# Properties

 Label 4650.2 Level 4650 Weight 2 Dimension 132446 Nonzero newspaces 84 Sturm bound 2304000

## Defining parameters

 Level: $$N$$ = $$4650 = 2 \cdot 3 \cdot 5^{2} \cdot 31$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$84$$ Sturm bound: $$2304000$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4650))$$.

Total New Old
Modular forms 582720 132446 450274
Cusp forms 569281 132446 436835
Eisenstein series 13439 0 13439

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4650))$$

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
4650.2.a $$\chi_{4650}(1, \cdot)$$ 4650.2.a.a 1 1
4650.2.a.b 1
4650.2.a.c 1
4650.2.a.d 1
4650.2.a.e 1
4650.2.a.f 1
4650.2.a.g 1
4650.2.a.h 1
4650.2.a.i 1
4650.2.a.j 1
4650.2.a.k 1
4650.2.a.l 1
4650.2.a.m 1
4650.2.a.n 1
4650.2.a.o 1
4650.2.a.p 1
4650.2.a.q 1
4650.2.a.r 1
4650.2.a.s 1
4650.2.a.t 1
4650.2.a.u 1
4650.2.a.v 1
4650.2.a.w 1
4650.2.a.x 1
4650.2.a.y 1
4650.2.a.z 1
4650.2.a.ba 1
4650.2.a.bb 1
4650.2.a.bc 1
4650.2.a.bd 1
4650.2.a.be 1
4650.2.a.bf 1
4650.2.a.bg 1
4650.2.a.bh 1
4650.2.a.bi 1
4650.2.a.bj 1
4650.2.a.bk 1
4650.2.a.bl 1
4650.2.a.bm 1
4650.2.a.bn 1
4650.2.a.bo 1
4650.2.a.bp 1
4650.2.a.bq 1
4650.2.a.br 1
4650.2.a.bs 1
4650.2.a.bt 1
4650.2.a.bu 1
4650.2.a.bv 1
4650.2.a.bw 1
4650.2.a.bx 1
4650.2.a.by 2
4650.2.a.bz 2
4650.2.a.ca 2
4650.2.a.cb 2
4650.2.a.cc 2
4650.2.a.cd 2
4650.2.a.ce 2
4650.2.a.cf 2
4650.2.a.cg 2
4650.2.a.ch 2
4650.2.a.ci 3
4650.2.a.cj 3
4650.2.a.ck 3
4650.2.a.cl 3
4650.2.a.cm 3
4650.2.a.cn 3
4650.2.a.co 3
4650.2.a.cp 3
4650.2.d $$\chi_{4650}(3349, \cdot)$$ 4650.2.d.a 2 1
4650.2.d.b 2
4650.2.d.c 2
4650.2.d.d 2
4650.2.d.e 2
4650.2.d.f 2
4650.2.d.g 2
4650.2.d.h 2
4650.2.d.i 2
4650.2.d.j 2
4650.2.d.k 2
4650.2.d.l 2
4650.2.d.m 2
4650.2.d.n 2
4650.2.d.o 2
4650.2.d.p 2
4650.2.d.q 2
4650.2.d.r 2
4650.2.d.s 2
4650.2.d.t 2
4650.2.d.u 2
4650.2.d.v 2
4650.2.d.w 2
4650.2.d.x 2
4650.2.d.y 2
4650.2.d.z 2
4650.2.d.ba 2
4650.2.d.bb 2
4650.2.d.bc 4
4650.2.d.bd 4
4650.2.d.be 4
4650.2.d.bf 4
4650.2.d.bg 4
4650.2.d.bh 4
4650.2.d.bi 6
4650.2.d.bj 6
4650.2.e $$\chi_{4650}(4649, \cdot)$$ n/a 192 1
4650.2.h $$\chi_{4650}(1301, \cdot)$$ n/a 204 1
4650.2.i $$\chi_{4650}(3001, \cdot)$$ n/a 204 2
4650.2.j $$\chi_{4650}(2357, \cdot)$$ n/a 360 2
4650.2.k $$\chi_{4650}(2107, \cdot)$$ n/a 192 2
4650.2.n $$\chi_{4650}(721, \cdot)$$ n/a 640 4
4650.2.o $$\chi_{4650}(901, \cdot)$$ n/a 400 4
4650.2.p $$\chi_{4650}(1831, \cdot)$$ n/a 640 4
4650.2.q $$\chi_{4650}(1771, \cdot)$$ n/a 640 4
4650.2.r $$\chi_{4650}(481, \cdot)$$ n/a 640 4
4650.2.s $$\chi_{4650}(931, \cdot)$$ n/a 608 4
4650.2.t $$\chi_{4650}(2351, \cdot)$$ n/a 404 2
4650.2.w $$\chi_{4650}(1049, \cdot)$$ n/a 384 2
4650.2.x $$\chi_{4650}(1699, \cdot)$$ n/a 192 2
4650.2.ba $$\chi_{4650}(929, \cdot)$$ n/a 1280 4
4650.2.bb $$\chi_{4650}(559, \cdot)$$ n/a 592 4
4650.2.bg $$\chi_{4650}(581, \cdot)$$ n/a 1280 4
4650.2.bh $$\chi_{4650}(401, \cdot)$$ n/a 816 4
4650.2.bi $$\chi_{4650}(3191, \cdot)$$ n/a 1280 4
4650.2.bj $$\chi_{4650}(461, \cdot)$$ n/a 1280 4
4650.2.bs $$\chi_{4650}(1391, \cdot)$$ n/a 1280 4
4650.2.bv $$\chi_{4650}(109, \cdot)$$ n/a 640 4
4650.2.bw $$\chi_{4650}(89, \cdot)$$ n/a 1280 4
4650.2.bx $$\chi_{4650}(959, \cdot)$$ n/a 1280 4
4650.2.by $$\chi_{4650}(449, \cdot)$$ n/a 768 4
4650.2.bz $$\chi_{4650}(2209, \cdot)$$ n/a 640 4
4650.2.ca $$\chi_{4650}(349, \cdot)$$ n/a 384 4
4650.2.cb $$\chi_{4650}(469, \cdot)$$ n/a 640 4
4650.2.cc $$\chi_{4650}(1889, \cdot)$$ n/a 1280 4
4650.2.cl $$\chi_{4650}(29, \cdot)$$ n/a 1280 4
