# Properties

 Label 4620.2 Level 4620 Weight 2 Dimension 207904 Nonzero newspaces 96 Sturm bound 2211840

## Defining parameters

 Level: $$N$$ = $$4620 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$96$$ Sturm bound: $$2211840$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4620))$$.

Total New Old
Modular forms 562560 210048 352512
Cusp forms 543361 207904 335457
Eisenstein series 19199 2144 17055

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4620))$$

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
4620.2.a $$\chi_{4620}(1, \cdot)$$ 4620.2.a.a 1 1
4620.2.a.b 1
4620.2.a.c 1
4620.2.a.d 1
4620.2.a.e 1
4620.2.a.f 1
4620.2.a.g 1
4620.2.a.h 1
4620.2.a.i 1
4620.2.a.j 1
4620.2.a.k 1
4620.2.a.l 1
4620.2.a.m 1
4620.2.a.n 1
4620.2.a.o 2
4620.2.a.p 2
4620.2.a.q 2
4620.2.a.r 2
4620.2.a.s 2
4620.2.a.t 3
4620.2.a.u 3
4620.2.a.v 3
4620.2.a.w 3
4620.2.a.x 4
4620.2.f $$\chi_{4620}(769, \cdot)$$ 4620.2.f.a 4 1
4620.2.f.b 4
4620.2.f.c 4
4620.2.f.d 4
4620.2.f.e 40
4620.2.f.f 40
4620.2.g $$\chi_{4620}(1891, \cdot)$$ n/a 288 1
4620.2.h $$\chi_{4620}(1849, \cdot)$$ 4620.2.h.a 2 1
4620.2.h.b 2
4620.2.h.c 2
4620.2.h.d 14
4620.2.h.e 14
4620.2.h.f 14
4620.2.h.g 16
4620.2.i $$\chi_{4620}(1651, \cdot)$$ n/a 320 1
4620.2.j $$\chi_{4620}(1079, \cdot)$$ n/a 720 1
4620.2.k $$\chi_{4620}(881, \cdot)$$ n/a 104 1
4620.2.l $$\chi_{4620}(4619, \cdot)$$ n/a 1136 1
4620.2.m $$\chi_{4620}(1121, \cdot)$$ 4620.2.m.a 48 1
4620.2.m.b 48
4620.2.r $$\chi_{4620}(2729, \cdot)$$ n/a 160 1
4620.2.s $$\chi_{4620}(3851, \cdot)$$ n/a 480 1
4620.2.t $$\chi_{4620}(2969, \cdot)$$ n/a 144 1
4620.2.u $$\chi_{4620}(2771, \cdot)$$ n/a 768 1
4620.2.bd $$\chi_{4620}(3739, \cdot)$$ n/a 432 1
4620.2.be $$\chi_{4620}(3541, \cdot)$$ 4620.2.be.a 4 1
4620.2.be.b 4
4620.2.be.c 12
4620.2.be.d 12
4620.2.be.e 32
4620.2.bf $$\chi_{4620}(3499, \cdot)$$ n/a 480 1
4620.2.bg $$\chi_{4620}(2641, \cdot)$$ n/a 104 2
4620.2.bh $$\chi_{4620}(3233, \cdot)$$ n/a 384 2
4620.2.bi $$\chi_{4620}(1583, \cdot)$$ n/a 1728 2
4620.2.bn $$\chi_{4620}(617, \cdot)$$ n/a 240 2
4620.2.bo $$\chi_{4620}(1343, \cdot)$$ n/a 1920 2
4620.2.bp $$\chi_{4620}(2113, \cdot)$$ n/a 160 2
4620.2.bq $$\chi_{4620}(463, \cdot)$$ n/a 720 2
4620.2.bv $$\chi_{4620}(2353, \cdot)$$ n/a 144 2
4620.2.bw $$\chi_{4620}(307, \cdot)$$ n/a 1152 2
4620.2.bx $$\chi_{4620}(421, \cdot)$$ n/a 192 4
4620.2.cc $$\chi_{4620}(2201, \cdot)$$ n/a 216 2
4620.2.cd $$\chi_{4620}(3719, \cdot)$$ n/a 1920 2
4620.2.ce $$\chi_{4620}(3761, \cdot)$$ n/a 256 2
4620.2.cf $$\chi_{4620}(1319, \cdot)$$ n/a 2272 2
4620.2.cg $$\chi_{4620}(571, \cdot)$$ n/a 768 2
4620.2.ch $$\chi_{4620}(2089, \cdot)$$ n/a 192 2
4620.2.ci $$\chi_{4620}(2971, \cdot)$$ n/a 640 2
4620.2.cj $$\chi_{4620}(529, \cdot)$$ n/a 160 2
4620.2.co $$\chi_{4620}(241, \cdot)$$ n/a 128 2
4620.2.cp $$\chi_{4620}(1759, \cdot)$$ n/a 1152 2
4620.2.cq $$\chi_{4620}(199, \cdot)$$ n/a 960 2
4620.2.cz $$\chi_{4620}(1871, \cdot)$$ n/a 1280 2
4620.2.da $$\chi_{4620}(89, \cdot)$$ n/a 320 2
4620.2.db $$\chi_{4620}(131, \cdot)$$ n/a 1536 2
4620.2.dc $$\chi_{4620}(989, \cdot)$$ n/a 384 2
4620.2.dd $$\chi_{4620}(559, \cdot)$$ n/a 2304 4
4620.2.de $$\chi_{4620}(601, \cdot)$$ n/a 256 4
4620.2.df $$\chi_{4620}(799, \cdot)$$ n/a 1728 4
4620.2.do $$\chi_{4620}(1091, \cdot)$$ n/a 3072 4
4620.2.dp $$\chi_{4620}(29, \cdot)$$ n/a 576 4
4620.2.dq $$\chi_{4620}(71, \cdot)$$ n/a 2304 4
4620.2.dr $$\chi_{4620}(1049, \cdot)$$ n/a 768 4
4620.2.dw $$\chi_{4620}(281, \cdot)$$ n/a 384 4
4620.2.dx $$\chi_{4620}(1679, \cdot)$$ n/a 4544 4
4620.2.dy $$\chi_{4620}(1301, \cdot)$$ n/a 512 4
4620.2.dz $$\chi_{4620}(1499, \cdot)$$ n/a 3456 4
4620.2.ea $$\chi_{4620}(2071, \cdot)$$ n/a 1536 4
4620.2.eb $$\chi_{4620}(169, \cdot)$$ n/a 288 4
