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Properties

Label 7175.2
Level 7175
Weight 2
Dimension 1770542
Nonzero newspaces 196
Sturm bound 8064000

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Defining parameters

Level: \( N \) = \( 7175 = 5^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 196 \)
Sturm bound: \(8064000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7175))\).

Total New Old
Modular forms 2029440 1786534 242906
Cusp forms 2002561 1770542 232019
Eisenstein series 26879 15992 10887

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7175))\)

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
7175.2.a \(\chi_{7175}(1, \cdot)\) 7175.2.a.a 1 1
7175.2.a.b 1
7175.2.a.c 1
7175.2.a.d 1
7175.2.a.e 1
7175.2.a.f 1
7175.2.a.g 2
7175.2.a.h 2
7175.2.a.i 3
7175.2.a.j 3
7175.2.a.k 3
7175.2.a.l 3
7175.2.a.m 4
7175.2.a.n 5
7175.2.a.o 5
7175.2.a.p 6
7175.2.a.q 8
7175.2.a.r 11
7175.2.a.s 12
7175.2.a.t 12
7175.2.a.u 12
7175.2.a.v 13
7175.2.a.w 13
7175.2.a.x 14
7175.2.a.y 15
7175.2.a.z 26
7175.2.a.ba 26
7175.2.a.bb 28
7175.2.a.bc 28
7175.2.a.bd 30
7175.2.a.be 30
7175.2.a.bf 30
7175.2.a.bg 30
7175.2.c \(\chi_{7175}(1149, \cdot)\) n/a 360 1
7175.2.d \(\chi_{7175}(3074, \cdot)\) n/a 380 1
7175.2.f \(\chi_{7175}(1926, \cdot)\) n/a 398 1
7175.2.i \(\chi_{7175}(1026, \cdot)\) n/a 1012 2
7175.2.k \(\chi_{7175}(2451, \cdot)\) n/a 800 2
7175.2.m \(\chi_{7175}(132, \cdot)\) n/a 1000 2
7175.2.o \(\chi_{7175}(657, \cdot)\) n/a 960 2
7175.2.p \(\chi_{7175}(2582, \cdot)\) n/a 1000 2
7175.2.r \(\chi_{7175}(993, \cdot)\) n/a 1000 2
7175.2.u \(\chi_{7175}(624, \cdot)\) n/a 752 2
7175.2.v \(\chi_{7175}(1436, \cdot)\) n/a 2400 4
7175.2.w \(\chi_{7175}(666, \cdot)\) n/a 2528 4
7175.2.x \(\chi_{7175}(2066, \cdot)\) n/a 2528 4
7175.2.y \(\chi_{7175}(141, \cdot)\) n/a 2528 4
7175.2.z \(\chi_{7175}(1226, \cdot)\) n/a 1592 4
7175.2.ba \(\chi_{7175}(631, \cdot)\) n/a 2528 4
7175.2.bd \(\chi_{7175}(2951, \cdot)\) n/a 1052 2
7175.2.bf \(\chi_{7175}(1024, \cdot)\) n/a 1000 2
7175.2.bg \(\chi_{7175}(2174, \cdot)\) n/a 960 2
7175.2.bi \(\chi_{7175}(232, \cdot)\) n/a 1512 4
7175.2.bl \(\chi_{7175}(1749, \cdot)\) n/a 2000 4
7175.2.bn \(\chi_{7175}(601, \cdot)\) n/a 2104 4
7175.2.bo \(\chi_{7175}(407, \cdot)\) n/a 1512 4
7175.2.br \(\chi_{7175}(2444, \cdot)\) n/a 2512 4
7175.2.bs \(\chi_{7175}(344, \cdot)\) n/a 2512 4
7175.2.bv \(\chi_{7175}(351, \cdot)\) n/a 1592 4
7175.2.cb \(\chi_{7175}(2696, \cdot)\) n/a 2528 4
7175.2.cc \(\chi_{7175}(1786, \cdot)\) n/a 2528 4
7175.2.cf \(\chi_{7175}(1296, \cdot)\) n/a 2528 4
7175.2.cg \(\chi_{7175}(491, \cdot)\) n/a 2528 4
7175.2.cj \(\chi_{7175}(2374, \cdot)\) n/a 1520 4
7175.2.cm \(\chi_{7175}(2934, \cdot)\) n/a 2512 4
7175.2.cn \(\chi_{7175}(64, \cdot)\) n/a 2512 4
7175.2.cq \(\chi_{7175}(204, \cdot)\) n/a 2512 4
