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Properties

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

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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

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