# Properties

 Label 5472.2 Level 5472 Weight 2 Dimension 365778 Nonzero newspaces 96 Sturm bound 3317760

# Learn more about

## Defining parameters

 Level: $$N$$ = $$5472 = 2^{5} \cdot 3^{2} \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$96$$ Sturm bound: $$3317760$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(5472))$$.

Total New Old
Modular forms 838656 368838 469818
Cusp forms 820225 365778 454447
Eisenstein series 18431 3060 15371

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(5472))$$

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 the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
5472.2.a $$\chi_{5472}(1, \cdot)$$ 5472.2.a.a 1 1
5472.2.a.b 1
5472.2.a.c 1
5472.2.a.d 1
5472.2.a.e 1
5472.2.a.f 1
5472.2.a.g 1
5472.2.a.h 1
5472.2.a.i 1
5472.2.a.j 1
5472.2.a.k 1
5472.2.a.l 1
5472.2.a.m 1
5472.2.a.n 1
5472.2.a.o 1
5472.2.a.p 1
5472.2.a.q 1
5472.2.a.r 1
5472.2.a.s 1
5472.2.a.t 1
5472.2.a.u 1
5472.2.a.v 1
5472.2.a.w 2
5472.2.a.x 2
5472.2.a.y 2
5472.2.a.z 2
5472.2.a.ba 2
5472.2.a.bb 2
5472.2.a.bc 2
5472.2.a.bd 2
5472.2.a.be 2
5472.2.a.bf 2
5472.2.a.bg 2
5472.2.a.bh 2
5472.2.a.bi 2
5472.2.a.bj 2
5472.2.a.bk 2
5472.2.a.bl 2
5472.2.a.bm 3
5472.2.a.bn 3
5472.2.a.bo 3
5472.2.a.bp 3
5472.2.a.bq 4
5472.2.a.br 4
5472.2.a.bs 4
5472.2.a.bt 4
5472.2.a.bu 4
5472.2.a.bv 4
5472.2.d $$\chi_{5472}(2015, \cdot)$$ 5472.2.d.a 4 1
5472.2.d.b 4
5472.2.d.c 4
5472.2.d.d 8
5472.2.d.e 8
5472.2.d.f 8
5472.2.d.g 16
5472.2.d.h 20
5472.2.e $$\chi_{5472}(5167, \cdot)$$ 5472.2.e.a 2 1
5472.2.e.b 4
5472.2.e.c 8
5472.2.e.d 8
5472.2.e.e 12
5472.2.e.f 24
5472.2.e.g 40
5472.2.f $$\chi_{5472}(1025, \cdot)$$ 5472.2.f.a 20 1
5472.2.f.b 20
5472.2.f.c 20
5472.2.f.d 20
5472.2.g $$\chi_{5472}(2737, \cdot)$$ 5472.2.g.a 2 1
5472.2.g.b 16
5472.2.g.c 18
5472.2.g.d 18
5472.2.g.e 36
5472.2.j $$\chi_{5472}(4751, \cdot)$$ 5472.2.j.a 4 1
5472.2.j.b 4
5472.2.j.c 28
5472.2.j.d 36
5472.2.k $$\chi_{5472}(2431, \cdot)$$ 5472.2.k.a 20 1
5472.2.k.b 20
5472.2.k.c 20
5472.2.k.d 40
5472.2.p $$\chi_{5472}(3761, \cdot)$$ 5472.2.p.a 80 1
5472.2.q $$\chi_{5472}(1825, \cdot)$$ n/a 432 2
5472.2.r $$\chi_{5472}(2401, \cdot)$$ n/a 480 2
5472.2.s $$\chi_{5472}(577, \cdot)$$ n/a 200 2
5472.2.t $$\chi_{5472}(961, \cdot)$$ n/a 480 2
5472.2.u $$\chi_{5472}(2393, \cdot)$$ None 0 2
5472.2.x $$\chi_{5472}(1369, \cdot)$$ None 0 2
5472.2.y $$\chi_{5472}(647, \cdot)$$ None 0 2
5472.2.bb $$\chi_{5472}(1063, \cdot)$$ None 0 2
5472.2.be $$\chi_{5472}(1489, \cdot)$$ n/a 472 2
5472.2.bf $$\chi_{5472}(65, \cdot)$$ n/a 480 2
5472.2.bg $$\chi_{5472}(2383, \cdot)$$ n/a 472 2
5472.2.bh $$\chi_{5472}(4415, \cdot)$$ n/a 480 2
5472.2.bm $$\chi_{5472}(1855, \cdot)$$ n/a 200 2
5472.2.bn $$\chi_{5472}(3887, \cdot)$$ n/a 160 2
5472.2.bq $$\chi_{5472}(113, \cdot)$$ n/a 472 2
5472.2.bt $$\chi_{5472}(977, \cdot)$$ n/a 472 2
5472.2.bu $$\chi_{5472}(1471, \cdot)$$ n/a 480 2
5472.2.bv $$\chi_{5472}(239, \cdot)$$ n/a 472 2
5472.2.by $$\chi_{5472}(1103, \cdot)$$ n/a 432 2
5472.2.bz $$\chi_{5472}(607, \cdot)$$ n/a 480 2
