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Properties

Label 7872.2
Level 7872
Weight 2
Dimension 723180
Nonzero newspaces 88
Sturm bound 6881280

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Defining parameters

Level: \( N \) = \( 7872 = 2^{6} \cdot 3 \cdot 41 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 88 \)
Sturm bound: \(6881280\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7872))\).

Total New Old
Modular forms 1731840 726612 1005228
Cusp forms 1708801 723180 985621
Eisenstein series 23039 3432 19607

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7872))\)

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
7872.2.a \(\chi_{7872}(1, \cdot)\) 7872.2.a.a 1 1
7872.2.a.b 1
7872.2.a.c 1
7872.2.a.d 1
7872.2.a.e 1
7872.2.a.f 1
7872.2.a.g 1
7872.2.a.h 1
7872.2.a.i 1
7872.2.a.j 1
7872.2.a.k 1
7872.2.a.l 1
7872.2.a.m 1
7872.2.a.n 1
7872.2.a.o 1
7872.2.a.p 1
7872.2.a.q 1
7872.2.a.r 1
7872.2.a.s 1
7872.2.a.t 1
7872.2.a.u 1
7872.2.a.v 1
7872.2.a.w 1
7872.2.a.x 1
7872.2.a.y 1
7872.2.a.z 1
7872.2.a.ba 1
7872.2.a.bb 1
7872.2.a.bc 1
7872.2.a.bd 1
7872.2.a.be 1
7872.2.a.bf 1
7872.2.a.bg 1
7872.2.a.bh 1
7872.2.a.bi 1
7872.2.a.bj 1
7872.2.a.bk 2
7872.2.a.bl 2
7872.2.a.bm 2
7872.2.a.bn 2
7872.2.a.bo 2
7872.2.a.bp 2
7872.2.a.bq 2
7872.2.a.br 2
7872.2.a.bs 3
7872.2.a.bt 3
7872.2.a.bu 3
7872.2.a.bv 3
7872.2.a.bw 3
7872.2.a.bx 3
7872.2.a.by 3
7872.2.a.bz 3
7872.2.a.ca 3
7872.2.a.cb 3
7872.2.a.cc 4
7872.2.a.cd 4
7872.2.a.ce 4
7872.2.a.cf 4
7872.2.a.cg 4
7872.2.a.ch 4
7872.2.a.ci 4
7872.2.a.cj 4
7872.2.a.ck 5
7872.2.a.cl 5
7872.2.a.cm 5
7872.2.a.cn 5
7872.2.a.co 6
7872.2.a.cp 6
7872.2.a.cq 7
7872.2.a.cr 7
7872.2.d \(\chi_{7872}(575, \cdot)\) n/a 320 1
7872.2.e \(\chi_{7872}(3361, \cdot)\) n/a 168 1
7872.2.f \(\chi_{7872}(3937, \cdot)\) n/a 160 1
7872.2.g \(\chi_{7872}(7871, \cdot)\) n/a 332 1
7872.2.j \(\chi_{7872}(7297, \cdot)\) n/a 168 1
7872.2.k \(\chi_{7872}(4511, \cdot)\) n/a 320 1
7872.2.p \(\chi_{7872}(3935, \cdot)\) n/a 336 1
7872.2.s \(\chi_{7872}(1631, \cdot)\) n/a 672 2
7872.2.t \(\chi_{7872}(2305, \cdot)\) n/a 336 2
7872.2.w \(\chi_{7872}(1967, \cdot)\) n/a 664 2
7872.2.x \(\chi_{7872}(1969, \cdot)\) n/a 320 2
7872.2.ba \(\chi_{7872}(3025, \cdot)\) n/a 336 2
7872.2.bb \(\chi_{7872}(911, \cdot)\) n/a 664 2
7872.2.bc \(\chi_{7872}(3599, \cdot)\) n/a 664 2
7872.2.bd \(\chi_{7872}(337, \cdot)\) n/a 336 2
7872.2.bg \(\chi_{7872}(2543, \cdot)\) n/a 640 2
7872.2.bh \(\chi_{7872}(1393, \cdot)\) n/a 336 2
7872.2.bm \(\chi_{7872}(2879, \cdot)\) n/a 664 2
7872.2.bn \(\chi_{7872}(1057, \cdot)\) n/a 336 2
7872.2.bo \(\chi_{7872}(385, \cdot)\) n/a 672 4
7872.2.bp \(\chi_{7872}(2129, \cdot)\) n/a 1328 4
7872.2.bq \(\chi_{7872}(79, \cdot)\) n/a 672 4
7872.2.bu \(\chi_{7872}(647, \cdot)\) None 0 4
