# Properties

 Label 5775.2 Level 5775 Weight 2 Dimension 746736 Nonzero newspaces 168 Sturm bound 4608000

## Defining parameters

 Level: $$N$$ = $$5775 = 3 \cdot 5^{2} \cdot 7 \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$168$$ Sturm bound: $$4608000$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(5775))$$.

Total New Old
Modular forms 1165440 754112 411328
Cusp forms 1138561 746736 391825
Eisenstein series 26879 7376 19503

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(5775))$$

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
5775.2.a $$\chi_{5775}(1, \cdot)$$ 5775.2.a.a 1 1
5775.2.a.b 1
5775.2.a.c 1
5775.2.a.d 1
5775.2.a.e 1
5775.2.a.f 1
5775.2.a.g 1
5775.2.a.h 1
5775.2.a.i 1
5775.2.a.j 1
5775.2.a.k 1
5775.2.a.l 1
5775.2.a.m 1
5775.2.a.n 1
5775.2.a.o 1
5775.2.a.p 1
5775.2.a.q 1
5775.2.a.r 1
5775.2.a.s 1
5775.2.a.t 1
5775.2.a.u 1
5775.2.a.v 1
5775.2.a.w 1
5775.2.a.x 1
5775.2.a.y 1
5775.2.a.z 1
5775.2.a.ba 1
5775.2.a.bb 2
5775.2.a.bc 2
5775.2.a.bd 2
5775.2.a.be 2
5775.2.a.bf 2
5775.2.a.bg 2
5775.2.a.bh 2
5775.2.a.bi 2
5775.2.a.bj 2
5775.2.a.bk 2
5775.2.a.bl 2
5775.2.a.bm 2
5775.2.a.bn 2
5775.2.a.bo 2
5775.2.a.bp 3
5775.2.a.bq 3
5775.2.a.br 3
5775.2.a.bs 3
5775.2.a.bt 3
5775.2.a.bu 3
5775.2.a.bv 3
5775.2.a.bw 3
5775.2.a.bx 4
5775.2.a.by 4
5775.2.a.bz 4
5775.2.a.ca 4
5775.2.a.cb 4
5775.2.a.cc 4
5775.2.a.cd 5
5775.2.a.ce 5
5775.2.a.cf 5
5775.2.a.cg 5
5775.2.a.ch 5
5775.2.a.ci 5
5775.2.a.cj 5
5775.2.a.ck 5
5775.2.a.cl 5
5775.2.a.cm 10
5775.2.a.cn 10
5775.2.a.co 10
5775.2.a.cp 10
5775.2.c $$\chi_{5775}(1849, \cdot)$$ n/a 184 1
5775.2.d $$\chi_{5775}(5501, \cdot)$$ n/a 508 1
5775.2.f $$\chi_{5775}(4124, \cdot)$$ n/a 432 1
5775.2.i $$\chi_{5775}(76, \cdot)$$ n/a 304 1
5775.2.k $$\chi_{5775}(1924, \cdot)$$ n/a 288 1
5775.2.l $$\chi_{5775}(2276, \cdot)$$ n/a 456 1
5775.2.n $$\chi_{5775}(1574, \cdot)$$ n/a 480 1
5775.2.q $$\chi_{5775}(3301, \cdot)$$ n/a 508 2
5775.2.s $$\chi_{5775}(4082, \cdot)$$ n/a 720 2
5775.2.t $$\chi_{5775}(4157, \cdot)$$ n/a 1136 2
5775.2.v $$\chi_{5775}(1882, \cdot)$$ n/a 480 2
5775.2.y $$\chi_{5775}(43, \cdot)$$ n/a 432 2
5775.2.z $$\chi_{5775}(841, \cdot)$$ n/a 1440 4
5775.2.ba $$\chi_{5775}(1156, \cdot)$$ n/a 1216 4
5775.2.bb $$\chi_{5775}(526, \cdot)$$ n/a 912 4
5775.2.bc $$\chi_{5775}(421, \cdot)$$ n/a 1440 4
5775.2.bd $$\chi_{5775}(2941, \cdot)$$ n/a 1440 4
5775.2.be $$\chi_{5775}(1681, \cdot)$$ n/a 1440 4
5775.2.bg $$\chi_{5775}(1451, \cdot)$$ n/a 1192 2
5775.2.bh $$\chi_{5775}(2749, \cdot)$$ n/a 576 2
5775.2.bl $$\chi_{5775}(2399, \cdot)$$ n/a 960 2
5775.2.bn $$\chi_{5775}(551, \cdot)$$ n/a 1012 2
5775.2.bo $$\chi_{5775}(1024, \cdot)$$ n/a 480 2