7175.2.cr \(\chi_{7175}(414, \cdot)\) n/a 2512 4
7175.2.cu \(\chi_{7175}(939, \cdot)\) n/a 2512 4
7175.2.cv \(\chi_{7175}(2584, \cdot)\) n/a 2400 4
7175.2.cy \(\chi_{7175}(1289, \cdot)\) n/a 2512 4
7175.2.cz \(\chi_{7175}(379, \cdot)\) n/a 2512 4
7175.2.dc \(\chi_{7175}(974, \cdot)\) n/a 1520 4
7175.2.df \(\chi_{7175}(1261, \cdot)\) n/a 2528 4
7175.2.dg \(\chi_{7175}(1549, \cdot)\) n/a 2000 4
7175.2.di \(\chi_{7175}(2082, \cdot)\) n/a 2000 4
7175.2.dk \(\chi_{7175}(493, \cdot)\) n/a 1920 4
7175.2.dn \(\chi_{7175}(1557, \cdot)\) n/a 2000 4
7175.2.dp \(\chi_{7175}(2182, \cdot)\) n/a 2000 4
7175.2.dq \(\chi_{7175}(401, \cdot)\) n/a 2104 4
7175.2.ds \(\chi_{7175}(816, \cdot)\) n/a 6688 8
7175.2.dt \(\chi_{7175}(51, \cdot)\) n/a 4208 8
7175.2.du \(\chi_{7175}(16, \cdot)\) n/a 6688 8
7175.2.dv \(\chi_{7175}(821, \cdot)\) n/a 6400 8
7175.2.dw \(\chi_{7175}(221, \cdot)\) n/a 6688 8
7175.2.dx \(\chi_{7175}(1166, \cdot)\) n/a 6688 8
7175.2.dz \(\chi_{7175}(1891, \cdot)\) n/a 5024 8
7175.2.ea \(\chi_{7175}(449, \cdot)\) n/a 3008 8
7175.2.ec \(\chi_{7175}(729, \cdot)\) n/a 5056 8
7175.2.ee \(\chi_{7175}(169, \cdot)\) n/a 5056 8
7175.2.ef \(\chi_{7175}(869, \cdot)\) n/a 5056 8
7175.2.eg \(\chi_{7175}(484, \cdot)\) n/a 5056 8
7175.2.ek \(\chi_{7175}(118, \cdot)\) n/a 4000 8
7175.2.en \(\chi_{7175}(538, \cdot)\) n/a 6688 8
7175.2.ep \(\chi_{7175}(4108, \cdot)\) n/a 6688 8
7175.2.eq \(\chi_{7175}(412, \cdot)\) n/a 6688 8
7175.2.es \(\chi_{7175}(237, \cdot)\) n/a 6688 8
7175.2.ev \(\chi_{7175}(1238, \cdot)\) n/a 6688 8
7175.2.ex \(\chi_{7175}(517, \cdot)\) n/a 6688 8
7175.2.ey \(\chi_{7175}(748, \cdot)\) n/a 6688 8
7175.2.fa \(\chi_{7175}(1308, \cdot)\) n/a 6688 8
7175.2.fd \(\chi_{7175}(482, \cdot)\) n/a 4000 8
7175.2.fe \(\chi_{7175}(1917, \cdot)\) n/a 6688 8
7175.2.fh \(\chi_{7175}(573, \cdot)\) n/a 6688 8
7175.2.fi \(\chi_{7175}(433, \cdot)\) n/a 6688 8
7175.2.fk \(\chi_{7175}(1882, \cdot)\) n/a 4000 8
7175.2.fn \(\chi_{7175}(1658, \cdot)\) n/a 6688 8
7175.2.fo \(\chi_{7175}(83, \cdot)\) n/a 6400 8
7175.2.fr \(\chi_{7175}(223, \cdot)\) n/a 6688 8
7175.2.ft \(\chi_{7175}(783, \cdot)\) n/a 6688 8
7175.2.fu \(\chi_{7175}(377, \cdot)\) n/a 6688 8
7175.2.fw \(\chi_{7175}(1392, \cdot)\) n/a 6688 8
7175.2.fz \(\chi_{7175}(1098, \cdot)\) n/a 6688 8
7175.2.gb \(\chi_{7175}(853, \cdot)\) n/a 6688 8
7175.2.gc \(\chi_{7175}(62, \cdot)\) n/a 6688 8
7175.2.gf \(\chi_{7175}(307, \cdot)\) n/a 4000 8
7175.2.gg \(\chi_{7175}(2276, \cdot)\) n/a 3200 8
7175.2.gi \(\chi_{7175}(456, \cdot)\) n/a 5024 8
7175.2.gj \(\chi_{7175}(36, \cdot)\) n/a 5024 8
7175.2.gk \(\chi_{7175}(736, \cdot)\) n/a 5024 8
7175.2.go \(\chi_{7175}(911, \cdot)\) n/a 5024 8
7175.2.gr \(\chi_{7175}(904, \cdot)\) n/a 5056 8
7175.2.gt \(\chi_{7175}(793, \cdot)\) n/a 4000 8
7175.2.gu \(\chi_{7175}(1151, \cdot)\) n/a 4208 8
