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Properties

Label 8712.2
Level 8712
Weight 2
Dimension 913240
Nonzero newspaces 48
Sturm bound 8363520

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Defining parameters

Level: \( N \) = \( 8712 = 2^{3} \cdot 3^{2} \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(8363520\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8712))\).

Total New Old
Modular forms 2106240 918298 1187942
Cusp forms 2075521 913240 1162281
Eisenstein series 30719 5058 25661

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8712))\)

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
8712.2.a \(\chi_{8712}(1, \cdot)\) 8712.2.a.a 1 1
8712.2.a.b 1
8712.2.a.c 1
8712.2.a.d 1
8712.2.a.e 1
8712.2.a.f 1
8712.2.a.g 1
8712.2.a.h 1
8712.2.a.i 1
8712.2.a.j 1
8712.2.a.k 1
8712.2.a.l 1
8712.2.a.m 1
8712.2.a.n 1
8712.2.a.o 1
8712.2.a.p 1
8712.2.a.q 1
8712.2.a.r 1
8712.2.a.s 1
8712.2.a.t 1
8712.2.a.u 1
8712.2.a.v 1
8712.2.a.w 1
8712.2.a.x 1
8712.2.a.y 1
8712.2.a.z 1
8712.2.a.ba 2
8712.2.a.bb 2
8712.2.a.bc 2
8712.2.a.bd 2
8712.2.a.be 2
8712.2.a.bf 2
8712.2.a.bg 2
8712.2.a.bh 2
8712.2.a.bi 2
8712.2.a.bj 2
8712.2.a.bk 2
8712.2.a.bl 2
8712.2.a.bm 2
8712.2.a.bn 2
8712.2.a.bo 2
8712.2.a.bp 2
8712.2.a.bq 2
8712.2.a.br 2
8712.2.a.bs 2
8712.2.a.bt 2
8712.2.a.bu 2
8712.2.a.bv 3
8712.2.a.bw 3
8712.2.a.bx 3
8712.2.a.by 3
8712.2.a.bz 4
8712.2.a.ca 4
8712.2.a.cb 4
8712.2.a.cc 4
8712.2.a.cd 4
8712.2.a.ce 4
8712.2.a.cf 4
8712.2.a.cg 4
8712.2.a.ch 6
8712.2.a.ci 6
8712.2.a.cj 6
8712.2.a.ck 6
8712.2.b \(\chi_{8712}(2177, \cdot)\) n/a 108 1
8712.2.d \(\chi_{8712}(2663, \cdot)\) None 0 1
8712.2.f \(\chi_{8712}(4357, \cdot)\) n/a 536 1
8712.2.h \(\chi_{8712}(8227, \cdot)\) n/a 532 1
8712.2.k \(\chi_{8712}(7019, \cdot)\) n/a 436 1
8712.2.m \(\chi_{8712}(6533, \cdot)\) n/a 432 1
8712.2.o \(\chi_{8712}(3871, \cdot)\) None 0 1
8712.2.q \(\chi_{8712}(2905, \cdot)\) n/a 654 2
8712.2.r \(\chi_{8712}(1945, \cdot)\) n/a 540 4
8712.2.u \(\chi_{8712}(967, \cdot)\) None 0 2
8712.2.w \(\chi_{8712}(725, \cdot)\) n/a 2560 2
8712.2.y \(\chi_{8712}(1211, \cdot)\) n/a 2580 2
8712.2.z \(\chi_{8712}(2419, \cdot)\) n/a 2560 2
8712.2.bb \(\chi_{8712}(1453, \cdot)\) n/a 2580 2
8712.2.bd \(\chi_{8712}(5567, \cdot)\) None 0 2
8712.2.bf \(\chi_{8712}(5081, \cdot)\) n/a 648 2
8712.2.bi \(\chi_{8712}(1207, \cdot)\) None 0 4
8712.2.bk \(\chi_{8712}(3869, \cdot)\) n/a 1728 4
8712.2.bm \(\chi_{8712}(251, \cdot)\) n/a 1728 4
8712.2.bp \(\chi_{8712}(5563, \cdot)\) n/a 2128 4
8712.2.br \(\chi_{8712}(4141, \cdot)\) n/a 2128 4
8712.2.bt \(\chi_{8712}(2447, \cdot)\) None 0 4
8712.2.bv \(\chi_{8712}(161, \cdot)\) n/a 432 4
8712.2.bw \(\chi_{8712}(793, \cdot)\) n/a 1650 10
8712.2.bx \(\chi_{8712}(2689, \cdot)\) n/a 2592 8
