# Properties

 Label 4275.2 Level 4275 Weight 2 Dimension 467052 Nonzero newspaces 96 Sturm bound 2592000

## Defining parameters

 Level: $$N$$ = $$4275 = 3^{2} \cdot 5^{2} \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$96$$ Sturm bound: $$2592000$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4275))$$.

Total New Old
Modular forms 656064 473324 182740
Cusp forms 639937 467052 172885
Eisenstein series 16127 6272 9855

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4275))$$

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
4275.2.a $$\chi_{4275}(1, \cdot)$$ 4275.2.a.a 1 1
4275.2.a.b 1
4275.2.a.c 1
4275.2.a.d 1
4275.2.a.e 1
4275.2.a.f 1
4275.2.a.g 1
4275.2.a.h 1
4275.2.a.i 1
4275.2.a.j 1
4275.2.a.k 1
4275.2.a.l 1
4275.2.a.m 1
4275.2.a.n 1
4275.2.a.o 1
4275.2.a.p 1
4275.2.a.q 1
4275.2.a.r 2
4275.2.a.s 2
4275.2.a.t 2
4275.2.a.u 2
4275.2.a.v 2
4275.2.a.w 2
4275.2.a.x 2
4275.2.a.y 2
4275.2.a.z 3
4275.2.a.ba 3
4275.2.a.bb 3
4275.2.a.bc 3
4275.2.a.bd 3
4275.2.a.be 3
4275.2.a.bf 3
4275.2.a.bg 3
4275.2.a.bh 3
4275.2.a.bi 3
4275.2.a.bj 3
4275.2.a.bk 3
4275.2.a.bl 3
4275.2.a.bm 3
4275.2.a.bn 3
4275.2.a.bo 4
4275.2.a.bp 4
4275.2.a.bq 6
4275.2.a.br 6
4275.2.a.bs 6
4275.2.a.bt 6
4275.2.a.bu 6
4275.2.a.bv 7
4275.2.a.bw 7
4275.2.a.bx 12
4275.2.b $$\chi_{4275}(4274, \cdot)$$ n/a 120 1
4275.2.c $$\chi_{4275}(2224, \cdot)$$ n/a 136 1
4275.2.h $$\chi_{4275}(2051, \cdot)$$ n/a 128 1
4275.2.i $$\chi_{4275}(1426, \cdot)$$ n/a 684 2
4275.2.j $$\chi_{4275}(976, \cdot)$$ n/a 748 2
4275.2.k $$\chi_{4275}(676, \cdot)$$ n/a 312 2
4275.2.l $$\chi_{4275}(2101, \cdot)$$ n/a 748 2
4275.2.n $$\chi_{4275}(818, \cdot)$$ n/a 216 2
4275.2.p $$\chi_{4275}(1918, \cdot)$$ n/a 296 2
4275.2.q $$\chi_{4275}(856, \cdot)$$ n/a 904 4
4275.2.t $$\chi_{4275}(49, \cdot)$$ n/a 712 2
4275.2.u $$\chi_{4275}(1874, \cdot)$$ n/a 712 2
4275.2.x $$\chi_{4275}(626, \cdot)$$ n/a 748 2
4275.2.y $$\chi_{4275}(1076, \cdot)$$ n/a 748 2
4275.2.bd $$\chi_{4275}(1376, \cdot)$$ n/a 256 2
4275.2.be $$\chi_{4275}(449, \cdot)$$ n/a 240 2
4275.2.bf $$\chi_{4275}(1774, \cdot)$$ n/a 296 2
4275.2.bk $$\chi_{4275}(799, \cdot)$$ n/a 648 2
4275.2.bl $$\chi_{4275}(1474, \cdot)$$ n/a 712 2
4275.2.bm $$\chi_{4275}(1424, \cdot)$$ n/a 712 2
4275.2.bn $$\chi_{4275}(749, \cdot)$$ n/a 712 2
4275.2.bq $$\chi_{4275}(3926, \cdot)$$ n/a 748 2
4275.2.bt $$\chi_{4275}(226, \cdot)$$ n/a 930 6
4275.2.bu $$\chi_{4275}(301, \cdot)$$ n/a 2244 6
4275.2.bv $$\chi_{4275}(1201, \cdot)$$ n/a 2244 6
4275.2.by $$\chi_{4275}(341, \cdot)$$ n/a 800 4
4275.2.bz $$\chi_{4275}(514, \cdot)$$ n/a 896 4
4275.2.ca $$\chi_{4275}(854, \cdot)$$ n/a 800 4
4275.2.cd $$\chi_{4275}(943, \cdot)$$ n/a 1424 4
4275.2.cf $$\chi_{4275}(68, \cdot)$$ n/a 1424 4
4275.2.ch $$\chi_{4275}(368, \cdot)$$ n/a 480 4
4275.2.ck $$\chi_{4275}(493, \cdot)$$ n/a 1424 4
4275.2.cm $$\chi_{4275}(1057, \cdot)$$ n/a 1424 4
4275.2.co $$\chi_{4275}(932, \cdot)$$ n/a 1296 4
4275.2.cq $$\chi_{4275}(182, \cdot)$$ n/a 1424 4
4275.2.cr $$\chi_{4275}(1243, \cdot)$$ n/a 592 4
4275.2.ct $$\chi_{4275}(391, \cdot)$$ n/a 4768 8
4275.2.cu $$\chi_{4275}(106, \cdot)$$ n/a 4768 8
4275.2.cv $$\chi_{4275}(286, \cdot)$$ n/a 4320 8
4275.2.cw $$\chi_{4275}(406, \cdot)$$ n/a 1984 8
4275.2.cz $$\chi_{4275}(1024, \cdot)$$ n/a 2136 6
4275.2.da $$\chi_{4275}(299, \cdot)$$ n/a 2136 6
