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Properties

Label 8775.2
Level 8775
Weight 2
Dimension 1951142
Nonzero newspaces 160
Sturm bound 10886400

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Defining parameters

Level: \( N \) = \( 8775 = 3^{3} \cdot 5^{2} \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 160 \)
Sturm bound: \(10886400\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8775))\).

Total New Old
Modular forms 2741760 1965574 776186
Cusp forms 2701441 1951142 750299
Eisenstein series 40319 14432 25887

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8775))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
8775.2.a \(\chi_{8775}(1, \cdot)\) 8775.2.a.a 1 1
8775.2.a.b 1
8775.2.a.c 1
8775.2.a.d 1
8775.2.a.e 1
8775.2.a.f 1
8775.2.a.g 1
8775.2.a.h 1
8775.2.a.i 1
8775.2.a.j 1
8775.2.a.k 1
8775.2.a.l 1
8775.2.a.m 1
8775.2.a.n 1
8775.2.a.o 1
8775.2.a.p 1
8775.2.a.q 1
8775.2.a.r 1
8775.2.a.s 2
8775.2.a.t 2
8775.2.a.u 2
8775.2.a.v 2
8775.2.a.w 2
8775.2.a.x 2
8775.2.a.y 2
8775.2.a.z 2
8775.2.a.ba 2
8775.2.a.bb 2
8775.2.a.bc 2
8775.2.a.bd 2
8775.2.a.be 2
8775.2.a.bf 2
8775.2.a.bg 4
8775.2.a.bh 4
8775.2.a.bi 4
8775.2.a.bj 4
8775.2.a.bk 4
8775.2.a.bl 4
8775.2.a.bm 4
8775.2.a.bn 4
8775.2.a.bo 4
8775.2.a.bp 4
8775.2.a.bq 4
8775.2.a.br 4
8775.2.a.bs 4
8775.2.a.bt 4
8775.2.a.bu 6
8775.2.a.bv 6
8775.2.a.bw 7
8775.2.a.bx 7
8775.2.a.by 8
8775.2.a.bz 8
8775.2.a.ca 8
8775.2.a.cb 8
8775.2.a.cc 8
8775.2.a.cd 8
8775.2.a.ce 8
8775.2.a.cf 8
8775.2.a.cg 8
8775.2.a.ch 8
8775.2.a.ci 8
8775.2.a.cj 8
8775.2.a.ck 12
8775.2.a.cl 12
8775.2.a.cm 12
8775.2.a.cn 12
8775.2.a.co 16
8775.2.a.cp 16
8775.2.b \(\chi_{8775}(1351, \cdot)\) n/a 354 1
8775.2.c \(\chi_{8775}(8074, \cdot)\) n/a 288 1
8775.2.h \(\chi_{8775}(649, \cdot)\) n/a 336 1
8775.2.i \(\chi_{8775}(2926, \cdot)\) n/a 456 2
8775.2.j \(\chi_{8775}(3376, \cdot)\) n/a 710 2
8775.2.k \(\chi_{8775}(451, \cdot)\) n/a 520 2
8775.2.l \(\chi_{8775}(4501, \cdot)\) n/a 520 2
8775.2.n \(\chi_{8775}(3268, \cdot)\) n/a 672 2
8775.2.p \(\chi_{8775}(1457, \cdot)\) n/a 576 2
8775.2.q \(\chi_{8775}(2699, \cdot)\) n/a 672 2
8775.2.r \(\chi_{8775}(3401, \cdot)\) n/a 708 2
8775.2.v \(\chi_{8775}(2807, \cdot)\) n/a 672 2
8775.2.w \(\chi_{8775}(1243, \cdot)\) n/a 672 2
8775.2.y \(\chi_{8775}(1756, \cdot)\) n/a 1920 4
8775.2.bb \(\chi_{8775}(901, \cdot)\) n/a 520 2
8775.2.bc \(\chi_{8775}(3799, \cdot)\) n/a 496 2
8775.2.bf \(\chi_{8775}(3574, \cdot)\) n/a 496 2
8775.2.bg \(\chi_{8775}(1999, \cdot)\) n/a 672 2
8775.2.bl \(\chi_{8775}(3124, \cdot)\) n/a 496 2