8712.2.bz \(\chi_{8712}(703, \cdot)\) None 0 10
8712.2.cb \(\chi_{8712}(197, \cdot)\) n/a 5280 10
8712.2.cd \(\chi_{8712}(683, \cdot)\) n/a 5280 10
8712.2.cg \(\chi_{8712}(307, \cdot)\) n/a 6580 10
8712.2.ci \(\chi_{8712}(397, \cdot)\) n/a 6580 10
8712.2.ck \(\chi_{8712}(287, \cdot)\) None 0 10
8712.2.cm \(\chi_{8712}(593, \cdot)\) n/a 1320 10
8712.2.co \(\chi_{8712}(2417, \cdot)\) n/a 2592 8
8712.2.cq \(\chi_{8712}(1703, \cdot)\) None 0 8
8712.2.cs \(\chi_{8712}(493, \cdot)\) n/a 10240 8
8712.2.cu \(\chi_{8712}(403, \cdot)\) n/a 10240 8
8712.2.cv \(\chi_{8712}(995, \cdot)\) n/a 10240 8
8712.2.cx \(\chi_{8712}(941, \cdot)\) n/a 10240 8
8712.2.cz \(\chi_{8712}(1183, \cdot)\) None 0 8
8712.2.dc \(\chi_{8712}(265, \cdot)\) n/a 7920 20
8712.2.dd \(\chi_{8712}(289, \cdot)\) n/a 6600 40
8712.2.df \(\chi_{8712}(65, \cdot)\) n/a 7920 20
8712.2.dh \(\chi_{8712}(23, \cdot)\) None 0 20
8712.2.dj \(\chi_{8712}(133, \cdot)\) n/a 31600 20
8712.2.dl \(\chi_{8712}(43, \cdot)\) n/a 31600 20
8712.2.dm \(\chi_{8712}(155, \cdot)\) n/a 31600 20
8712.2.do \(\chi_{8712}(461, \cdot)\) n/a 31600 20
8712.2.dq \(\chi_{8712}(175, \cdot)\) None 0 20
8712.2.dt \(\chi_{8712}(17, \cdot)\) n/a 5280 40
8712.2.dv \(\chi_{8712}(71, \cdot)\) None 0 40
8712.2.dx \(\chi_{8712}(37, \cdot)\) n/a 26320 40
8712.2.dz \(\chi_{8712}(19, \cdot)\) n/a 26320 40
8712.2.ec \(\chi_{8712}(179, \cdot)\) n/a 21120 40
8712.2.ee \(\chi_{8712}(413, \cdot)\) n/a 21120 40
8712.2.eg \(\chi_{8712}(127, \cdot)\) None 0 40
8712.2.ei \(\chi_{8712}(25, \cdot)\) n/a 31680 80
8712.2.el \(\chi_{8712}(7, \cdot)\) None 0 80
8712.2.en \(\chi_{8712}(29, \cdot)\) n/a 126400 80
8712.2.ep \(\chi_{8712}(59, \cdot)\) n/a 126400 80
8712.2.eq \(\chi_{8712}(139, \cdot)\) n/a 126400 80
8712.2.es \(\chi_{8712}(157, \cdot)\) n/a 126400 80
8712.2.eu \(\chi_{8712}(47, \cdot)\) None 0 80
8712.2.ew \(\chi_{8712}(41, \cdot)\) n/a 31680 80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8712))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8712)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(264))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(363))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(396))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(484))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(726))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(792))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(968))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1089))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1452))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2178))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2904))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4356))\)\(^{\oplus 2}\)