5472.2.cc $$\chi_{5472}(3185, \cdot)$$ n/a 160 2
5472.2.cf $$\chi_{5472}(559, \cdot)$$ n/a 196 2
5472.2.cg $$\chi_{5472}(1151, \cdot)$$ n/a 160 2
5472.2.cj $$\chi_{5472}(49, \cdot)$$ n/a 472 2
5472.2.ck $$\chi_{5472}(3713, \cdot)$$ n/a 480 2
5472.2.cn $$\chi_{5472}(2849, \cdot)$$ n/a 480 2
5472.2.co $$\chi_{5472}(913, \cdot)$$ n/a 432 2
5472.2.ct $$\chi_{5472}(191, \cdot)$$ n/a 432 2
5472.2.cu $$\chi_{5472}(1519, \cdot)$$ n/a 472 2
5472.2.cx $$\chi_{5472}(943, \cdot)$$ n/a 472 2
5472.2.cy $$\chi_{5472}(767, \cdot)$$ n/a 480 2
5472.2.db $$\chi_{5472}(1873, \cdot)$$ n/a 196 2
5472.2.dc $$\chi_{5472}(449, \cdot)$$ n/a 160 2
5472.2.dd $$\chi_{5472}(2801, \cdot)$$ n/a 472 2
5472.2.di $$\chi_{5472}(31, \cdot)$$ n/a 480 2
5472.2.dj $$\chi_{5472}(1679, \cdot)$$ n/a 472 2
5472.2.dm $$\chi_{5472}(685, \cdot)$$ n/a 1440 4
5472.2.dn $$\chi_{5472}(379, \cdot)$$ n/a 1592 4
5472.2.do $$\chi_{5472}(1331, \cdot)$$ n/a 1152 4
5472.2.dp $$\chi_{5472}(341, \cdot)$$ n/a 1280 4
5472.2.ds $$\chi_{5472}(289, \cdot)$$ n/a 600 6
5472.2.dt $$\chi_{5472}(2113, \cdot)$$ n/a 1440 6
5472.2.du $$\chi_{5472}(385, \cdot)$$ n/a 1440 6
5472.2.dw $$\chi_{5472}(505, \cdot)$$ None 0 4
5472.2.dx $$\chi_{5472}(521, \cdot)$$ None 0 4
5472.2.ea $$\chi_{5472}(1559, \cdot)$$ None 0 4
5472.2.eb $$\chi_{5472}(1015, \cdot)$$ None 0 4
5472.2.ed $$\chi_{5472}(103, \cdot)$$ None 0 4
5472.2.eg $$\chi_{5472}(1607, \cdot)$$ None 0 4
5472.2.ei $$\chi_{5472}(311, \cdot)$$ None 0 4
5472.2.ej $$\chi_{5472}(151, \cdot)$$ None 0 4
5472.2.em $$\chi_{5472}(569, \cdot)$$ None 0 4
5472.2.en $$\chi_{5472}(1033, \cdot)$$ None 0 4
5472.2.ep $$\chi_{5472}(121, \cdot)$$ None 0 4
5472.2.es $$\chi_{5472}(905, \cdot)$$ None 0 4
5472.2.eu $$\chi_{5472}(2345, \cdot)$$ None 0 4
5472.2.ev $$\chi_{5472}(457, \cdot)$$ None 0 4
5472.2.ey $$\chi_{5472}(487, \cdot)$$ None 0 4
5472.2.ez $$\chi_{5472}(1223, \cdot)$$ None 0 4
5472.2.fc $$\chi_{5472}(79, \cdot)$$ n/a 1416 6
5472.2.fe $$\chi_{5472}(671, \cdot)$$ n/a 1440 6
5472.2.ff $$\chi_{5472}(223, \cdot)$$ n/a 1440 6
5472.2.fh $$\chi_{5472}(1391, \cdot)$$ n/a 1416 6
5472.2.fj $$\chi_{5472}(1409, \cdot)$$ n/a 1440 6
5472.2.fl $$\chi_{5472}(625, \cdot)$$ n/a 1416 6
5472.2.fp $$\chi_{5472}(1169, \cdot)$$ n/a 480 6
5472.2.fq $$\chi_{5472}(1297, \cdot)$$ n/a 588 6
5472.2.fs $$\chi_{5472}(737, \cdot)$$ n/a 480 6
5472.2.fv $$\chi_{5472}(401, \cdot)$$ n/a 1416 6
5472.2.fx $$\chi_{5472}(47, \cdot)$$ n/a 1416 6
5472.2.fz $$\chi_{5472}(895, \cdot)$$ n/a 1440 6
5472.2.gc $$\chi_{5472}(1135, \cdot)$$ n/a 588 6
5472.2.ge $$\chi_{5472}(575, \cdot)$$ n/a 480 6
5472.2.gf $$\chi_{5472}(127, \cdot)$$ n/a 600 6
5472.2.gh $$\chi_{5472}(719, \cdot)$$ n/a 480 6
5472.2.gk $$\chi_{5472}(479, \cdot)$$ n/a 1440 6
5472.2.gm $$\chi_{5472}(1231, \cdot)$$ n/a 1416 6
5472.2.gp $$\chi_{5472}(497, \cdot)$$ n/a 1416 6
5472.2.gq $$\chi_{5472}(529, \cdot)$$ n/a 1416 6
5472.2.gs $$\chi_{5472}(257, \cdot)$$ n/a 1440 6
5472.2.gu $$\chi_{5472}(835, \cdot)$$ n/a 7648 8
5472.2.gv $$\chi_{5472}(229, \cdot)$$ n/a 6912 8
5472.2.gy $$\chi_{5472}(1133, \cdot)$$ n/a 2560 8
