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Properties

Label 8352.2
Level 8352
Weight 2
Dimension 857358
Nonzero newspaces 80
Sturm bound 7741440

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Defining parameters

Level: \( N \) = \( 8352 = 2^{5} \cdot 3^{2} \cdot 29 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 80 \)
Sturm bound: \(7741440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8352))\).

Total New Old
Modular forms 1949696 862218 1087478
Cusp forms 1921025 857358 1063667
Eisenstein series 28671 4860 23811

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8352))\)

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
8352.2.a \(\chi_{8352}(1, \cdot)\) 8352.2.a.a 1 1
8352.2.a.b 1
8352.2.a.c 1
8352.2.a.d 1
8352.2.a.e 1
8352.2.a.f 1
8352.2.a.g 1
8352.2.a.h 1
8352.2.a.i 1
8352.2.a.j 1
8352.2.a.k 2
8352.2.a.l 2
8352.2.a.m 2
8352.2.a.n 2
8352.2.a.o 2
8352.2.a.p 2
8352.2.a.q 2
8352.2.a.r 2
8352.2.a.s 2
8352.2.a.t 3
8352.2.a.u 3
8352.2.a.v 3
8352.2.a.w 3
8352.2.a.x 4
8352.2.a.y 4
8352.2.a.z 4
8352.2.a.ba 4
8352.2.a.bb 4
8352.2.a.bc 5
8352.2.a.bd 5
8352.2.a.be 5
8352.2.a.bf 5
8352.2.a.bg 5
8352.2.a.bh 5
8352.2.a.bi 6
8352.2.a.bj 7
8352.2.a.bk 7
8352.2.a.bl 7
8352.2.a.bm 7
8352.2.a.bn 8
8352.2.a.bo 8
8352.2.c \(\chi_{8352}(8351, \cdot)\) n/a 120 1
8352.2.e \(\chi_{8352}(8063, \cdot)\) n/a 112 1
8352.2.f \(\chi_{8352}(4177, \cdot)\) n/a 140 1
8352.2.h \(\chi_{8352}(4465, \cdot)\) n/a 148 1
8352.2.j \(\chi_{8352}(3887, \cdot)\) n/a 112 1
8352.2.l \(\chi_{8352}(4175, \cdot)\) n/a 120 1
8352.2.o \(\chi_{8352}(289, \cdot)\) n/a 150 1
8352.2.q \(\chi_{8352}(2785, \cdot)\) n/a 672 2
8352.2.r \(\chi_{8352}(4159, \cdot)\) n/a 300 2
8352.2.u \(\chi_{8352}(17, \cdot)\) n/a 240 2
8352.2.v \(\chi_{8352}(2105, \cdot)\) None 0 2
8352.2.x \(\chi_{8352}(2377, \cdot)\) None 0 2
8352.2.z \(\chi_{8352}(2089, \cdot)\) None 0 2
8352.2.bc \(\chi_{8352}(6281, \cdot)\) None 0 2
8352.2.be \(\chi_{8352}(1351, \cdot)\) None 0 2
8352.2.bf \(\chi_{8352}(1799, \cdot)\) None 0 2
8352.2.bh \(\chi_{8352}(2087, \cdot)\) None 0 2
8352.2.bj \(\chi_{8352}(5527, \cdot)\) None 0 2
8352.2.bm \(\chi_{8352}(3439, \cdot)\) n/a 296 2
8352.2.bn \(\chi_{8352}(737, \cdot)\) n/a 240 2
8352.2.bq \(\chi_{8352}(3073, \cdot)\) n/a 720 2
8352.2.bt \(\chi_{8352}(1391, \cdot)\) n/a 712 2
8352.2.bv \(\chi_{8352}(1103, \cdot)\) n/a 672 2
8352.2.bx \(\chi_{8352}(1681, \cdot)\) n/a 712 2
8352.2.bz \(\chi_{8352}(1393, \cdot)\) n/a 672 2
8352.2.ca \(\chi_{8352}(2495, \cdot)\) n/a 672 2
8352.2.cc \(\chi_{8352}(2783, \cdot)\) n/a 720 2