4650.2.cm $$\chi_{4650}(529, \cdot)$$ n/a 640 4
4650.2.cn $$\chi_{4650}(371, \cdot)$$ n/a 1280 4
4650.2.cs $$\chi_{4650}(3157, \cdot)$$ n/a 384 4
4650.2.ct $$\chi_{4650}(707, \cdot)$$ n/a 768 4
4650.2.cu $$\chi_{4650}(211, \cdot)$$ n/a 1280 8
4650.2.cv $$\chi_{4650}(1291, \cdot)$$ n/a 1280 8
4650.2.cw $$\chi_{4650}(661, \cdot)$$ n/a 1280 8
4650.2.cx $$\chi_{4650}(751, \cdot)$$ n/a 816 8
4650.2.cy $$\chi_{4650}(391, \cdot)$$ n/a 1280 8
4650.2.cz $$\chi_{4650}(121, \cdot)$$ n/a 1280 8
4650.2.da $$\chi_{4650}(337, \cdot)$$ n/a 1280 8
4650.2.db $$\chi_{4650}(233, \cdot)$$ n/a 2560 8
4650.2.dm $$\chi_{4650}(977, \cdot)$$ n/a 2560 8
4650.2.dn $$\chi_{4650}(247, \cdot)$$ n/a 1280 8
4650.2.do $$\chi_{4650}(277, \cdot)$$ n/a 1280 8
4650.2.dp $$\chi_{4650}(457, \cdot)$$ n/a 768 8
4650.2.dq $$\chi_{4650}(497, \cdot)$$ n/a 2400 8
4650.2.dr $$\chi_{4650}(407, \cdot)$$ n/a 1536 8
4650.2.ds $$\chi_{4650}(1163, \cdot)$$ n/a 2560 8
4650.2.dt $$\chi_{4650}(463, \cdot)$$ n/a 1280 8
4650.2.du $$\chi_{4650}(523, \cdot)$$ n/a 1280 8
4650.2.dv $$\chi_{4650}(47, \cdot)$$ n/a 2560 8
4650.2.ea $$\chi_{4650}(161, \cdot)$$ n/a 2560 8
4650.2.eb $$\chi_{4650}(1309, \cdot)$$ n/a 1280 8
4650.2.ec $$\chi_{4650}(239, \cdot)$$ n/a 2560 8
4650.2.el $$\chi_{4650}(179, \cdot)$$ n/a 2560 8
4650.2.em $$\chi_{4650}(19, \cdot)$$ n/a 1280 8
4650.2.en $$\chi_{4650}(919, \cdot)$$ n/a 1280 8
4650.2.eo $$\chi_{4650}(49, \cdot)$$ n/a 768 8
4650.2.ep $$\chi_{4650}(269, \cdot)$$ n/a 2560 8
4650.2.eq $$\chi_{4650}(1199, \cdot)$$ n/a 1536 8
4650.2.er $$\chi_{4650}(569, \cdot)$$ n/a 2560 8
4650.2.es $$\chi_{4650}(169, \cdot)$$ n/a 1280 8
4650.2.ev $$\chi_{4650}(611, \cdot)$$ n/a 2560 8
4650.2.fe $$\chi_{4650}(641, \cdot)$$ n/a 2560 8
4650.2.ff $$\chi_{4650}(251, \cdot)$$ n/a 1616 8
4650.2.fg $$\chi_{4650}(11, \cdot)$$ n/a 2560 8
4650.2.fh $$\chi_{4650}(911, \cdot)$$ n/a 2560 8
4650.2.fm $$\chi_{4650}(439, \cdot)$$ n/a 1280 8
4650.2.fn $$\chi_{4650}(119, \cdot)$$ n/a 2560 8
4650.2.fq $$\chi_{4650}(127, \cdot)$$ n/a 2560 16
4650.2.fr $$\chi_{4650}(227, \cdot)$$ n/a 5120 16
4650.2.fs $$\chi_{4650}(107, \cdot)$$ n/a 3072 16
4650.2.ft $$\chi_{4650}(377, \cdot)$$ n/a 5120 16
4650.2.fu $$\chi_{4650}(43, \cdot)$$ n/a 1536 16
4650.2.fv $$\chi_{4650}(13, \cdot)$$ n/a 2560 16
4650.2.fw $$\chi_{4650}(37, \cdot)$$ n/a 2560 16
4650.2.fx $$\chi_{4650}(173, \cdot)$$ n/a 5120 16
4650.2.fy $$\chi_{4650}(803, \cdot)$$ n/a 5120 16
4650.2.fz $$\chi_{4650}(73, \cdot)$$ n/a 2560 16
4650.2.gk $$\chi_{4650}(113, \cdot)$$ n/a 5120 16
4650.2.gl $$\chi_{4650}(613, \cdot)$$ n/a 2560 16

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(4650))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(4650)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(31))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(62))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(75))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(93))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(150))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(155))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(186))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(310))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(465))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(775))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(930))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1550))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2325))$$$$^{\oplus 2}$$