7872.2.bv \(\chi_{7872}(73, \cdot)\) None 0 4
7872.2.by \(\chi_{7872}(823, \cdot)\) None 0 4
7872.2.bz \(\chi_{7872}(905, \cdot)\) None 0 4
7872.2.cb \(\chi_{7872}(1145, \cdot)\) None 0 4
7872.2.ce \(\chi_{7872}(2791, \cdot)\) None 0 4
7872.2.cf \(\chi_{7872}(983, \cdot)\) None 0 4
7872.2.ch \(\chi_{7872}(985, \cdot)\) None 0 4
7872.2.cn \(\chi_{7872}(161, \cdot)\) n/a 1344 4
7872.2.co \(\chi_{7872}(4097, \cdot)\) n/a 1328 4
7872.2.cp \(\chi_{7872}(5983, \cdot)\) n/a 672 4
7872.2.cq \(\chi_{7872}(2047, \cdot)\) n/a 672 4
7872.2.cs \(\chi_{7872}(1559, \cdot)\) None 0 4
7872.2.cu \(\chi_{7872}(409, \cdot)\) None 0 4
7872.2.cw \(\chi_{7872}(55, \cdot)\) None 0 4
7872.2.cx \(\chi_{7872}(137, \cdot)\) None 0 4
7872.2.cz \(\chi_{7872}(1913, \cdot)\) None 0 4
7872.2.dc \(\chi_{7872}(2023, \cdot)\) None 0 4
7872.2.dd \(\chi_{7872}(1895, \cdot)\) None 0 4
7872.2.dg \(\chi_{7872}(1321, \cdot)\) None 0 4
7872.2.dh \(\chi_{7872}(2897, \cdot)\) n/a 1328 4
7872.2.di \(\chi_{7872}(847, \cdot)\) n/a 672 4
7872.2.dl \(\chi_{7872}(1439, \cdot)\) n/a 1344 4
7872.2.dq \(\chi_{7872}(3167, \cdot)\) n/a 1344 4
7872.2.dr \(\chi_{7872}(769, \cdot)\) n/a 672 4
7872.2.du \(\chi_{7872}(1343, \cdot)\) n/a 1328 4
7872.2.dv \(\chi_{7872}(2593, \cdot)\) n/a 672 4
7872.2.dw \(\chi_{7872}(865, \cdot)\) n/a 672 4
7872.2.dx \(\chi_{7872}(959, \cdot)\) n/a 1328 4
7872.2.ea \(\chi_{7872}(1531, \cdot)\) n/a 5376 8
7872.2.ed \(\chi_{7872}(413, \cdot)\) n/a 10720 8
7872.2.ee \(\chi_{7872}(1549, \cdot)\) n/a 5376 8
7872.2.eg \(\chi_{7872}(155, \cdot)\) n/a 10720 8
7872.2.ei \(\chi_{7872}(355, \cdot)\) n/a 5376 8
7872.2.ej \(\chi_{7872}(331, \cdot)\) n/a 5376 8
7872.2.en \(\chi_{7872}(901, \cdot)\) n/a 5376 8
7872.2.eo \(\chi_{7872}(493, \cdot)\) n/a 5120 8
7872.2.eq \(\chi_{7872}(1397, \cdot)\) n/a 10720 8
7872.2.er \(\chi_{7872}(1613, \cdot)\) n/a 10720 8
7872.2.eu \(\chi_{7872}(83, \cdot)\) n/a 10240 8
7872.2.ex \(\chi_{7872}(491, \cdot)\) n/a 10720 8
7872.2.ez \(\chi_{7872}(565, \cdot)\) n/a 5376 8
7872.2.fb \(\chi_{7872}(1139, \cdot)\) n/a 10720 8
7872.2.fd \(\chi_{7872}(1315, \cdot)\) n/a 5376 8
7872.2.fe \(\chi_{7872}(437, \cdot)\) n/a 10720 8
7872.2.fg \(\chi_{7872}(289, \cdot)\) n/a 1344 8
7872.2.fh \(\chi_{7872}(1727, \cdot)\) n/a 2656 8
7872.2.fm \(\chi_{7872}(433, \cdot)\) n/a 1344 8
7872.2.fn \(\chi_{7872}(1103, \cdot)\) n/a 2656 8
7872.2.fq \(\chi_{7872}(241, \cdot)\) n/a 1344 8
7872.2.fr \(\chi_{7872}(143, \cdot)\) n/a 2656 8
7872.2.fs \(\chi_{7872}(815, \cdot)\) n/a 2656 8
7872.2.ft \(\chi_{7872}(49, \cdot)\) n/a 1344 8
7872.2.fw \(\chi_{7872}(529, \cdot)\) n/a 1344 8
7872.2.fx \(\chi_{7872}(1007, \cdot)\) n/a 2656 8
7872.2.ga \(\chi_{7872}(1153, \cdot)\) n/a 1344 8
7872.2.gb \(\chi_{7872}(863, \cdot)\) n/a 2688 8
7872.2.gg \(\chi_{7872}(175, \cdot)\) n/a 2688 16