7175.2.gw \(\chi_{7175}(724, \cdot)\) n/a 4000 8
7175.2.gz \(\chi_{7175}(618, \cdot)\) n/a 4000 8
7175.2.ha \(\chi_{7175}(291, \cdot)\) n/a 6688 8
7175.2.hd \(\chi_{7175}(599, \cdot)\) n/a 4000 8
7175.2.hf \(\chi_{7175}(529, \cdot)\) n/a 6688 8
7175.2.hi \(\chi_{7175}(1964, \cdot)\) n/a 6688 8
7175.2.hj \(\chi_{7175}(534, \cdot)\) n/a 6400 8
7175.2.hm \(\chi_{7175}(1164, \cdot)\) n/a 6688 8
7175.2.hn \(\chi_{7175}(884, \cdot)\) n/a 6688 8
7175.2.hq \(\chi_{7175}(1229, \cdot)\) n/a 6688 8
7175.2.hr \(\chi_{7175}(359, \cdot)\) n/a 6688 8
7175.2.hu \(\chi_{7175}(4, \cdot)\) n/a 6688 8
7175.2.hw \(\chi_{7175}(324, \cdot)\) n/a 4000 8
7175.2.hy \(\chi_{7175}(646, \cdot)\) n/a 6688 8
7175.2.ib \(\chi_{7175}(86, \cdot)\) n/a 6688 8
7175.2.ic \(\chi_{7175}(81, \cdot)\) n/a 6688 8
7175.2.if \(\chi_{7175}(1521, \cdot)\) n/a 6688 8
7175.2.ik \(\chi_{7175}(851, \cdot)\) n/a 4208 8
7175.2.in \(\chi_{7175}(879, \cdot)\) n/a 6688 8
7175.2.io \(\chi_{7175}(394, \cdot)\) n/a 6688 8
7175.2.iq \(\chi_{7175}(463, \cdot)\) n/a 10080 16
7175.2.ix \(\chi_{7175}(372, \cdot)\) n/a 10080 16
7175.2.iy \(\chi_{7175}(792, \cdot)\) n/a 10080 16
7175.2.iz \(\chi_{7175}(393, \cdot)\) n/a 6048 16
7175.2.ja \(\chi_{7175}(827, \cdot)\) n/a 10080 16
7175.2.jb \(\chi_{7175}(498, \cdot)\) n/a 10080 16
7175.2.jd \(\chi_{7175}(1336, \cdot)\) n/a 13376 16
7175.2.jf \(\chi_{7175}(384, \cdot)\) n/a 13376 16
7175.2.jg \(\chi_{7175}(314, \cdot)\) n/a 13376 16
7175.2.ji \(\chi_{7175}(6, \cdot)\) n/a 13376 16
7175.2.jj \(\chi_{7175}(76, \cdot)\) n/a 8416 16
7175.2.jk \(\chi_{7175}(1406, \cdot)\) n/a 13376 16
7175.2.jl \(\chi_{7175}(181, \cdot)\) n/a 13376 16
7175.2.jq \(\chi_{7175}(34, \cdot)\) n/a 13376 16
7175.2.jr \(\chi_{7175}(69, \cdot)\) n/a 13376 16
7175.2.js \(\chi_{7175}(874, \cdot)\) n/a 8000 16
7175.2.jt \(\chi_{7175}(839, \cdot)\) n/a 13376 16
7175.2.jy \(\chi_{7175}(741, \cdot)\) n/a 13376 16
7175.2.kf \(\chi_{7175}(22, \cdot)\) n/a 10080 16
7175.2.kg \(\chi_{7175}(1247, \cdot)\) n/a 10080 16
7175.2.kh \(\chi_{7175}(358, \cdot)\) n/a 10080 16
7175.2.ki \(\chi_{7175}(218, \cdot)\) n/a 6048 16
7175.2.kj \(\chi_{7175}(547, \cdot)\) n/a 10080 16
7175.2.kk \(\chi_{7175}(183, \cdot)\) n/a 10080 16
7175.2.km \(\chi_{7175}(144, \cdot)\) n/a 13376 16
7175.2.kp \(\chi_{7175}(296, \cdot)\) n/a 13376 16
7175.2.kt \(\chi_{7175}(746, \cdot)\) n/a 13376 16
7175.2.ku \(\chi_{7175}(46, \cdot)\) n/a 13376 16
7175.2.kv \(\chi_{7175}(471, \cdot)\) n/a 13376 16
7175.2.kx \(\chi_{7175}(226, \cdot)\) n/a 8416 16
7175.2.kz \(\chi_{7175}(418, \cdot)\) n/a 8000 16
7175.2.la \(\chi_{7175}(33, \cdot)\) n/a 13376 16
7175.2.lc \(\chi_{7175}(367, \cdot)\) n/a 13376 16
7175.2.lf \(\chi_{7175}(73, \cdot)\) n/a 13376 16
7175.2.lh \(\chi_{7175}(292, \cdot)\) n/a 13376 16
7175.2.li \(\chi_{7175}(87, \cdot)\) n/a 13376 16
