# Properties

 Label 4284.2 Level 4284 Weight 2 Dimension 217372 Nonzero newspaces 100 Sturm bound 1990656

## Defining parameters

 Level: $$N$$ = $$4284 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 17$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$100$$ Sturm bound: $$1990656$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4284))$$.

Total New Old
Modular forms 505344 220068 285276
Cusp forms 489985 217372 272613
Eisenstein series 15359 2696 12663

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4284))$$

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
4284.2.a $$\chi_{4284}(1, \cdot)$$ 4284.2.a.a 1 1
4284.2.a.b 1
4284.2.a.c 1
4284.2.a.d 1
4284.2.a.e 1
4284.2.a.f 1
4284.2.a.g 1
4284.2.a.h 1
4284.2.a.i 1
4284.2.a.j 2
4284.2.a.k 2
4284.2.a.l 2
4284.2.a.m 2
4284.2.a.n 2
4284.2.a.o 2
4284.2.a.p 2
4284.2.a.q 2
4284.2.a.r 3
4284.2.a.s 3
4284.2.a.t 3
4284.2.a.u 3
4284.2.a.v 3
4284.2.c $$\chi_{4284}(307, \cdot)$$ n/a 320 1
4284.2.d $$\chi_{4284}(3025, \cdot)$$ 4284.2.d.a 2 1
4284.2.d.b 2
4284.2.d.c 2
4284.2.d.d 6
4284.2.d.e 8
4284.2.d.f 12
4284.2.d.g 12
4284.2.g $$\chi_{4284}(2141, \cdot)$$ 4284.2.g.a 48 1
4284.2.h $$\chi_{4284}(3095, \cdot)$$ n/a 192 1
4284.2.j $$\chi_{4284}(3401, \cdot)$$ 4284.2.j.a 20 1
4284.2.j.b 20
4284.2.m $$\chi_{4284}(1835, \cdot)$$ n/a 216 1
4284.2.n $$\chi_{4284}(3331, \cdot)$$ n/a 356 1
4284.2.q $$\chi_{4284}(1633, \cdot)$$ n/a 256 2
4284.2.r $$\chi_{4284}(1429, \cdot)$$ n/a 192 2
4284.2.s $$\chi_{4284}(613, \cdot)$$ n/a 108 2
4284.2.t $$\chi_{4284}(205, \cdot)$$ n/a 256 2
4284.2.v $$\chi_{4284}(55, \cdot)$$ n/a 712 2
4284.2.x $$\chi_{4284}(2393, \cdot)$$ 4284.2.x.a 96 2
4284.2.z $$\chi_{4284}(3277, \cdot)$$ 4284.2.z.a 4 2
4284.2.z.b 16
4284.2.z.c 16
4284.2.z.d 20
4284.2.z.e 32
4284.2.bb $$\chi_{4284}(2087, \cdot)$$ n/a 432 2
4284.2.bd $$\chi_{4284}(2209, \cdot)$$ n/a 288 2
4284.2.be $$\chi_{4284}(2551, \cdot)$$ n/a 1536 2
4284.2.bh $$\chi_{4284}(443, \cdot)$$ n/a 1536 2
4284.2.bi $$\chi_{4284}(1937, \cdot)$$ n/a 288 2
4284.2.bl $$\chi_{4284}(271, \cdot)$$ n/a 712 2
4284.2.bo $$\chi_{4284}(3127, \cdot)$$ n/a 1712 2
4284.2.br $$\chi_{4284}(475, \cdot)$$ n/a 1712 2
4284.2.bu $$\chi_{4284}(341, \cdot)$$ 4284.2.bu.a 4 2
4284.2.bu.b 4
4284.2.bu.c 4
4284.2.bu.d 4
4284.2.bu.e 36
4284.2.bu.f 36
4284.2.bv $$\chi_{4284}(407, \cdot)$$ n/a 1296 2
4284.2.by $$\chi_{4284}(1019, \cdot)$$ n/a 1712 2
4284.2.ca $$\chi_{4284}(545, \cdot)$$ n/a 256 2
4284.2.cb $$\chi_{4284}(1361, \cdot)$$ n/a 256 2
4284.2.cd $$\chi_{4284}(611, \cdot)$$ n/a 576 2
4284.2.cf $$\chi_{4284}(1529, \cdot)$$ 4284.2.cf.a 96 2
4284.2.ci $$\chi_{4284}(239, \cdot)$$ n/a 1152 2
4284.2.cj $$\chi_{4284}(2279, \cdot)$$ n/a 1536 2
4284.2.cl $$\chi_{4284}(713, \cdot)$$ n/a 288 2
4284.2.co $$\chi_{4284}(101, \cdot)$$ n/a 288 2
4284.2.cq $$\chi_{4284}(1871, \cdot)$$ n/a 512 2
4284.2.cr $$\chi_{4284}(1531, \cdot)$$ n/a 640 2
4284.2.ct $$\chi_{4284}(373, \cdot)$$ n/a 288 2
4284.2.cw $$\chi_{4284}(169, \cdot)$$ n/a 216 2
4284.2.cy $$\chi_{4284}(103, \cdot)$$ n/a 1536 2
4284.2.cz $$\chi_{4284}(1735, \cdot)$$ n/a 1536 2
4284.2.dc $$\chi_{4284}(1801, \cdot)$$ n/a 120 2
4284.2.dd $$\chi_{4284}(3467, \cdot)$$ n/a 1712 2
4284.2.dg $$\chi_{4284}(3197, \cdot)$$ n/a 256 2
4284.2.dj $$\chi_{4284}(1291, \cdot)$$ n/a 1712 2
4284.2.dk $$\chi_{4284}(253, \cdot)$$ n/a 184 4
4284.2.dl $$\chi_{4284}(1079, \cdot)$$ n/a 864 4
4284.2.do $$\chi_{4284}(559, \cdot)$$ n/a 1424 4
4284.2.dp $$\chi_{4284}(1385, \cdot)$$ n/a 192 4
4284.2.ds $$\chi_{4284}(89, \cdot)$$ n/a 192 4
4284.2.du $$\chi_{4284}(523, \cdot)$$ n/a 1424 4
4284.2.dw $$\chi_{4284}(421, \cdot)$$ n/a 432 4
4284.2.dy $$\chi_{4284}(191, \cdot)$$ n/a 3424 4
4284.2.eb $$\chi_{4284}(1271, \cdot)$$ n/a 3424 4