8775.2.bm \(\chi_{8775}(874, \cdot)\) n/a 496 2
8775.2.bn \(\chi_{8775}(3826, \cdot)\) n/a 520 2
8775.2.bs \(\chi_{8775}(2224, \cdot)\) n/a 432 2
8775.2.bt \(\chi_{8775}(2674, \cdot)\) n/a 672 2
8775.2.bu \(\chi_{8775}(4276, \cdot)\) n/a 520 2
8775.2.bv \(\chi_{8775}(2701, \cdot)\) n/a 710 2
8775.2.by \(\chi_{8775}(199, \cdot)\) n/a 496 2
8775.2.cb \(\chi_{8775}(976, \cdot)\) n/a 4104 6
8775.2.cc \(\chi_{8775}(2401, \cdot)\) n/a 4752 6
8775.2.cd \(\chi_{8775}(601, \cdot)\) n/a 4752 6
8775.2.cg \(\chi_{8775}(2404, \cdot)\) n/a 2240 4
8775.2.ch \(\chi_{8775}(1054, \cdot)\) n/a 1920 4
8775.2.ci \(\chi_{8775}(3106, \cdot)\) n/a 2240 4
8775.2.cl \(\chi_{8775}(982, \cdot)\) n/a 992 4
8775.2.cn \(\chi_{8775}(2143, \cdot)\) n/a 992 4
8775.2.cq \(\chi_{8775}(1432, \cdot)\) n/a 1344 4
8775.2.cr \(\chi_{8775}(2332, \cdot)\) n/a 992 4
8775.2.ct \(\chi_{8775}(1907, \cdot)\) n/a 992 4
8775.2.cx \(\chi_{8775}(1151, \cdot)\) n/a 1040 4
8775.2.cy \(\chi_{8775}(449, \cdot)\) n/a 992 4
8775.2.cz \(\chi_{8775}(368, \cdot)\) n/a 992 4
8775.2.dc \(\chi_{8775}(1232, \cdot)\) n/a 992 4
8775.2.dd \(\chi_{8775}(818, \cdot)\) n/a 992 4
8775.2.dg \(\chi_{8775}(3293, \cdot)\) n/a 1344 4
8775.2.dh \(\chi_{8775}(1376, \cdot)\) n/a 1420 4
8775.2.di \(\chi_{8775}(674, \cdot)\) n/a 1344 4
8775.2.dn \(\chi_{8775}(1799, \cdot)\) n/a 992 4
8775.2.do \(\chi_{8775}(4526, \cdot)\) n/a 1040 4
8775.2.dp \(\chi_{8775}(3824, \cdot)\) n/a 992 4
8775.2.dq \(\chi_{8775}(476, \cdot)\) n/a 1040 4
8775.2.du \(\chi_{8775}(2393, \cdot)\) n/a 864 4
8775.2.dv \(\chi_{8775}(1043, \cdot)\) n/a 992 4
8775.2.dy \(\chi_{8775}(107, \cdot)\) n/a 1344 4
8775.2.ea \(\chi_{8775}(2593, \cdot)\) n/a 1344 4
8775.2.eb \(\chi_{8775}(307, \cdot)\) n/a 992 4
8775.2.ee \(\chi_{8775}(3907, \cdot)\) n/a 992 4
8775.2.eg \(\chi_{8775}(1657, \cdot)\) n/a 992 4
8775.2.eh \(\chi_{8775}(991, \cdot)\) n/a 3328 8
8775.2.ei \(\chi_{8775}(406, \cdot)\) n/a 4480 8
8775.2.ej \(\chi_{8775}(586, \cdot)\) n/a 2880 8
8775.2.ek \(\chi_{8775}(2206, \cdot)\) n/a 3328 8
8775.2.el \(\chi_{8775}(1024, \cdot)\) n/a 4512 6
8775.2.ep \(\chi_{8775}(49, \cdot)\) n/a 4512 6
8775.2.es \(\chi_{8775}(1624, \cdot)\) n/a 4512 6
8775.2.ev \(\chi_{8775}(724, \cdot)\) n/a 4512 6
8775.2.ex \(\chi_{8775}(751, \cdot)\) n/a 4752 6
8775.2.ey \(\chi_{8775}(376, \cdot)\) n/a 4752 6
8775.2.fa \(\chi_{8775}(274, \cdot)\) n/a 3888 6
8775.2.fd \(\chi_{8775}(1699, \cdot)\) n/a 4512 6
8775.2.ff \(\chi_{8775}(1726, \cdot)\) n/a 4752 6
8775.2.fg \(\chi_{8775}(1162, \cdot)\) n/a 4480 8
