Space of modular forms of level 7448 and weight 2

• Label: 7448.2
• Level: 7448
• Weight: 2
• Dimension: 905709
• Nonzero newspaces: 96
• Sturm bound: 6773760

Defining parameters

Level:	$N$	=	$7448 = 2^{3} \cdot 7^{2} \cdot 19$
Weight:	$k$	=	$2$
Nonzero newspaces:			$96$
Sturm bound:			$6773760$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_1(7448))$.

	Total	New	Old
Modular forms	1706400	912305	794095
Cusp forms	1680481	905709	774772
Eisenstein series	25919	6596	19323

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_1(7448))$

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
7448.2.a	$\chi_{7448}(1, \cdot)$	7448.2.a.a	1	1
		7448.2.a.b	1
		7448.2.a.c	1
		7448.2.a.d	1
		7448.2.a.e	1
		7448.2.a.f	1
		7448.2.a.g	1
		7448.2.a.h	1
		7448.2.a.i	1
		7448.2.a.j	1
		7448.2.a.k	1
		7448.2.a.l	1
		7448.2.a.m	1
		7448.2.a.n	1
		7448.2.a.o	1
		7448.2.a.p	1
		7448.2.a.q	1
		7448.2.a.r	1
		7448.2.a.s	1
		7448.2.a.t	1
		7448.2.a.u	1
		7448.2.a.v	1
		7448.2.a.w	2
		7448.2.a.x	2
		7448.2.a.y	2
		7448.2.a.z	2
		7448.2.a.ba	2
		7448.2.a.bb	2
		7448.2.a.bc	2
		7448.2.a.bd	2
		7448.2.a.be	2
		7448.2.a.bf	3
		7448.2.a.bg	3
		7448.2.a.bh	3
		7448.2.a.bi	3
		7448.2.a.bj	4
		7448.2.a.bk	4
		7448.2.a.bl	5
		7448.2.a.bm	6
		7448.2.a.bn	6
		7448.2.a.bo	7
		7448.2.a.bp	7
		7448.2.a.bq	8
		7448.2.a.br	8
		7448.2.a.bs	11
		7448.2.a.bt	11
		7448.2.a.bu	14
		7448.2.a.bv	14
		7448.2.a.bw	14
		7448.2.a.bx	14
7448.2.b	$\chi_{7448}(3725, \cdot)$	n/a	738	1
7448.2.e	$\chi_{7448}(6763, \cdot)$	n/a	810	1
7448.2.f	$\chi_{7448}(1861, \cdot)$	n/a	792	1
7448.2.i	$\chi_{7448}(2547, \cdot)$	n/a	720	1
7448.2.j	$\chi_{7448}(6271, \cdot)$	None	0	1
7448.2.m	$\chi_{7448}(5585, \cdot)$	n/a	200	1
7448.2.n	$\chi_{7448}(3039, \cdot)$	None	0	1
7448.2.q	$\chi_{7448}(3497, \cdot)$	n/a	360	2
7448.2.r	$\chi_{7448}(1569, \cdot)$	n/a	410	2
7448.2.s	$\chi_{7448}(3313, \cdot)$	n/a	400	2
7448.2.t	$\chi_{7448}(961, \cdot)$	n/a	400	2
7448.2.u	$\chi_{7448}(2971, \cdot)$	n/a	1584	2
7448.2.x	$\chi_{7448}(901, \cdot)$	n/a	1584	2
7448.2.y	$\chi_{7448}(4587, \cdot)$	n/a	1584	2
7448.2.bb	$\chi_{7448}(3693, \cdot)$	n/a	1584	2
7448.2.bc	$\chi_{7448}(521, \cdot)$	n/a	400	2
7448.2.bf	$\chi_{7448}(3351, \cdot)$	None	0	2
7448.2.bh	$\chi_{7448}(1471, \cdot)$	None	0	2
7448.2.bj	$\chi_{7448}(2431, \cdot)$	None	0	2
7448.2.bn	$\chi_{7448}(391, \cdot)$	None	0	2
7448.2.bp	$\chi_{7448}(2089, \cdot)$	n/a	400	2
7448.2.bq	$\chi_{7448}(2775, \cdot)$	None	0	2
7448.2.bs	$\chi_{7448}(1665, \cdot)$	n/a	400	2
7448.2.bw	$\chi_{7448}(4967, \cdot)$	None	0	2
7448.2.bx	$\chi_{7448}(1243, \cdot)$	n/a	1584	2
7448.2.ca	$\chi_{7448}(1341, \cdot)$	n/a	1584	2
7448.2.cc	$\chi_{7448}(293, \cdot)$	n/a	1584	2
7448.2.ce	$\chi_{7448}(3155, \cdot)$	n/a	1440	2
7448.2.cf	$\chi_{7448}(2469, \cdot)$	n/a	1584	2
7448.2.ch	$\chi_{7448}(4115, \cdot)$	n/a	1584	2
7448.2.ck	$\chi_{7448}(197, \cdot)$	n/a	1620	2