5472.2.gz $$\chi_{5472}(467, \cdot)$$ n/a 2560 8
5472.2.he $$\chi_{5472}(11, \cdot)$$ n/a 7648 8
5472.2.hf $$\chi_{5472}(293, \cdot)$$ n/a 7648 8
5472.2.hg $$\chi_{5472}(83, \cdot)$$ n/a 7648 8
5472.2.hh $$\chi_{5472}(221, \cdot)$$ n/a 7648 8
5472.2.hm $$\chi_{5472}(277, \cdot)$$ n/a 7648 8
5472.2.hn $$\chi_{5472}(259, \cdot)$$ n/a 7648 8
5472.2.ho $$\chi_{5472}(349, \cdot)$$ n/a 7648 8
5472.2.hp $$\chi_{5472}(331, \cdot)$$ n/a 7648 8
5472.2.hu $$\chi_{5472}(1171, \cdot)$$ n/a 3184 8
5472.2.hv $$\chi_{5472}(1189, \cdot)$$ n/a 3184 8
5472.2.hy $$\chi_{5472}(797, \cdot)$$ n/a 7648 8
5472.2.hz $$\chi_{5472}(419, \cdot)$$ n/a 6912 8
5472.2.ia $$\chi_{5472}(169, \cdot)$$ None 0 12
5472.2.ic $$\chi_{5472}(857, \cdot)$$ None 0 12
5472.2.ie $$\chi_{5472}(1031, \cdot)$$ None 0 12
5472.2.ih $$\chi_{5472}(775, \cdot)$$ None 0 12
5472.2.ij $$\chi_{5472}(215, \cdot)$$ None 0 12
5472.2.ik $$\chi_{5472}(295, \cdot)$$ None 0 12
5472.2.in $$\chi_{5472}(41, \cdot)$$ None 0 12
5472.2.io $$\chi_{5472}(73, \cdot)$$ None 0 12
5472.2.iq $$\chi_{5472}(89, \cdot)$$ None 0 12
5472.2.it $$\chi_{5472}(25, \cdot)$$ None 0 12
5472.2.iv $$\chi_{5472}(439, \cdot)$$ None 0 12
5472.2.ix $$\chi_{5472}(23, \cdot)$$ None 0 12
5472.2.iz $$\chi_{5472}(131, \cdot)$$ n/a 22944 24
5472.2.ja $$\chi_{5472}(29, \cdot)$$ n/a 22944 24
5472.2.jd $$\chi_{5472}(85, \cdot)$$ n/a 22944 24
5472.2.je $$\chi_{5472}(67, \cdot)$$ n/a 22944 24
5472.2.jh $$\chi_{5472}(253, \cdot)$$ n/a 9552 24
5472.2.ji $$\chi_{5472}(91, \cdot)$$ n/a 9552 24
5472.2.jk $$\chi_{5472}(173, \cdot)$$ n/a 22944 24
5472.2.jn $$\chi_{5472}(275, \cdot)$$ n/a 22944 24
5472.2.jo $$\chi_{5472}(53, \cdot)$$ n/a 7680 24
5472.2.jr $$\chi_{5472}(35, \cdot)$$ n/a 7680 24
5472.2.js $$\chi_{5472}(211, \cdot)$$ n/a 22944 24
5472.2.jv $$\chi_{5472}(61, \cdot)$$ n/a 22944 24

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(5472))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(5472)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 15}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(57))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(96))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(114))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(144))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(152))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(171))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(228))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(288))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(304))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(342))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(456))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(608))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(684))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(912))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1368))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1824))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2736))$$$$^{\oplus 2}$$