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Properties

Label 8112.2
Level 8112
Weight 2
Dimension 755699
Nonzero newspaces 56
Sturm bound 7268352

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Defining parameters

Level: \( N \) = \( 8112 = 2^{4} \cdot 3 \cdot 13^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 56 \)
Sturm bound: \(7268352\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8112))\).

Total New Old
Modular forms 1829856 759379 1070477
Cusp forms 1804321 755699 1048622
Eisenstein series 25535 3680 21855

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8112))\)

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
8112.2.a \(\chi_{8112}(1, \cdot)\) 8112.2.a.a 1 1
8112.2.a.b 1
8112.2.a.c 1
8112.2.a.d 1
8112.2.a.e 1
8112.2.a.f 1
8112.2.a.g 1
8112.2.a.h 1
8112.2.a.i 1
8112.2.a.j 1
8112.2.a.k 1
8112.2.a.l 1
8112.2.a.m 1
8112.2.a.n 1
8112.2.a.o 1
8112.2.a.p 1
8112.2.a.q 1
8112.2.a.r 1
8112.2.a.s 1
8112.2.a.t 1
8112.2.a.u 1
8112.2.a.v 1
8112.2.a.w 1
8112.2.a.x 1
8112.2.a.y 1
8112.2.a.z 1
8112.2.a.ba 1
8112.2.a.bb 1
8112.2.a.bc 1
8112.2.a.bd 1
8112.2.a.be 1
8112.2.a.bf 1
8112.2.a.bg 1
8112.2.a.bh 1
8112.2.a.bi 1
8112.2.a.bj 2
8112.2.a.bk 2
8112.2.a.bl 2
8112.2.a.bm 2
8112.2.a.bn 2
8112.2.a.bo 2
8112.2.a.bp 2
8112.2.a.bq 2
8112.2.a.br 2
8112.2.a.bs 2
8112.2.a.bt 2
8112.2.a.bu 2
8112.2.a.bv 2
8112.2.a.bw 2
8112.2.a.bx 2
8112.2.a.by 3
8112.2.a.bz 3
8112.2.a.ca 3
8112.2.a.cb 3
8112.2.a.cc 3
8112.2.a.cd 3
8112.2.a.ce 3
8112.2.a.cf 3
8112.2.a.cg 3
8112.2.a.ch 3
8112.2.a.ci 3
8112.2.a.cj 3
8112.2.a.ck 3
8112.2.a.cl 3
8112.2.a.cm 3
8112.2.a.cn 3
8112.2.a.co 3
8112.2.a.cp 3
8112.2.a.cq 4
8112.2.a.cr 4
8112.2.a.cs 4
8112.2.a.ct 6
8112.2.a.cu 6
8112.2.a.cv 6
8112.2.a.cw 6
8112.2.c \(\chi_{8112}(337, \cdot)\) n/a 154 1
8112.2.d \(\chi_{8112}(7775, \cdot)\) n/a 310 1
8112.2.g \(\chi_{8112}(4057, \cdot)\) None 0 1
8112.2.h \(\chi_{8112}(4055, \cdot)\) None 0 1
8112.2.j \(\chi_{8112}(3719, \cdot)\) None 0 1
8112.2.m \(\chi_{8112}(4393, \cdot)\) None 0 1
8112.2.n \(\chi_{8112}(8111, \cdot)\) n/a 308 1
8112.2.q \(\chi_{8112}(529, \cdot)\) n/a 308 2
8112.2.r \(\chi_{8112}(3619, \cdot)\) n/a 1232 2
8112.2.u \(\chi_{8112}(1253, \cdot)\) n/a 2424 2
8112.2.v \(\chi_{8112}(2027, \cdot)\) n/a 2424 2
8112.2.x \(\chi_{8112}(2029, \cdot)\) n/a 1240 2
8112.2.bb \(\chi_{8112}(775, \cdot)\) None 0 2
8112.2.bc \(\chi_{8112}(4831, \cdot)\) n/a 308 2
8112.2.bf \(\chi_{8112}(2465, \cdot)\) n/a 596 2
8112.2.bg \(\chi_{8112}(6521, \cdot)\) None 0 2
8112.2.bh \(\chi_{8112}(1691, \cdot)\) n/a 2436 2
8112.2.bj \(\chi_{8112}(2365, \cdot)\) n/a 1232 2
8112.2.bm \(\chi_{8112}(437, \cdot)\) n/a 2424 2
8112.2.bn \(\chi_{8112}(2803, \cdot)\) n/a 1232 2
8112.2.bq \(\chi_{8112}(23, \cdot)\) None 0 2
8112.2.br \(\chi_{8112}(4585, \cdot)\) None 0 2
8112.2.bu \(\chi_{8112}(191, \cdot)\) n/a 616 2
8112.2.bv \(\chi_{8112}(4417, \cdot)\) n/a 308 2
8112.2.bz \(\chi_{8112}(4079, \cdot)\) n/a 616 2
8112.2.ca \(\chi_{8112}(361, \cdot)\) None 0 2
8112.2.cd \(\chi_{8112}(4247, \cdot)\) None 0 2
8112.2.ce \(\chi_{8112}(5765, \cdot)\) n/a 4848 4
8112.2.ch \(\chi_{8112}(19, \cdot)\) n/a 2464 4
8112.2.cj \(\chi_{8112}(1837, \cdot)\) n/a 2464 4
8112.2.cl \(\chi_{8112}(1667, \cdot)\) n/a 4848 4