7872.2.gh \(\chi_{7872}(17, \cdot)\) n/a 5312 16
7872.2.gi \(\chi_{7872}(169, \cdot)\) None 0 16
7872.2.gl \(\chi_{7872}(743, \cdot)\) None 0 16
7872.2.gm \(\chi_{7872}(199, \cdot)\) None 0 16
7872.2.gp \(\chi_{7872}(809, \cdot)\) None 0 16
7872.2.gr \(\chi_{7872}(425, \cdot)\) None 0 16
7872.2.gs \(\chi_{7872}(7, \cdot)\) None 0 16
7872.2.gv \(\chi_{7872}(25, \cdot)\) None 0 16
7872.2.gx \(\chi_{7872}(119, \cdot)\) None 0 16
7872.2.gy \(\chi_{7872}(511, \cdot)\) n/a 2688 16
7872.2.gz \(\chi_{7872}(991, \cdot)\) n/a 2688 16
7872.2.ha \(\chi_{7872}(65, \cdot)\) n/a 5312 16
7872.2.hb \(\chi_{7872}(545, \cdot)\) n/a 5376 16
7872.2.hg \(\chi_{7872}(1369, \cdot)\) None 0 16
7872.2.hi \(\chi_{7872}(23, \cdot)\) None 0 16
7872.2.hk \(\chi_{7872}(919, \cdot)\) None 0 16
7872.2.hn \(\chi_{7872}(89, \cdot)\) None 0 16
7872.2.hp \(\chi_{7872}(233, \cdot)\) None 0 16
7872.2.hq \(\chi_{7872}(151, \cdot)\) None 0 16
7872.2.ht \(\chi_{7872}(121, \cdot)\) None 0 16
7872.2.hu \(\chi_{7872}(695, \cdot)\) None 0 16
7872.2.hy \(\chi_{7872}(463, \cdot)\) n/a 2688 16
7872.2.hz \(\chi_{7872}(977, \cdot)\) n/a 5312 16
7872.2.ib \(\chi_{7872}(101, \cdot)\) n/a 42880 32
7872.2.ic \(\chi_{7872}(259, \cdot)\) n/a 21504 32
7872.2.if \(\chi_{7872}(203, \cdot)\) n/a 42880 32
7872.2.ih \(\chi_{7872}(349, \cdot)\) n/a 21504 32
7872.2.ii \(\chi_{7872}(107, \cdot)\) n/a 42880 32
7872.2.il \(\chi_{7872}(59, \cdot)\) n/a 42880 32
7872.2.io \(\chi_{7872}(53, \cdot)\) n/a 42880 32
7872.2.ip \(\chi_{7872}(341, \cdot)\) n/a 42880 32
7872.2.ir \(\chi_{7872}(37, \cdot)\) n/a 21504 32
7872.2.is \(\chi_{7872}(277, \cdot)\) n/a 21504 32
7872.2.iw \(\chi_{7872}(67, \cdot)\) n/a 21504 32
7872.2.ix \(\chi_{7872}(19, \cdot)\) n/a 21504 32
7872.2.iy \(\chi_{7872}(131, \cdot)\) n/a 42880 32
7872.2.ja \(\chi_{7872}(61, \cdot)\) n/a 21504 32
7872.2.jc \(\chi_{7872}(29, \cdot)\) n/a 42880 32
7872.2.jf \(\chi_{7872}(499, \cdot)\) n/a 21504 32

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7872))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7872)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(82))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(123))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(164))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(246))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(328))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(492))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(656))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(984))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1312))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1968))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2624))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3936))\)\(^{\oplus 2}\)