5775.2.bq $$\chi_{5775}(901, \cdot)$$ n/a 608 2
5775.2.bt $$\chi_{5775}(1649, \cdot)$$ n/a 1136 2
5775.2.bv $$\chi_{5775}(706, \cdot)$$ n/a 1920 4
5775.2.bw $$\chi_{5775}(2129, \cdot)$$ n/a 2880 4
5775.2.by $$\chi_{5775}(1406, \cdot)$$ n/a 3808 4
5775.2.cb $$\chi_{5775}(379, \cdot)$$ n/a 1440 4
5775.2.cd $$\chi_{5775}(281, \cdot)$$ n/a 2880 4
5775.2.ce $$\chi_{5775}(2554, \cdot)$$ n/a 1920 4
5775.2.ch $$\chi_{5775}(2414, \cdot)$$ n/a 3808 4
5775.2.co $$\chi_{5775}(1259, \cdot)$$ n/a 3808 4
5775.2.cp $$\chi_{5775}(419, \cdot)$$ n/a 3200 4
5775.2.cq $$\chi_{5775}(1049, \cdot)$$ n/a 2272 4
5775.2.cs $$\chi_{5775}(1294, \cdot)$$ n/a 1920 4
5775.2.cx $$\chi_{5775}(701, \cdot)$$ n/a 1824 4
5775.2.cy $$\chi_{5775}(1121, \cdot)$$ n/a 2880 4
5775.2.cz $$\chi_{5775}(1646, \cdot)$$ n/a 2880 4
5775.2.da $$\chi_{5775}(349, \cdot)$$ n/a 1152 4
5775.2.db $$\chi_{5775}(769, \cdot)$$ n/a 1920 4
5775.2.dc $$\chi_{5775}(1084, \cdot)$$ n/a 1920 4
5775.2.dh $$\chi_{5775}(1436, \cdot)$$ n/a 2880 4
5775.2.dk $$\chi_{5775}(839, \cdot)$$ n/a 3808 4
5775.2.dm $$\chi_{5775}(2666, \cdot)$$ n/a 3808 4
5775.2.dn $$\chi_{5775}(1114, \cdot)$$ n/a 1440 4
5775.2.dq $$\chi_{5775}(134, \cdot)$$ n/a 2880 4
5775.2.dr $$\chi_{5775}(1231, \cdot)$$ n/a 1920 4
5775.2.ds $$\chi_{5775}(391, \cdot)$$ n/a 1920 4
5775.2.dt $$\chi_{5775}(601, \cdot)$$ n/a 1216 4
5775.2.ea $$\chi_{5775}(659, \cdot)$$ n/a 2880 4
5775.2.eb $$\chi_{5775}(29, \cdot)$$ n/a 2880 4
5775.2.ec $$\chi_{5775}(974, \cdot)$$ n/a 1728 4
5775.2.ed $$\chi_{5775}(1756, \cdot)$$ n/a 1920 4
5775.2.ef $$\chi_{5775}(169, \cdot)$$ n/a 1440 4
5775.2.ek $$\chi_{5775}(251, \cdot)$$ n/a 2384 4
5775.2.el $$\chi_{5775}(566, \cdot)$$ n/a 3808 4
5775.2.em $$\chi_{5775}(881, \cdot)$$ n/a 3200 4
5775.2.en $$\chi_{5775}(1324, \cdot)$$ n/a 864 4
5775.2.eo $$\chi_{5775}(64, \cdot)$$ n/a 1440 4
5775.2.ep $$\chi_{5775}(694, \cdot)$$ n/a 1184 4
5775.2.eu $$\chi_{5775}(146, \cdot)$$ n/a 3808 4
5775.2.ev $$\chi_{5775}(811, \cdot)$$ n/a 1920 4
5775.2.ey $$\chi_{5775}(239, \cdot)$$ n/a 2880 4
5775.2.fa $$\chi_{5775}(104, \cdot)$$ n/a 3808 4
5775.2.fc $$\chi_{5775}(2906, \cdot)$$ n/a 2880 4
5775.2.ff $$\chi_{5775}(139, \cdot)$$ n/a 1920 4
5775.2.fg $$\chi_{5775}(1957, \cdot)$$ n/a 1152 4
5775.2.fj $$\chi_{5775}(2707, \cdot)$$ n/a 960 4
5775.2.fl $$\chi_{5775}(593, \cdot)$$ n/a 2272 4
5775.2.fm $$\chi_{5775}(1607, \cdot)$$ n/a 1920 4
5775.2.fo $$\chi_{5775}(856, \cdot)$$ n/a 3840 8
5775.2.fp $$\chi_{5775}(1516, \cdot)$$ n/a 3840 8
5775.2.fq $$\chi_{5775}(676, \cdot)$$ n/a 2432 8
5775.2.fr $$\chi_{5775}(331, \cdot)$$ n/a 3200 8
5775.2.fs $$\chi_{5775}(16, \cdot)$$ n/a 3840 8
5775.2.ft $$\chi_{5775}(466, \cdot)$$ n/a 3840 8
