# Properties

 Label 4725.2 Level 4725 Weight 2 Dimension 539398 Nonzero newspaces 96 Sturm bound 3.1104e+06

## Defining parameters

 Level: $$N$$ = $$4725 = 3^{3} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$96$$ Sturm bound: $$3110400$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4725))$$.

Total New Old
Modular forms 787680 545958 241722
Cusp forms 767521 539398 228123
Eisenstein series 20159 6560 13599

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4725))$$

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
4725.2.a $$\chi_{4725}(1, \cdot)$$ 4725.2.a.a 1 1
4725.2.a.b 1
4725.2.a.c 1
4725.2.a.d 1
4725.2.a.e 1
4725.2.a.f 1
4725.2.a.g 1
4725.2.a.h 1
4725.2.a.i 1
4725.2.a.j 1
4725.2.a.k 1
4725.2.a.l 1
4725.2.a.m 1
4725.2.a.n 1
4725.2.a.o 1
4725.2.a.p 1
4725.2.a.q 1
4725.2.a.r 1
4725.2.a.s 1
4725.2.a.t 1
4725.2.a.u 2
4725.2.a.v 2
4725.2.a.w 2
4725.2.a.x 2
4725.2.a.y 2
4725.2.a.z 2
4725.2.a.ba 2
4725.2.a.bb 2
4725.2.a.bc 2
4725.2.a.bd 2
4725.2.a.be 2
4725.2.a.bf 2
4725.2.a.bg 2
4725.2.a.bh 2
4725.2.a.bi 3
4725.2.a.bj 3
4725.2.a.bk 3
4725.2.a.bl 3
4725.2.a.bm 4
4725.2.a.bn 4
4725.2.a.bo 4
4725.2.a.bp 4
4725.2.a.bq 4
4725.2.a.br 4
4725.2.a.bs 4
4725.2.a.bt 4
4725.2.a.bu 4
4725.2.a.bv 4
4725.2.a.bw 4
4725.2.a.bx 4
4725.2.a.by 4
4725.2.a.bz 4
4725.2.a.ca 5
4725.2.a.cb 5
4725.2.a.cc 5
4725.2.a.cd 5
4725.2.a.ce 8
4725.2.a.cf 8
4725.2.b $$\chi_{4725}(3401, \cdot)$$ n/a 202 1
4725.2.d $$\chi_{4725}(1324, \cdot)$$ n/a 144 1
4725.2.g $$\chi_{4725}(4724, \cdot)$$ n/a 192 1
4725.2.i $$\chi_{4725}(1576, \cdot)$$ n/a 228 2
4725.2.j $$\chi_{4725}(676, \cdot)$$ n/a 406 2
4725.2.k $$\chi_{4725}(1801, \cdot)$$ n/a 292 2
4725.2.l $$\chi_{4725}(226, \cdot)$$ n/a 292 2
4725.2.m $$\chi_{4725}(1268, \cdot)$$ n/a 288 2
4725.2.p $$\chi_{4725}(3268, \cdot)$$ n/a 384 2
4725.2.q $$\chi_{4725}(946, \cdot)$$ n/a 960 4
4725.2.s $$\chi_{4725}(424, \cdot)$$ n/a 280 2
4725.2.u $$\chi_{4725}(3176, \cdot)$$ n/a 292 2
4725.2.v $$\chi_{4725}(2474, \cdot)$$ n/a 280 2
4725.2.ba $$\chi_{4725}(1574, \cdot)$$ n/a 280 2
4725.2.bc $$\chi_{4725}(1349, \cdot)$$ n/a 384 2
4725.2.bf $$\chi_{4725}(1151, \cdot)$$ n/a 292 2
4725.2.bg $$\chi_{4725}(1999, \cdot)$$ n/a 384 2
4725.2.bi $$\chi_{4725}(2899, \cdot)$$ n/a 216 2
4725.2.bk $$\chi_{4725}(26, \cdot)$$ n/a 406 2
4725.2.bm $$\chi_{4725}(251, \cdot)$$ n/a 292 2
4725.2.bp $$\chi_{4725}(3124, \cdot)$$ n/a 280 2
4725.2.br $$\chi_{4725}(899, \cdot)$$ n/a 280 2
4725.2.bt $$\chi_{4725}(1201, \cdot)$$ n/a 2700 6
4725.2.bu $$\chi_{4725}(526, \cdot)$$ n/a 2052 6
4725.2.bv $$\chi_{4725}(151, \cdot)$$ n/a 2700 6
4725.2.bx $$\chi_{4725}(944, \cdot)$$ n/a 1280 4
4725.2.ca $$\chi_{4725}(379, \cdot)$$ n/a 960 4
4725.2.cc $$\chi_{4725}(566, \cdot)$$ n/a 1280 4
4725.2.cd $$\chi_{4725}(1018, \cdot)$$ n/a 560 4
4725.2.cg $$\chi_{4725}(3068, \cdot)$$ n/a 560 4
4725.2.ci $$\chi_{4725}(368, \cdot)$$ n/a 560 4
4725.2.ck $$\chi_{4725}(82, \cdot)$$ n/a 768 4
4725.2.cm $$\chi_{4725}(118, \cdot)$$ n/a 560 4
4725.2.cn $$\chi_{4725}(2843, \cdot)$$ n/a 432 4
4725.2.cp $$\chi_{4725}(107, \cdot)$$ n/a 768 4
4725.2.cr $$\chi_{4725}(3043, \cdot)$$ n/a 560 4
4725.2.ct $$\chi_{4725}(46, \cdot)$$ n/a 1888 8
4725.2.cu $$\chi_{4725}(361, \cdot)$$ n/a 1888 8
4725.2.cv $$\chi_{4725}(541, \cdot)$$ n/a 2560 8
4725.2.cw $$\chi_{4725}(316, \cdot)$$ n/a 1440 8
4725.2.cx $$\chi_{4725}(824, \cdot)$$ n/a 2568 6
4725.2.dc $$\chi_{4725}(299, \cdot)$$ n/a 2568 6
4725.2.de $$\chi_{4725}(524, \cdot)$$ n/a 2568 6
