# Properties

 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

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