5775.2.fv $$\chi_{5775}(167, \cdot)$$ n/a 7616 8
5775.2.fw $$\chi_{5775}(113, \cdot)$$ n/a 5760 8
5775.2.fy $$\chi_{5775}(442, \cdot)$$ n/a 2880 8
5775.2.gb $$\chi_{5775}(202, \cdot)$$ n/a 3840 8
5775.2.gd $$\chi_{5775}(727, \cdot)$$ n/a 3200 8
5775.2.gf $$\chi_{5775}(568, \cdot)$$ n/a 1728 8
5775.2.gg $$\chi_{5775}(127, \cdot)$$ n/a 2880 8
5775.2.gh $$\chi_{5775}(337, \cdot)$$ n/a 2880 8
5775.2.gl $$\chi_{5775}(673, \cdot)$$ n/a 2880 8
5775.2.gm $$\chi_{5775}(412, \cdot)$$ n/a 3840 8
5775.2.gq $$\chi_{5775}(97, \cdot)$$ n/a 3840 8
5775.2.gr $$\chi_{5775}(433, \cdot)$$ n/a 3840 8
5775.2.gs $$\chi_{5775}(643, \cdot)$$ n/a 2304 8
5775.2.gu $$\chi_{5775}(967, \cdot)$$ n/a 2880 8
5775.2.gw $$\chi_{5775}(617, \cdot)$$ n/a 4800 8
5775.2.gy $$\chi_{5775}(398, \cdot)$$ n/a 7616 8
5775.2.hc $$\chi_{5775}(272, \cdot)$$ n/a 7616 8
5775.2.hd $$\chi_{5775}(62, \cdot)$$ n/a 7616 8
5775.2.he $$\chi_{5775}(293, \cdot)$$ n/a 4544 8
5775.2.hh $$\chi_{5775}(218, \cdot)$$ n/a 3456 8
5775.2.hi $$\chi_{5775}(533, \cdot)$$ n/a 5760 8
5775.2.hj $$\chi_{5775}(92, \cdot)$$ n/a 5760 8
5775.2.hn $$\chi_{5775}(1247, \cdot)$$ n/a 5760 8
5775.2.hp $$\chi_{5775}(692, \cdot)$$ n/a 7616 8
5775.2.hr $$\chi_{5775}(509, \cdot)$$ n/a 7616 8
5775.2.ht $$\chi_{5775}(754, \cdot)$$ n/a 3840 8
5775.2.hw $$\chi_{5775}(431, \cdot)$$ n/a 7616 8
5775.2.hy $$\chi_{5775}(289, \cdot)$$ n/a 3840 8
5775.2.hz $$\chi_{5775}(311, \cdot)$$ n/a 7616 8
5775.2.ic $$\chi_{5775}(61, \cdot)$$ n/a 3840 8
5775.2.id $$\chi_{5775}(74, \cdot)$$ n/a 4544 8
5775.2.ie $$\chi_{5775}(464, \cdot)$$ n/a 7616 8
5775.2.if $$\chi_{5775}(494, \cdot)$$ n/a 7616 8
5775.2.im $$\chi_{5775}(376, \cdot)$$ n/a 2432 8
5775.2.in $$\chi_{5775}(271, \cdot)$$ n/a 3840 8
5775.2.io $$\chi_{5775}(241, \cdot)$$ n/a 3840 8
5775.2.ip $$\chi_{5775}(1019, \cdot)$$ n/a 7616 8
5775.2.ir $$\chi_{5775}(236, \cdot)$$ n/a 7616 8
5775.2.iw $$\chi_{5775}(529, \cdot)$$ n/a 3200 8
5775.2.ix $$\chi_{5775}(4, \cdot)$$ n/a 3840 8
5775.2.iy $$\chi_{5775}(499, \cdot)$$ n/a 2304 8
5775.2.iz $$\chi_{5775}(1046, \cdot)$$ n/a 6400 8
5775.2.ja $$\chi_{5775}(521, \cdot)$$ n/a 7616 8
5775.2.jb $$\chi_{5775}(26, \cdot)$$ n/a 4768 8
5775.2.jg $$\chi_{5775}(214, \cdot)$$ n/a 3840 8
5775.2.jh $$\chi_{5775}(359, \cdot)$$ n/a 7616 8
5775.2.jk $$\chi_{5775}(556, \cdot)$$ n/a 3840 8
5775.2.jm $$\chi_{5775}(94, \cdot)$$ n/a 3840 8
5775.2.jn $$\chi_{5775}(536, \cdot)$$ n/a 7616 8
5775.2.jq $$\chi_{5775}(1424, \cdot)$$ n/a 4544 8
5775.2.jr $$\chi_{5775}(89, \cdot)$$ n/a 6400 8
5775.2.js $$\chi_{5775}(614, \cdot)$$ n/a 7616 8
5775.2.jz $$\chi_{5775}(719, \cdot)$$ n/a 7616 8
5775.2.kb $$\chi_{5775}(611, \cdot)$$ n/a 7616 8