4284.2.ec $$\chi_{4284}(2461, \cdot)$$ n/a 576 4
4284.2.ef $$\chi_{4284}(625, \cdot)$$ n/a 576 4
4284.2.eg $$\chi_{4284}(659, \cdot)$$ n/a 2592 4
4284.2.ei $$\chi_{4284}(727, \cdot)$$ n/a 3424 4
4284.2.ek $$\chi_{4284}(2189, \cdot)$$ n/a 576 4
4284.2.en $$\chi_{4284}(353, \cdot)$$ n/a 576 4
4284.2.eo $$\chi_{4284}(1543, \cdot)$$ n/a 3424 4
4284.2.er $$\chi_{4284}(115, \cdot)$$ n/a 3424 4
4284.2.es $$\chi_{4284}(293, \cdot)$$ n/a 576 4
4284.2.eu $$\chi_{4284}(863, \cdot)$$ n/a 1152 4
4284.2.ew $$\chi_{4284}(361, \cdot)$$ n/a 240 4
4284.2.fa $$\chi_{4284}(181, \cdot)$$ n/a 480 8
4284.2.fb $$\chi_{4284}(197, \cdot)$$ n/a 288 8
4284.2.fc $$\chi_{4284}(379, \cdot)$$ n/a 2160 8
4284.2.fd $$\chi_{4284}(503, \cdot)$$ n/a 2304 8
4284.2.fi $$\chi_{4284}(865, \cdot)$$ n/a 480 8
4284.2.fj $$\chi_{4284}(179, \cdot)$$ n/a 2304 8
4284.2.fk $$\chi_{4284}(355, \cdot)$$ n/a 6848 8
4284.2.fl $$\chi_{4284}(257, \cdot)$$ n/a 1152 8
4284.2.fq $$\chi_{4284}(535, \cdot)$$ n/a 6848 8
4284.2.fr $$\chi_{4284}(223, \cdot)$$ n/a 6848 8
4284.2.fs $$\chi_{4284}(461, \cdot)$$ n/a 1152 8
4284.2.ft $$\chi_{4284}(185, \cdot)$$ n/a 1152 8
4284.2.fw $$\chi_{4284}(25, \cdot)$$ n/a 1152 8
4284.2.fx $$\chi_{4284}(263, \cdot)$$ n/a 6848 8
4284.2.gc $$\chi_{4284}(841, \cdot)$$ n/a 864 8
4284.2.gd $$\chi_{4284}(457, \cdot)$$ n/a 1152 8
4284.2.ge $$\chi_{4284}(695, \cdot)$$ n/a 6848 8
4284.2.gf $$\chi_{4284}(155, \cdot)$$ n/a 5184 8
4284.2.gk $$\chi_{4284}(19, \cdot)$$ n/a 2848 8
4284.2.gl $$\chi_{4284}(593, \cdot)$$ n/a 384 8
4284.2.gm $$\chi_{4284}(401, \cdot)$$ n/a 2304 16
4284.2.gn $$\chi_{4284}(241, \cdot)$$ n/a 2304 16
4284.2.gq $$\chi_{4284}(79, \cdot)$$ n/a 13696 16
4284.2.gr $$\chi_{4284}(299, \cdot)$$ n/a 13696 16
4284.2.gw $$\chi_{4284}(143, \cdot)$$ n/a 4608 16
4284.2.gx $$\chi_{4284}(167, \cdot)$$ n/a 13696 16
4284.2.gy $$\chi_{4284}(163, \cdot)$$ n/a 5696 16
4284.2.gz $$\chi_{4284}(211, \cdot)$$ n/a 10368 16
4284.2.he $$\chi_{4284}(233, \cdot)$$ n/a 768 16
4284.2.hf $$\chi_{4284}(29, \cdot)$$ n/a 1728 16
4284.2.hg $$\chi_{4284}(73, \cdot)$$ n/a 960 16
4284.2.hh $$\chi_{4284}(97, \cdot)$$ n/a 2304 16
4284.2.hm $$\chi_{4284}(61, \cdot)$$ n/a 2304 16
4284.2.hn $$\chi_{4284}(65, \cdot)$$ n/a 2304 16
4284.2.hq $$\chi_{4284}(131, \cdot)$$ n/a 13696 16
4284.2.hr $$\chi_{4284}(403, \cdot)$$ n/a 13696 16

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(4284))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(4284)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 36}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(34))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(51))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(68))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(84))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(102))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(119))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(126))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(153))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(204))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(238))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(252))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(306))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(357))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(476))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(612))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(714))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1071))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1428))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2142))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4284))$$$$^{\oplus 1}$$