4725.2.dg $$\chi_{4725}(499, \cdot)$$ n/a 2568 6
4725.2.dj $$\chi_{4725}(551, \cdot)$$ n/a 2700 6
4725.2.dl $$\chi_{4725}(776, \cdot)$$ n/a 2700 6
4725.2.dn $$\chi_{4725}(949, \cdot)$$ n/a 2568 6
4725.2.dp $$\chi_{4725}(274, \cdot)$$ n/a 1944 6
4725.2.dq $$\chi_{4725}(101, \cdot)$$ n/a 2700 6
4725.2.ds $$\chi_{4725}(433, \cdot)$$ n/a 2560 8
4725.2.dv $$\chi_{4725}(323, \cdot)$$ n/a 1920 8
4725.2.dx $$\chi_{4725}(719, \cdot)$$ n/a 1888 8
4725.2.dz $$\chi_{4725}(289, \cdot)$$ n/a 1888 8
4725.2.ec $$\chi_{4725}(881, \cdot)$$ n/a 1888 8
4725.2.ee $$\chi_{4725}(836, \cdot)$$ n/a 2560 8
4725.2.eg $$\chi_{4725}(64, \cdot)$$ n/a 1440 8
4725.2.ei $$\chi_{4725}(109, \cdot)$$ n/a 2560 8
4725.2.ej $$\chi_{4725}(206, \cdot)$$ n/a 1888 8
4725.2.em $$\chi_{4725}(269, \cdot)$$ n/a 2560 8
4725.2.eo $$\chi_{4725}(314, \cdot)$$ n/a 1888 8
4725.2.et $$\chi_{4725}(89, \cdot)$$ n/a 1888 8
4725.2.eu $$\chi_{4725}(341, \cdot)$$ n/a 1888 8
4725.2.ew $$\chi_{4725}(604, \cdot)$$ n/a 1888 8
4725.2.ez $$\chi_{4725}(893, \cdot)$$ n/a 5136 12
4725.2.fa $$\chi_{4725}(643, \cdot)$$ n/a 5136 12
4725.2.fc $$\chi_{4725}(157, \cdot)$$ n/a 5136 12
4725.2.fe $$\chi_{4725}(218, \cdot)$$ n/a 3888 12
4725.2.fg $$\chi_{4725}(32, \cdot)$$ n/a 5136 12
4725.2.fj $$\chi_{4725}(418, \cdot)$$ n/a 5136 12
4725.2.fk $$\chi_{4725}(121, \cdot)$$ n/a 17184 24
4725.2.fl $$\chi_{4725}(16, \cdot)$$ n/a 17184 24
4725.2.fm $$\chi_{4725}(106, \cdot)$$ n/a 12960 24
4725.2.fo $$\chi_{4725}(208, \cdot)$$ n/a 3776 16
4725.2.fq $$\chi_{4725}(53, \cdot)$$ n/a 5120 16
4725.2.fs $$\chi_{4725}(8, \cdot)$$ n/a 2880 16
4725.2.ft $$\chi_{4725}(748, \cdot)$$ n/a 3776 16
4725.2.fv $$\chi_{4725}(703, \cdot)$$ n/a 5120 16
4725.2.fx $$\chi_{4725}(548, \cdot)$$ n/a 3776 16
4725.2.fz $$\chi_{4725}(233, \cdot)$$ n/a 3776 16
4725.2.gc $$\chi_{4725}(73, \cdot)$$ n/a 3776 16
4725.2.gd $$\chi_{4725}(131, \cdot)$$ n/a 17184 24
4725.2.gg $$\chi_{4725}(4, \cdot)$$ n/a 17184 24
4725.2.gi $$\chi_{4725}(169, \cdot)$$ n/a 12960 24
4725.2.gk $$\chi_{4725}(236, \cdot)$$ n/a 17184 24
4725.2.gm $$\chi_{4725}(41, \cdot)$$ n/a 17184 24
4725.2.gn $$\chi_{4725}(184, \cdot)$$ n/a 17184 24
4725.2.gr $$\chi_{4725}(59, \cdot)$$ n/a 17184 24
4725.2.gt $$\chi_{4725}(104, \cdot)$$ n/a 17184 24
4725.2.gw $$\chi_{4725}(164, \cdot)$$ n/a 17184 24
4725.2.gz $$\chi_{4725}(52, \cdot)$$ n/a 34368 48
4725.2.ha $$\chi_{4725}(92, \cdot)$$ n/a 25920 48
4725.2.hc $$\chi_{4725}(2, \cdot)$$ n/a 34368 48
4725.2.he $$\chi_{4725}(13, \cdot)$$ n/a 34368 48
4725.2.hg $$\chi_{4725}(187, \cdot)$$ n/a 34368 48
4725.2.hj $$\chi_{4725}(23, \cdot)$$ n/a 34368 48

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(4725))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(4725)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(27))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(75))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(105))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(135))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(175))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(189))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(225))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(315))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(525))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(675))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(945))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1575))$$$$^{\oplus 2}$$