Space of modular forms of level 7865 and weight 2

• Label: 7865.2
• Level: 7865
• Weight: 2
• Dimension: 2163816
• Nonzero newspaces: 80
• Sturm bound: 9757440

Defining parameters

Level:	\( N \)	=	\( 7865 = 5 \cdot 11^{2} \cdot 13 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 80 \)
Sturm bound:			\(9757440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7865))\).

	Total	New	Old
Modular forms	2454720	2182364	272356
Cusp forms	2424001	2163816	260185
Eisenstein series	30719	18548	12171

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7865))\)

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
7865.2.a	\(\chi_{7865}(1, \cdot)\)	7865.2.a.a	1	1
		7865.2.a.b	1
		7865.2.a.c	1
		7865.2.a.d	1
		7865.2.a.e	1
		7865.2.a.f	2
		7865.2.a.g	2
		7865.2.a.h	2
		7865.2.a.i	2
		7865.2.a.j	2
		7865.2.a.k	3
		7865.2.a.l	3
		7865.2.a.m	4
		7865.2.a.n	4
		7865.2.a.o	6
		7865.2.a.p	6
		7865.2.a.q	7
		7865.2.a.r	7
		7865.2.a.s	8
		7865.2.a.t	8
		7865.2.a.u	8
		7865.2.a.v	9
		7865.2.a.w	9
		7865.2.a.x	9
		7865.2.a.y	9
		7865.2.a.z	9
		7865.2.a.ba	11
		7865.2.a.bb	11
		7865.2.a.bc	11
		7865.2.a.bd	11
		7865.2.a.be	16
		7865.2.a.bf	16
		7865.2.a.bg	18
		7865.2.a.bh	18
		7865.2.a.bi	22
		7865.2.a.bj	22
		7865.2.a.bk	22
		7865.2.a.bl	22
		7865.2.a.bm	26
		7865.2.a.bn	26
		7865.2.a.bo	30
		7865.2.a.bp	30
7865.2.b	\(\chi_{7865}(1574, \cdot)\)	n/a	654	1
7865.2.e	\(\chi_{7865}(5446, \cdot)\)	n/a	510	1
7865.2.f	\(\chi_{7865}(7019, \cdot)\)	n/a	744	1
7865.2.i	\(\chi_{7865}(1816, \cdot)\)	n/a	1016	2
7865.2.j	\(\chi_{7865}(3268, \cdot)\)	n/a	1490	2
7865.2.l	\(\chi_{7865}(3024, \cdot)\)	n/a	1480	2
7865.2.o	\(\chi_{7865}(3992, \cdot)\)	n/a	1296	2
7865.2.q	\(\chi_{7865}(1572, \cdot)\)	n/a	1480	2
7865.2.s	\(\chi_{7865}(1451, \cdot)\)	n/a	1008	2
7865.2.t	\(\chi_{7865}(122, \cdot)\)	n/a	1490	2
7865.2.v	\(\chi_{7865}(4486, \cdot)\)	n/a	1728	4
7865.2.y	\(\chi_{7865}(4599, \cdot)\)	n/a	1488	2
7865.2.z	\(\chi_{7865}(3026, \cdot)\)	n/a	1016	2
7865.2.bc	\(\chi_{7865}(3389, \cdot)\)	n/a	1492	2
7865.2.bf	\(\chi_{7865}(3639, \cdot)\)	n/a	2960	4
7865.2.bg	\(\chi_{7865}(2066, \cdot)\)	n/a	2016	4
7865.2.bj	\(\chi_{7865}(729, \cdot)\)	n/a	2592	4
7865.2.bk	\(\chi_{7865}(716, \cdot)\)	n/a	5280	10
7865.2.bm	\(\chi_{7865}(1332, \cdot)\)	n/a	2980	4
7865.2.bn	\(\chi_{7865}(241, \cdot)\)	n/a	2016	4
7865.2.bp	\(\chi_{7865}(2298, \cdot)\)	n/a	2960	4
7865.2.br	\(\chi_{7865}(1088, \cdot)\)	n/a	2960	4
7865.2.bu	\(\chi_{7865}(604, \cdot)\)	n/a	2960	4
7865.2.bw	\(\chi_{7865}(2542, \cdot)\)	n/a	2980	4
7865.2.bx	\(\chi_{7865}(81, \cdot)\)	n/a	4032	8
7865.2.bz	\(\chi_{7865}(3518, \cdot)\)	n/a	5920	8
7865.2.ca	\(\chi_{7865}(161, \cdot)\)	n/a	4032	8
7865.2.cc	\(\chi_{7865}(233, \cdot)\)	n/a	5920	8
7865.2.ce	\(\chi_{7865}(118, \cdot)\)	n/a	5184	8
7865.2.ch	\(\chi_{7865}(239, \cdot)\)	n/a	5920	8
7865.2.cj	\(\chi_{7865}(148, \cdot)\)	n/a	5920	8