7175.2.ll \(\chi_{7175}(283, \cdot)\) n/a 13376 16
7175.2.ln \(\chi_{7175}(353, \cdot)\) n/a 13376 16
7175.2.lo \(\chi_{7175}(122, \cdot)\) n/a 13376 16
7175.2.lr \(\chi_{7175}(892, \cdot)\) n/a 13376 16
7175.2.ls \(\chi_{7175}(318, \cdot)\) n/a 8000 16
7175.2.lu \(\chi_{7175}(262, \cdot)\) n/a 13376 16
7175.2.lx \(\chi_{7175}(698, \cdot)\) n/a 12800 16
7175.2.ly \(\chi_{7175}(633, \cdot)\) n/a 13376 16
7175.2.mb \(\chi_{7175}(857, \cdot)\) n/a 8000 16
7175.2.mc \(\chi_{7175}(187, \cdot)\) n/a 13376 16
7175.2.me \(\chi_{7175}(523, \cdot)\) n/a 13376 16
7175.2.mh \(\chi_{7175}(467, \cdot)\) n/a 13376 16
7175.2.mi \(\chi_{7175}(1853, \cdot)\) n/a 13376 16
7175.2.mk \(\chi_{7175}(173, \cdot)\) n/a 13376 16
7175.2.mn \(\chi_{7175}(103, \cdot)\) n/a 13376 16
7175.2.mp \(\chi_{7175}(1027, \cdot)\) n/a 13376 16
7175.2.mr \(\chi_{7175}(402, \cdot)\) n/a 13376 16
7175.2.ms \(\chi_{7175}(143, \cdot)\) n/a 8000 16
7175.2.mx \(\chi_{7175}(254, \cdot)\) n/a 13376 16
7175.2.my \(\chi_{7175}(459, \cdot)\) n/a 13376 16
7175.2.mz \(\chi_{7175}(39, \cdot)\) n/a 13376 16
7175.2.nb \(\chi_{7175}(9, \cdot)\) n/a 13376 16
7175.2.nd \(\chi_{7175}(74, \cdot)\) n/a 8000 16
7175.2.ne \(\chi_{7175}(121, \cdot)\) n/a 13376 16
7175.2.nh \(\chi_{7175}(417, \cdot)\) n/a 26752 32
7175.2.ni \(\chi_{7175}(93, \cdot)\) n/a 16000 32
7175.2.nj \(\chi_{7175}(53, \cdot)\) n/a 26752 32
7175.2.nk \(\chi_{7175}(67, \cdot)\) n/a 26752 32
7175.2.nl \(\chi_{7175}(233, \cdot)\) n/a 26752 32
7175.2.nm \(\chi_{7175}(137, \cdot)\) n/a 26752 32
7175.2.nt \(\chi_{7175}(96, \cdot)\) n/a 26752 32
7175.2.ny \(\chi_{7175}(89, \cdot)\) n/a 26752 32
7175.2.nz \(\chi_{7175}(24, \cdot)\) n/a 16000 32
7175.2.oa \(\chi_{7175}(439, \cdot)\) n/a 26752 32
7175.2.ob \(\chi_{7175}(194, \cdot)\) n/a 26752 32
7175.2.og \(\chi_{7175}(136, \cdot)\) n/a 26752 32
7175.2.oh \(\chi_{7175}(341, \cdot)\) n/a 26752 32
7175.2.oi \(\chi_{7175}(26, \cdot)\) n/a 16832 32
7175.2.oj \(\chi_{7175}(171, \cdot)\) n/a 26752 32
7175.2.ol \(\chi_{7175}(864, \cdot)\) n/a 26752 32
7175.2.om \(\chi_{7175}(19, \cdot)\) n/a 26752 32
7175.2.oo \(\chi_{7175}(306, \cdot)\) n/a 26752 32
7175.2.oq \(\chi_{7175}(478, \cdot)\) n/a 26752 32
7175.2.or \(\chi_{7175}(58, \cdot)\) n/a 26752 32
7175.2.os \(\chi_{7175}(88, \cdot)\) n/a 26752 32
7175.2.ot \(\chi_{7175}(268, \cdot)\) n/a 16000 32
7175.2.ou \(\chi_{7175}(158, \cdot)\) n/a 26752 32
7175.2.pb \(\chi_{7175}(142, \cdot)\) n/a 26752 32

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7175))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7175)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(205))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(287))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1025))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1435))\)\(^{\oplus 2}\)