8352.2.ce \(\chi_{8352}(865, \cdot)\) n/a 900 6
8352.2.ch \(\chi_{8352}(1045, \cdot)\) n/a 2240 4
8352.2.ci \(\chi_{8352}(1043, \cdot)\) n/a 1920 4
8352.2.cl \(\chi_{8352}(1061, \cdot)\) n/a 1920 4
8352.2.cm \(\chi_{8352}(307, \cdot)\) n/a 2392 4
8352.2.cn \(\chi_{8352}(1781, \cdot)\) n/a 1920 4
8352.2.co \(\chi_{8352}(1027, \cdot)\) n/a 2392 4
8352.2.cr \(\chi_{8352}(755, \cdot)\) n/a 1792 4
8352.2.cs \(\chi_{8352}(1333, \cdot)\) n/a 2392 4
8352.2.cw \(\chi_{8352}(1409, \cdot)\) n/a 1440 4
8352.2.cx \(\chi_{8352}(655, \cdot)\) n/a 1424 4
8352.2.cz \(\chi_{8352}(679, \cdot)\) None 0 4
8352.2.dc \(\chi_{8352}(407, \cdot)\) None 0 4
8352.2.de \(\chi_{8352}(695, \cdot)\) None 0 4
8352.2.dg \(\chi_{8352}(4135, \cdot)\) None 0 4
8352.2.di \(\chi_{8352}(713, \cdot)\) None 0 4
8352.2.dk \(\chi_{8352}(985, \cdot)\) None 0 4
8352.2.dm \(\chi_{8352}(697, \cdot)\) None 0 4
8352.2.dn \(\chi_{8352}(41, \cdot)\) None 0 4
8352.2.dp \(\chi_{8352}(2129, \cdot)\) n/a 1424 4
8352.2.ds \(\chi_{8352}(1375, \cdot)\) n/a 1440 4
8352.2.du \(\chi_{8352}(1153, \cdot)\) n/a 900 6
8352.2.dx \(\chi_{8352}(2159, \cdot)\) n/a 720 6
8352.2.dz \(\chi_{8352}(431, \cdot)\) n/a 720 6
8352.2.eb \(\chi_{8352}(2449, \cdot)\) n/a 888 6
8352.2.ed \(\chi_{8352}(721, \cdot)\) n/a 888 6
8352.2.ee \(\chi_{8352}(575, \cdot)\) n/a 720 6
8352.2.eg \(\chi_{8352}(863, \cdot)\) n/a 720 6
8352.2.ei \(\chi_{8352}(1921, \cdot)\) n/a 4320 12
8352.2.ej \(\chi_{8352}(347, \cdot)\) n/a 11488 8
8352.2.ek \(\chi_{8352}(349, \cdot)\) n/a 10752 8
8352.2.en \(\chi_{8352}(1003, \cdot)\) n/a 11488 8
8352.2.eo \(\chi_{8352}(365, \cdot)\) n/a 11488 8
8352.2.et \(\chi_{8352}(331, \cdot)\) n/a 11488 8
8352.2.eu \(\chi_{8352}(1085, \cdot)\) n/a 11488 8
8352.2.ex \(\chi_{8352}(637, \cdot)\) n/a 11488 8
8352.2.ey \(\chi_{8352}(59, \cdot)\) n/a 10752 8
8352.2.fa \(\chi_{8352}(449, \cdot)\) n/a 1440 12
8352.2.fb \(\chi_{8352}(271, \cdot)\) n/a 1776 12
8352.2.fe \(\chi_{8352}(1639, \cdot)\) None 0 12
8352.2.fg \(\chi_{8352}(935, \cdot)\) None 0 12
8352.2.fi \(\chi_{8352}(71, \cdot)\) None 0 12
8352.2.fj \(\chi_{8352}(55, \cdot)\) None 0 12
8352.2.fl \(\chi_{8352}(665, \cdot)\) None 0 12
8352.2.fo \(\chi_{8352}(361, \cdot)\) None 0 12
8352.2.fq \(\chi_{8352}(1225, \cdot)\) None 0 12
8352.2.fs \(\chi_{8352}(89, \cdot)\) None 0 12
8352.2.ft \(\chi_{8352}(305, \cdot)\) n/a 1440 12
8352.2.fw \(\chi_{8352}(127, \cdot)\) n/a 1800 12
8352.2.fy \(\chi_{8352}(383, \cdot)\) n/a 4320 12
8352.2.ga \(\chi_{8352}(1631, \cdot)\) n/a 4320 12
8352.2.gb \(\chi_{8352}(49, \cdot)\) n/a 4272 12
8352.2.gd \(\chi_{8352}(241, \cdot)\) n/a 4272 12