7865.2.cl	\(\chi_{7865}(584, \cdot)\)	n/a	9200	10
7865.2.co	\(\chi_{7865}(144, \cdot)\)	n/a	7920	10
7865.2.cp	\(\chi_{7865}(441, \cdot)\)	n/a	6160	10
7865.2.cr	\(\chi_{7865}(9, \cdot)\)	n/a	5920	8
7865.2.cu	\(\chi_{7865}(251, \cdot)\)	n/a	4032	8
7865.2.cv	\(\chi_{7865}(1219, \cdot)\)	n/a	5920	8
7865.2.cy	\(\chi_{7865}(276, \cdot)\)	n/a	12320	20
7865.2.da	\(\chi_{7865}(463, \cdot)\)	n/a	18400	20
7865.2.dc	\(\chi_{7865}(109, \cdot)\)	n/a	18400	20
7865.2.dd	\(\chi_{7865}(142, \cdot)\)	n/a	18400	20
7865.2.df	\(\chi_{7865}(417, \cdot)\)	n/a	15840	20
7865.2.dh	\(\chi_{7865}(21, \cdot)\)	n/a	12320	20
7865.2.dk	\(\chi_{7865}(177, \cdot)\)	n/a	18400	20
7865.2.dl	\(\chi_{7865}(196, \cdot)\)	n/a	21120	40
7865.2.dm	\(\chi_{7865}(202, \cdot)\)	n/a	11840	16
7865.2.do	\(\chi_{7865}(1129, \cdot)\)	n/a	11840	16
7865.2.dr	\(\chi_{7865}(282, \cdot)\)	n/a	11840	16
7865.2.dt	\(\chi_{7865}(602, \cdot)\)	n/a	11840	16
7865.2.dv	\(\chi_{7865}(336, \cdot)\)	n/a	8064	16
7865.2.dw	\(\chi_{7865}(323, \cdot)\)	n/a	11840	16
7865.2.dz	\(\chi_{7865}(56, \cdot)\)	n/a	12320	20
7865.2.ea	\(\chi_{7865}(419, \cdot)\)	n/a	18400	20
7865.2.ed	\(\chi_{7865}(199, \cdot)\)	n/a	18400	20
7865.2.eg	\(\chi_{7865}(181, \cdot)\)	n/a	24640	40
7865.2.eh	\(\chi_{7865}(14, \cdot)\)	n/a	31680	40
7865.2.ek	\(\chi_{7865}(64, \cdot)\)	n/a	36800	40
7865.2.em	\(\chi_{7865}(188, \cdot)\)	n/a	36800	40
7865.2.ep	\(\chi_{7865}(76, \cdot)\)	n/a	24640	40
7865.2.er	\(\chi_{7865}(87, \cdot)\)	n/a	36800	40
7865.2.et	\(\chi_{7865}(43, \cdot)\)	n/a	36800	40
7865.2.eu	\(\chi_{7865}(54, \cdot)\)	n/a	36800	40
7865.2.ew	\(\chi_{7865}(67, \cdot)\)	n/a	36800	40
7865.2.ey	\(\chi_{7865}(16, \cdot)\)	n/a	49280	80
7865.2.ez	\(\chi_{7865}(47, \cdot)\)	n/a	73600	80
7865.2.fc	\(\chi_{7865}(96, \cdot)\)	n/a	49280	80
7865.2.fe	\(\chi_{7865}(183, \cdot)\)	n/a	63360	80
7865.2.fg	\(\chi_{7865}(272, \cdot)\)	n/a	73600	80
7865.2.fh	\(\chi_{7865}(294, \cdot)\)	n/a	73600	80
7865.2.fj	\(\chi_{7865}(203, \cdot)\)	n/a	73600	80
7865.2.fm	\(\chi_{7865}(4, \cdot)\)	n/a	73600	80
7865.2.fp	\(\chi_{7865}(159, \cdot)\)	n/a	73600	80
7865.2.fq	\(\chi_{7865}(36, \cdot)\)	n/a	49280	80
7865.2.ft	\(\chi_{7865}(97, \cdot)\)	n/a	147200	160
7865.2.fv	\(\chi_{7865}(19, \cdot)\)	n/a	147200	160
7865.2.fw	\(\chi_{7865}(17, \cdot)\)	n/a	147200	160
7865.2.fy	\(\chi_{7865}(68, \cdot)\)	n/a	147200	160
7865.2.ga	\(\chi_{7865}(6, \cdot)\)	n/a	98560	160
7865.2.gd	\(\chi_{7865}(37, \cdot)\)	n/a	147200	160

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7865))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7865)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(143))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(605))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(715))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1573))\)\(^{\oplus 2}\)