5775.2.kg $$\chi_{5775}(19, \cdot)$$ n/a 3840 8
5775.2.kh $$\chi_{5775}(439, \cdot)$$ n/a 3840 8
5775.2.ki $$\chi_{5775}(1174, \cdot)$$ n/a 2304 8
5775.2.kj $$\chi_{5775}(116, \cdot)$$ n/a 7616 8
5775.2.kk $$\chi_{5775}(296, \cdot)$$ n/a 7616 8
5775.2.kl $$\chi_{5775}(326, \cdot)$$ n/a 4768 8
5775.2.kq $$\chi_{5775}(409, \cdot)$$ n/a 3840 8
5775.2.kr $$\chi_{5775}(59, \cdot)$$ n/a 7616 8
5775.2.kv $$\chi_{5775}(1304, \cdot)$$ n/a 7616 8
5775.2.kw $$\chi_{5775}(1531, \cdot)$$ n/a 3840 8
5775.2.ky $$\chi_{5775}(394, \cdot)$$ n/a 3840 8
5775.2.lb $$\chi_{5775}(1466, \cdot)$$ n/a 7616 8
5775.2.lc $$\chi_{5775}(362, \cdot)$$ n/a 15232 16
5775.2.le $$\chi_{5775}(137, \cdot)$$ n/a 15232 16
5775.2.li $$\chi_{5775}(368, \cdot)$$ n/a 9088 16
5775.2.lj $$\chi_{5775}(158, \cdot)$$ n/a 15232 16
5775.2.lk $$\chi_{5775}(53, \cdot)$$ n/a 15232 16
5775.2.ln $$\chi_{5775}(17, \cdot)$$ n/a 15232 16
5775.2.lo $$\chi_{5775}(248, \cdot)$$ n/a 15232 16
5775.2.lp $$\chi_{5775}(68, \cdot)$$ n/a 9088 16
5775.2.lt $$\chi_{5775}(1223, \cdot)$$ n/a 15232 16
5775.2.lv $$\chi_{5775}(23, \cdot)$$ n/a 12800 16
5775.2.lx $$\chi_{5775}(142, \cdot)$$ n/a 7680 16
5775.2.lz $$\chi_{5775}(262, \cdot)$$ n/a 7680 16
5775.2.ma $$\chi_{5775}(808, \cdot)$$ n/a 7680 16
5775.2.mb $$\chi_{5775}(82, \cdot)$$ n/a 4608 16
5775.2.mf $$\chi_{5775}(103, \cdot)$$ n/a 7680 16
5775.2.mg $$\chi_{5775}(172, \cdot)$$ n/a 7680 16
5775.2.mk $$\chi_{5775}(193, \cdot)$$ n/a 4608 16
5775.2.ml $$\chi_{5775}(772, \cdot)$$ n/a 7680 16
5775.2.mm $$\chi_{5775}(667, \cdot)$$ n/a 7680 16
5775.2.mo $$\chi_{5775}(397, \cdot)$$ n/a 6400 16
5775.2.mq $$\chi_{5775}(388, \cdot)$$ n/a 7680 16
5775.2.mt $$\chi_{5775}(508, \cdot)$$ n/a 7680 16
5775.2.mv $$\chi_{5775}(212, \cdot)$$ n/a 15232 16
5775.2.mw $$\chi_{5775}(227, \cdot)$$ n/a 15232 16

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(5775))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(5775)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(75))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(77))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(105))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(165))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(175))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(231))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(275))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(385))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(525))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(825))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1155))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1925))$$$$^{\oplus 2}$$