7448.2.cm	$\chi_{7448}(2811, \cdot)$	n/a	1584	2
7448.2.cn	$\chi_{7448}(3117, \cdot)$	n/a	1440	2
7448.2.cp	$\chi_{7448}(2843, \cdot)$	n/a	1620	2
7448.2.cr	$\chi_{7448}(619, \cdot)$	n/a	1584	2
7448.2.cu	$\chi_{7448}(4245, \cdot)$	n/a	1584	2
7448.2.cx	$\chi_{7448}(863, \cdot)$	None	0	2
7448.2.cy	$\chi_{7448}(4625, \cdot)$	n/a	400	2
7448.2.db	$\chi_{7448}(999, \cdot)$	None	0	2
7448.2.dc	$\chi_{7448}(1065, \cdot)$	n/a	1512	6
7448.2.dd	$\chi_{7448}(785, \cdot)$	n/a	1230	6
7448.2.de	$\chi_{7448}(177, \cdot)$	n/a	1200	6
7448.2.df	$\chi_{7448}(1745, \cdot)$	n/a	1200	6
7448.2.di	$\chi_{7448}(911, \cdot)$	None	0	6
7448.2.dj	$\chi_{7448}(265, \cdot)$	n/a	1680	6
7448.2.dm	$\chi_{7448}(951, \cdot)$	None	0	6
7448.2.dn	$\chi_{7448}(419, \cdot)$	n/a	6048	6
7448.2.dq	$\chi_{7448}(797, \cdot)$	n/a	6696	6
7448.2.dr	$\chi_{7448}(379, \cdot)$	n/a	6696	6
7448.2.du	$\chi_{7448}(533, \cdot)$	n/a	6048	6
7448.2.dv	$\chi_{7448}(1783, \cdot)$	None	0	6
7448.2.dw	$\chi_{7448}(79, \cdot)$	None	0	6
7448.2.dz	$\chi_{7448}(117, \cdot)$	n/a	4752	6
7448.2.ea	$\chi_{7448}(557, \cdot)$	n/a	4752	6
7448.2.ef	$\chi_{7448}(97, \cdot)$	n/a	1200	6
7448.2.ei	$\chi_{7448}(3449, \cdot)$	n/a	1200	6
7448.2.el	$\chi_{7448}(195, \cdot)$	n/a	4752	6
7448.2.em	$\chi_{7448}(1275, \cdot)$	n/a	4860	6
7448.2.ep	$\chi_{7448}(459, \cdot)$	n/a	4752	6
7448.2.eq	$\chi_{7448}(1403, \cdot)$	n/a	4752	6
7448.2.et	$\chi_{7448}(295, \cdot)$	None	0	6
7448.2.eu	$\chi_{7448}(783, \cdot)$	None	0	6
7448.2.ex	$\chi_{7448}(215, \cdot)$	None	0	6
7448.2.ey	$\chi_{7448}(471, \cdot)$	None	0	6
7448.2.fb	$\chi_{7448}(1373, \cdot)$	n/a	4860	6
7448.2.fc	$\chi_{7448}(1077, \cdot)$	n/a	4752	6
7448.2.ff	$\chi_{7448}(325, \cdot)$	n/a	4752	6
7448.2.fg	$\chi_{7448}(2125, \cdot)$	n/a	4752	6
7448.2.fh	$\chi_{7448}(129, \cdot)$	n/a	1200	6
7448.2.fk	$\chi_{7448}(67, \cdot)$	n/a	4752	6
7448.2.fl	$\chi_{7448}(803, \cdot)$	n/a	4752	6
7448.2.fo	$\chi_{7448}(1033, \cdot)$	n/a	3360	12
7448.2.fp	$\chi_{7448}(121, \cdot)$	n/a	3360	12
7448.2.fq	$\chi_{7448}(505, \cdot)$	n/a	3360	12
7448.2.fr	$\chi_{7448}(305, \cdot)$	n/a	3024	12
7448.2.fs	$\chi_{7448}(311, \cdot)$	None	0	12
7448.2.fv	$\chi_{7448}(297, \cdot)$	n/a	3360	12
7448.2.fw	$\chi_{7448}(487, \cdot)$	None	0	12
7448.2.fz	$\chi_{7448}(677, \cdot)$	n/a	13392	12
7448.2.gc	$\chi_{7448}(691, \cdot)$	n/a	13392	12
7448.2.ge	$\chi_{7448}(715, \cdot)$	n/a	13392	12
7448.2.gg	$\chi_{7448}(837, \cdot)$	n/a	12096	12
7448.2.gh	$\chi_{7448}(683, \cdot)$	n/a	13392	12
7448.2.gj	$\chi_{7448}(1037, \cdot)$	n/a	13392	12
7448.2.gm	$\chi_{7448}(83, \cdot)$	n/a	13392	12
7448.2.go	$\chi_{7448}(341, \cdot)$	n/a	13392	12
7448.2.gp	$\chi_{7448}(115, \cdot)$	n/a	12096	12
7448.2.gr	$\chi_{7448}(69, \cdot)$	n/a	13392	12
7448.2.gt	$\chi_{7448}(277, \cdot)$	n/a	13392	12
7448.2.gw	$\chi_{7448}(107, \cdot)$	n/a	13392	12
7448.2.gx	$\chi_{7448}(639, \cdot)$	None	0	12