4620.2.ec $$\chi_{4620}(211, \cdot)$$ n/a 1152 4
4620.2.ed $$\chi_{4620}(349, \cdot)$$ n/a 384 4
4620.2.ek $$\chi_{4620}(397, \cdot)$$ n/a 320 4
4620.2.el $$\chi_{4620}(67, \cdot)$$ n/a 1920 4
4620.2.em $$\chi_{4620}(373, \cdot)$$ n/a 384 4
4620.2.en $$\chi_{4620}(703, \cdot)$$ n/a 2304 4
4620.2.es $$\chi_{4620}(593, \cdot)$$ n/a 768 4
4620.2.et $$\chi_{4620}(263, \cdot)$$ n/a 4544 4
4620.2.eu $$\chi_{4620}(2333, \cdot)$$ n/a 640 4
4620.2.ev $$\chi_{4620}(2663, \cdot)$$ n/a 3840 4
4620.2.ey $$\chi_{4620}(361, \cdot)$$ n/a 512 8
4620.2.ez $$\chi_{4620}(1063, \cdot)$$ n/a 4608 8
4620.2.fa $$\chi_{4620}(337, \cdot)$$ n/a 576 8
4620.2.ff $$\chi_{4620}(883, \cdot)$$ n/a 3456 8
4620.2.fg $$\chi_{4620}(97, \cdot)$$ n/a 768 8
4620.2.fh $$\chi_{4620}(587, \cdot)$$ n/a 9088 8
4620.2.fi $$\chi_{4620}(113, \cdot)$$ n/a 1152 8
4620.2.fn $$\chi_{4620}(743, \cdot)$$ n/a 6912 8
4620.2.fo $$\chi_{4620}(293, \cdot)$$ n/a 1536 8
4620.2.fp $$\chi_{4620}(149, \cdot)$$ n/a 1536 8
4620.2.fq $$\chi_{4620}(1151, \cdot)$$ n/a 6144 8
4620.2.fr $$\chi_{4620}(269, \cdot)$$ n/a 1536 8
4620.2.fs $$\chi_{4620}(191, \cdot)$$ n/a 6144 8
4620.2.gb $$\chi_{4620}(619, \cdot)$$ n/a 4608 8
4620.2.gc $$\chi_{4620}(79, \cdot)$$ n/a 4608 8
4620.2.gd $$\chi_{4620}(61, \cdot)$$ n/a 512 8
4620.2.gi $$\chi_{4620}(289, \cdot)$$ n/a 768 8
4620.2.gj $$\chi_{4620}(31, \cdot)$$ n/a 3072 8
4620.2.gk $$\chi_{4620}(409, \cdot)$$ n/a 768 8
4620.2.gl $$\chi_{4620}(151, \cdot)$$ n/a 3072 8
4620.2.gm $$\chi_{4620}(299, \cdot)$$ n/a 9088 8
4620.2.gn $$\chi_{4620}(821, \cdot)$$ n/a 1024 8
4620.2.go $$\chi_{4620}(179, \cdot)$$ n/a 9088 8
4620.2.gp $$\chi_{4620}(521, \cdot)$$ n/a 1024 8
4620.2.gw $$\chi_{4620}(47, \cdot)$$ n/a 18176 16
4620.2.gx $$\chi_{4620}(53, \cdot)$$ n/a 3072 16
4620.2.gy $$\chi_{4620}(107, \cdot)$$ n/a 18176 16
4620.2.gz $$\chi_{4620}(17, \cdot)$$ n/a 3072 16
4620.2.he $$\chi_{4620}(283, \cdot)$$ n/a 9216 16
4620.2.hf $$\chi_{4620}(193, \cdot)$$ n/a 1536 16
4620.2.hg $$\chi_{4620}(163, \cdot)$$ n/a 9216 16
4620.2.hh $$\chi_{4620}(157, \cdot)$$ n/a 1536 16

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(4620))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(4620)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(44))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(66))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(70))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(77))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(84))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(105))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(110))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(132))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(140))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(154))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(165))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(210))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(220))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(231))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(308))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(330))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(385))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(420))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(462))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(660))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(770))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(924))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1155))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1540))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2310))$$$$^{\oplus 2}$$