8775.2.fi \(\chi_{8775}(1052, \cdot)\) n/a 4480 8
8775.2.fm \(\chi_{8775}(161, \cdot)\) n/a 4480 8
8775.2.fn \(\chi_{8775}(944, \cdot)\) n/a 4480 8
8775.2.fo \(\chi_{8775}(53, \cdot)\) n/a 3840 8
8775.2.fr \(\chi_{8775}(892, \cdot)\) n/a 4480 8
8775.2.fs \(\chi_{8775}(829, \cdot)\) n/a 3328 8
8775.2.fv \(\chi_{8775}(316, \cdot)\) n/a 3328 8
8775.2.fw \(\chi_{8775}(1504, \cdot)\) n/a 3328 8
8775.2.gb \(\chi_{8775}(946, \cdot)\) n/a 4480 8
8775.2.gc \(\chi_{8775}(181, \cdot)\) n/a 3328 8
8775.2.gd \(\chi_{8775}(919, \cdot)\) n/a 4480 8
8775.2.ge \(\chi_{8775}(469, \cdot)\) n/a 2880 8
8775.2.gj \(\chi_{8775}(244, \cdot)\) n/a 4480 8
8775.2.gk \(\chi_{8775}(64, \cdot)\) n/a 3328 8
8775.2.gp \(\chi_{8775}(1369, \cdot)\) n/a 3328 8
8775.2.gs \(\chi_{8775}(289, \cdot)\) n/a 3328 8
8775.2.gt \(\chi_{8775}(1531, \cdot)\) n/a 3328 8
8775.2.gu \(\chi_{8775}(268, \cdot)\) n/a 9024 12
8775.2.gx \(\chi_{8775}(193, \cdot)\) n/a 9024 12
8775.2.gy \(\chi_{8775}(457, \cdot)\) n/a 9024 12
8775.2.ha \(\chi_{8775}(149, \cdot)\) n/a 9024 12
8775.2.hc \(\chi_{8775}(551, \cdot)\) n/a 9504 12
8775.2.he \(\chi_{8775}(401, \cdot)\) n/a 9504 12
8775.2.hg \(\chi_{8775}(68, \cdot)\) n/a 9024 12
8775.2.hk \(\chi_{8775}(857, \cdot)\) n/a 9024 12
8775.2.hl \(\chi_{8775}(218, \cdot)\) n/a 9024 12
8775.2.hm \(\chi_{8775}(932, \cdot)\) n/a 9024 12
8775.2.hn \(\chi_{8775}(443, \cdot)\) n/a 7776 12
8775.2.hr \(\chi_{8775}(257, \cdot)\) n/a 9024 12
8775.2.ht \(\chi_{8775}(1424, \cdot)\) n/a 9024 12
8775.2.hv \(\chi_{8775}(749, \cdot)\) n/a 9024 12
8775.2.hx \(\chi_{8775}(176, \cdot)\) n/a 9504 12
8775.2.hz \(\chi_{8775}(232, \cdot)\) n/a 9024 12
8775.2.ia \(\chi_{8775}(7, \cdot)\) n/a 9024 12
8775.2.id \(\chi_{8775}(1282, \cdot)\) n/a 9024 12
8775.2.ie \(\chi_{8775}(16, \cdot)\) n/a 30144 24
8775.2.if \(\chi_{8775}(61, \cdot)\) n/a 30144 24
8775.2.ig \(\chi_{8775}(196, \cdot)\) n/a 25920 24
8775.2.ii \(\chi_{8775}(262, \cdot)\) n/a 6656 16
8775.2.ik \(\chi_{8775}(928, \cdot)\) n/a 6656 16
8775.2.il \(\chi_{8775}(28, \cdot)\) n/a 8960 16
8775.2.io \(\chi_{8775}(37, \cdot)\) n/a 6656 16
8775.2.ip \(\chi_{8775}(458, \cdot)\) n/a 8960 16
8775.2.is \(\chi_{8775}(692, \cdot)\) n/a 6656 16
8775.2.it \(\chi_{8775}(287, \cdot)\) n/a 5760 16
8775.2.ix \(\chi_{8775}(746, \cdot)\) n/a 6656 16
8775.2.iy \(\chi_{8775}(314, \cdot)\) n/a 6656 16
8775.2.iz \(\chi_{8775}(206, \cdot)\) n/a 6656 16
8775.2.ja \(\chi_{8775}(44, \cdot)\) n/a 6656 16
8775.2.jf \(\chi_{8775}(539, \cdot)\) n/a 8960 16
8775.2.jg \(\chi_{8775}(431, \cdot)\) n/a 8960 16
