328	16
4026.2.gf	\(\chi_{4026}(467, \cdot)\)	n/a	3968	16
4026.2.gg	\(\chi_{4026}(185, \cdot)\)	n/a	3968	16
4026.2.gh	\(\chi_{4026}(251, \cdot)\)	n/a	3968	16
4026.2.gi	\(\chi_{4026}(71, \cdot)\)	n/a	3968	16
4026.2.gk	\(\chi_{4026}(79, \cdot)\)	n/a	1984	16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4026))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4026)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(61))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(122))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(183))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(366))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(671))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1342))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2013))\)\(^{\oplus 2}\)