7448.2.hb	$\chi_{7448}(601, \cdot)$	n/a	3360	12
7448.2.hd	$\chi_{7448}(495, \cdot)$	None	0	12
7448.2.he	$\chi_{7448}(873, \cdot)$	n/a	3360	12
7448.2.hg	$\chi_{7448}(615, \cdot)$	None	0	12
7448.2.hk	$\chi_{7448}(151, \cdot)$	None	0	12
7448.2.hm	$\chi_{7448}(183, \cdot)$	None	0	12
7448.2.ho	$\chi_{7448}(87, \cdot)$	None	0	12
7448.2.hr	$\chi_{7448}(145, \cdot)$	n/a	3360	12
7448.2.hs	$\chi_{7448}(429, \cdot)$	n/a	13392	12
7448.2.hv	$\chi_{7448}(331, \cdot)$	n/a	13392	12
7448.2.hw	$\chi_{7448}(829, \cdot)$	n/a	13392	12
7448.2.hz	$\chi_{7448}(467, \cdot)$	n/a	13392	12
7448.2.ia	$\chi_{7448}(25, \cdot)$	n/a	10080	36
7448.2.ib	$\chi_{7448}(169, \cdot)$	n/a	10080	36
7448.2.ic	$\chi_{7448}(9, \cdot)$	n/a	10080	36
7448.2.id	$\chi_{7448}(131, \cdot)$	n/a	40176	36
7448.2.ie	$\chi_{7448}(611, \cdot)$	n/a	40176	36
7448.2.ih	$\chi_{7448}(33, \cdot)$	n/a	10080	36
7448.2.im	$\chi_{7448}(13, \cdot)$	n/a	40176	36
7448.2.in	$\chi_{7448}(85, \cdot)$	n/a	40176	36
7448.2.iq	$\chi_{7448}(541, \cdot)$	n/a	40176	36
7448.2.ir	$\chi_{7448}(269, \cdot)$	n/a	40176	36
7448.2.iu	$\chi_{7448}(55, \cdot)$	None	0	36
7448.2.iv	$\chi_{7448}(15, \cdot)$	None	0	36
7448.2.iy	$\chi_{7448}(375, \cdot)$	None	0	36
7448.2.iz	$\chi_{7448}(47, \cdot)$	None	0	36
7448.2.jc	$\chi_{7448}(155, \cdot)$	n/a	40176	36
7448.2.jd	$\chi_{7448}(139, \cdot)$	n/a	40176	36
7448.2.jg	$\chi_{7448}(283, \cdot)$	n/a	40176	36
7448.2.jh	$\chi_{7448}(51, \cdot)$	n/a	40176	36
7448.2.jk	$\chi_{7448}(41, \cdot)$	n/a	10080	36
7448.2.jn	$\chi_{7448}(89, \cdot)$	n/a	10080	36
7448.2.jo	$\chi_{7448}(93, \cdot)$	n/a	40176	36
7448.2.jp	$\chi_{7448}(173, \cdot)$	n/a	40176	36
7448.2.js	$\chi_{7448}(135, \cdot)$	None	0	36
7448.2.jt	$\chi_{7448}(199, \cdot)$	None	0	36

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

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_1(7448))$ into lower level spaces

$S_{2}^{\mathrm{old}}(\Gamma_1(7448)) \cong$ $S_{2}^{\mathrm{new}}(\Gamma_1(1))$$^{\oplus 24}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$^{\oplus 18}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$^{\oplus 16}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$^{\oplus 9}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(76))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(98))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(133))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(152))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(196))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(266))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(392))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(532))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(931))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(1064))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(1862))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(3724))$$^{\oplus 2}$