8775.2.jh \(\chi_{8775}(647, \cdot)\) n/a 8960 16
8775.2.jk \(\chi_{8775}(233, \cdot)\) n/a 6656 16
8775.2.jl \(\chi_{8775}(602, \cdot)\) n/a 6656 16
8775.2.jo \(\chi_{8775}(17, \cdot)\) n/a 6656 16
8775.2.jp \(\chi_{8775}(89, \cdot)\) n/a 6656 16
8775.2.jq \(\chi_{8775}(71, \cdot)\) n/a 6656 16
8775.2.ju \(\chi_{8775}(152, \cdot)\) n/a 6656 16
8775.2.jv \(\chi_{8775}(388, \cdot)\) n/a 6656 16
8775.2.jy \(\chi_{8775}(73, \cdot)\) n/a 6656 16
8775.2.jz \(\chi_{8775}(163, \cdot)\) n/a 8960 16
8775.2.kb \(\chi_{8775}(253, \cdot)\) n/a 6656 16
8775.2.kd \(\chi_{8775}(121, \cdot)\) n/a 30144 24
8775.2.kf \(\chi_{8775}(94, \cdot)\) n/a 30144 24
8775.2.ki \(\chi_{8775}(79, \cdot)\) n/a 25920 24
8775.2.kk \(\chi_{8775}(571, \cdot)\) n/a 30144 24
8775.2.kl \(\chi_{8775}(166, \cdot)\) n/a 30144 24
8775.2.kn \(\chi_{8775}(139, \cdot)\) n/a 30144 24
8775.2.kq \(\chi_{8775}(259, \cdot)\) n/a 30144 24
8775.2.kt \(\chi_{8775}(394, \cdot)\) n/a 30144 24
8775.2.kx \(\chi_{8775}(4, \cdot)\) n/a 30144 24
8775.2.ky \(\chi_{8775}(112, \cdot)\) n/a 60288 48
8775.2.lb \(\chi_{8775}(427, \cdot)\) n/a 60288 48
8775.2.lc \(\chi_{8775}(58, \cdot)\) n/a 60288 48
8775.2.lf \(\chi_{8775}(11, \cdot)\) n/a 60288 48
8775.2.lh \(\chi_{8775}(254, \cdot)\) n/a 60288 48
8775.2.lj \(\chi_{8775}(164, \cdot)\) n/a 60288 48
8775.2.lk \(\chi_{8775}(23, \cdot)\) n/a 60288 48
8775.2.lo \(\chi_{8775}(92, \cdot)\) n/a 51840 48
8775.2.lp \(\chi_{8775}(113, \cdot)\) n/a 60288 48
8775.2.lq \(\chi_{8775}(212, \cdot)\) n/a 60288 48
8775.2.lr \(\chi_{8775}(38, \cdot)\) n/a 60288 48
8775.2.lv \(\chi_{8775}(302, \cdot)\) n/a 60288 48
8775.2.lw \(\chi_{8775}(86, \cdot)\) n/a 60288 48
8775.2.ly \(\chi_{8775}(41, \cdot)\) n/a 60288 48
8775.2.ma \(\chi_{8775}(59, \cdot)\) n/a 60288 48
8775.2.md \(\chi_{8775}(292, \cdot)\) n/a 60288 48
8775.2.me \(\chi_{8775}(67, \cdot)\) n/a 60288 48
8775.2.mh \(\chi_{8775}(187, \cdot)\) n/a 60288 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8775))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8775)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(195))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(325))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(351))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(585))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(675))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(975))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1755))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2925))\)\(^{\oplus 2}\)