8112.2.cm \(\chi_{8112}(89, \cdot)\) None 0 4
8112.2.cn \(\chi_{8112}(1601, \cdot)\) n/a 1192 4
8112.2.cq \(\chi_{8112}(319, \cdot)\) n/a 616 4
8112.2.cr \(\chi_{8112}(2455, \cdot)\) None 0 4
8112.2.cv \(\chi_{8112}(2005, \cdot)\) n/a 2464 4
8112.2.cx \(\chi_{8112}(1499, \cdot)\) n/a 4848 4
8112.2.cz \(\chi_{8112}(4075, \cdot)\) n/a 2464 4
8112.2.da \(\chi_{8112}(1709, \cdot)\) n/a 4848 4
8112.2.dc \(\chi_{8112}(625, \cdot)\) n/a 2184 12
8112.2.df \(\chi_{8112}(623, \cdot)\) n/a 4368 12
8112.2.dg \(\chi_{8112}(25, \cdot)\) None 0 12
8112.2.dj \(\chi_{8112}(599, \cdot)\) None 0 12
8112.2.dl \(\chi_{8112}(311, \cdot)\) None 0 12
8112.2.dm \(\chi_{8112}(313, \cdot)\) None 0 12
8112.2.dp \(\chi_{8112}(287, \cdot)\) n/a 4368 12
8112.2.dq \(\chi_{8112}(961, \cdot)\) n/a 2184 12
8112.2.ds \(\chi_{8112}(289, \cdot)\) n/a 4368 24
8112.2.du \(\chi_{8112}(187, \cdot)\) n/a 17472 24
8112.2.dv \(\chi_{8112}(317, \cdot)\) n/a 34848 24
8112.2.dx \(\chi_{8112}(181, \cdot)\) n/a 17472 24
8112.2.dz \(\chi_{8112}(131, \cdot)\) n/a 34848 24
8112.2.ed \(\chi_{8112}(281, \cdot)\) None 0 24
8112.2.ee \(\chi_{8112}(161, \cdot)\) n/a 8688 24
8112.2.eh \(\chi_{8112}(31, \cdot)\) n/a 4368 24
8112.2.ei \(\chi_{8112}(151, \cdot)\) None 0 24
8112.2.ej \(\chi_{8112}(157, \cdot)\) n/a 17472 24
8112.2.el \(\chi_{8112}(155, \cdot)\) n/a 34848 24
8112.2.en \(\chi_{8112}(5, \cdot)\) n/a 34848 24
8112.2.eq \(\chi_{8112}(499, \cdot)\) n/a 17472 24
8112.2.er \(\chi_{8112}(263, \cdot)\) None 0 24
8112.2.eu \(\chi_{8112}(121, \cdot)\) None 0 24
8112.2.ev \(\chi_{8112}(95, \cdot)\) n/a 8736 24
8112.2.ez \(\chi_{8112}(49, \cdot)\) n/a 4368 24
8112.2.fa \(\chi_{8112}(575, \cdot)\) n/a 8736 24
8112.2.fd \(\chi_{8112}(217, \cdot)\) None 0 24
8112.2.fe \(\chi_{8112}(407, \cdot)\) None 0 24
8112.2.fh \(\chi_{8112}(245, \cdot)\) n/a 69696 48
8112.2.fi \(\chi_{8112}(115, \cdot)\) n/a 34944 48
8112.2.fl \(\chi_{8112}(179, \cdot)\) n/a 69696 48
8112.2.fn \(\chi_{8112}(61, \cdot)\) n/a 34944 48
8112.2.fo \(\chi_{8112}(7, \cdot)\) None 0 48
8112.2.fp \(\chi_{8112}(175, \cdot)\) n/a 8736 48
8112.2.fs \(\chi_{8112}(305, \cdot)\) n/a 17376 48
8112.2.ft \(\chi_{8112}(41, \cdot)\) None 0 48
8112.2.fx \(\chi_{8112}(35, \cdot)\) n/a 69696 48
8112.2.fz \(\chi_{8112}(205, \cdot)\) n/a 34944 48
8112.2.ga \(\chi_{8112}(67, \cdot)\) n/a 34944 48
8112.2.gd \(\chi_{8112}(149, \cdot)\) n/a 69696 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8112))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8112)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(208))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(312))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(338))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(507))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(624))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(676))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1014))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1352))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2028))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2704))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4056))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8112))\)\(^{\oplus 1}\)