4275.2.db $$\chi_{4275}(401, \cdot)$$ n/a 2244 6
4275.2.dc $$\chi_{4275}(926, \cdot)$$ n/a 756 6
4275.2.dl $$\chi_{4275}(1649, \cdot)$$ n/a 2136 6
4275.2.dm $$\chi_{4275}(199, \cdot)$$ n/a 888 6
4275.2.dn $$\chi_{4275}(224, \cdot)$$ n/a 720 6
4275.2.do $$\chi_{4275}(499, \cdot)$$ n/a 2136 6
4275.2.dp $$\chi_{4275}(326, \cdot)$$ n/a 2244 6
4275.2.ds $$\chi_{4275}(37, \cdot)$$ n/a 1984 8
4275.2.du $$\chi_{4275}(647, \cdot)$$ n/a 1440 8
4275.2.dw $$\chi_{4275}(506, \cdot)$$ n/a 4768 8
4275.2.dz $$\chi_{4275}(64, \cdot)$$ n/a 1984 8
4275.2.ea $$\chi_{4275}(179, \cdot)$$ n/a 1600 8
4275.2.ef $$\chi_{4275}(734, \cdot)$$ n/a 4768 8
4275.2.eg $$\chi_{4275}(284, \cdot)$$ n/a 4768 8
4275.2.eh $$\chi_{4275}(619, \cdot)$$ n/a 4768 8
4275.2.ei $$\chi_{4275}(229, \cdot)$$ n/a 4320 8
4275.2.en $$\chi_{4275}(221, \cdot)$$ n/a 4768 8
4275.2.eo $$\chi_{4275}(56, \cdot)$$ n/a 4768 8
4275.2.et $$\chi_{4275}(521, \cdot)$$ n/a 1600 8
4275.2.ew $$\chi_{4275}(164, \cdot)$$ n/a 4768 8
4275.2.ex $$\chi_{4275}(904, \cdot)$$ n/a 4768 8
4275.2.ez $$\chi_{4275}(218, \cdot)$$ n/a 4272 12
4275.2.fc $$\chi_{4275}(268, \cdot)$$ n/a 4272 12
4275.2.fd $$\chi_{4275}(307, \cdot)$$ n/a 1776 12
4275.2.fe $$\chi_{4275}(632, \cdot)$$ n/a 4272 12
4275.2.ff $$\chi_{4275}(332, \cdot)$$ n/a 1440 12
4275.2.fi $$\chi_{4275}(193, \cdot)$$ n/a 4272 12
4275.2.fk $$\chi_{4275}(61, \cdot)$$ n/a 14304 24
4275.2.fl $$\chi_{4275}(271, \cdot)$$ n/a 5952 24
4275.2.fm $$\chi_{4275}(16, \cdot)$$ n/a 14304 24
4275.2.fo $$\chi_{4275}(217, \cdot)$$ n/a 3968 16
4275.2.fp $$\chi_{4275}(353, \cdot)$$ n/a 9536 16
4275.2.fr $$\chi_{4275}(77, \cdot)$$ n/a 8640 16
4275.2.ft $$\chi_{4275}(202, \cdot)$$ n/a 9536 16
4275.2.fv $$\chi_{4275}(322, \cdot)$$ n/a 9536 16
4275.2.fy $$\chi_{4275}(197, \cdot)$$ n/a 3200 16
4275.2.ga $$\chi_{4275}(83, \cdot)$$ n/a 9536 16
4275.2.gc $$\chi_{4275}(88, \cdot)$$ n/a 9536 16
4275.2.gd $$\chi_{4275}(344, \cdot)$$ n/a 14304 24
4275.2.ge $$\chi_{4275}(4, \cdot)$$ n/a 14304 24
4275.2.gl $$\chi_{4275}(71, \cdot)$$ n/a 4800 24
4275.2.gm $$\chi_{4275}(41, \cdot)$$ n/a 14304 24
4275.2.gn $$\chi_{4275}(454, \cdot)$$ n/a 14304 24
4275.2.go $$\chi_{4275}(89, \cdot)$$ n/a 4800 24
4275.2.gp $$\chi_{4275}(244, \cdot)$$ n/a 5952 24
4275.2.gq $$\chi_{4275}(14, \cdot)$$ n/a 14304 24
4275.2.gx $$\chi_{4275}(86, \cdot)$$ n/a 14304 24
4275.2.gz $$\chi_{4275}(22, \cdot)$$ n/a 28608 48
4275.2.hc $$\chi_{4275}(23, \cdot)$$ n/a 28608 48
4275.2.hd $$\chi_{4275}(17, \cdot)$$ n/a 9600 48
4275.2.he $$\chi_{4275}(13, \cdot)$$ n/a 28608 48
4275.2.hf $$\chi_{4275}(127, \cdot)$$ n/a 11904 48
4275.2.hi $$\chi_{4275}(47, \cdot)$$ n/a 28608 48

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(4275))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(4275)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(57))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(75))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(95))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(171))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(225))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(285))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(475))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(855))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1425))$$$$^{\oplus 2}$$