8352.2.gf \(\chi_{8352}(239, \cdot)\) n/a 4272 12
8352.2.gh \(\chi_{8352}(527, \cdot)\) n/a 4272 12
8352.2.gk \(\chi_{8352}(673, \cdot)\) n/a 4320 12
8352.2.gm \(\chi_{8352}(35, \cdot)\) n/a 11520 24
8352.2.gn \(\chi_{8352}(181, \cdot)\) n/a 14352 24
8352.2.gq \(\chi_{8352}(19, \cdot)\) n/a 14352 24
8352.2.gr \(\chi_{8352}(269, \cdot)\) n/a 11520 24
8352.2.gw \(\chi_{8352}(163, \cdot)\) n/a 14352 24
8352.2.gx \(\chi_{8352}(917, \cdot)\) n/a 11520 24
8352.2.ha \(\chi_{8352}(109, \cdot)\) n/a 14352 24
8352.2.hb \(\chi_{8352}(107, \cdot)\) n/a 11520 24
8352.2.hc \(\chi_{8352}(31, \cdot)\) n/a 8640 24
8352.2.hf \(\chi_{8352}(113, \cdot)\) n/a 8544 24
8352.2.hh \(\chi_{8352}(185, \cdot)\) None 0 24
8352.2.hi \(\chi_{8352}(121, \cdot)\) None 0 24
8352.2.hk \(\chi_{8352}(25, \cdot)\) None 0 24
8352.2.hm \(\chi_{8352}(137, \cdot)\) None 0 24
8352.2.ho \(\chi_{8352}(247, \cdot)\) None 0 24
8352.2.hq \(\chi_{8352}(23, \cdot)\) None 0 24
8352.2.hs \(\chi_{8352}(167, \cdot)\) None 0 24
8352.2.hv \(\chi_{8352}(727, \cdot)\) None 0 24
8352.2.hx \(\chi_{8352}(79, \cdot)\) n/a 8544 24
8352.2.hy \(\chi_{8352}(641, \cdot)\) n/a 8640 24
8352.2.ic \(\chi_{8352}(277, \cdot)\) n/a 68928 48
8352.2.id \(\chi_{8352}(299, \cdot)\) n/a 68928 48
8352.2.ig \(\chi_{8352}(77, \cdot)\) n/a 68928 48
8352.2.ih \(\chi_{8352}(43, \cdot)\) n/a 68928 48
8352.2.ii \(\chi_{8352}(101, \cdot)\) n/a 68928 48
8352.2.ij \(\chi_{8352}(619, \cdot)\) n/a 68928 48
8352.2.im \(\chi_{8352}(83, \cdot)\) n/a 68928 48
8352.2.in \(\chi_{8352}(13, \cdot)\) n/a 68928 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8352))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8352)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(116))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(174))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(232))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(261))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(348))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(464))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(522))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(696))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(928))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1044))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1392))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2088))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2784))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4176))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8352))\)\(^{\oplus 1}\)