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Properties

Label 8624.2
Level 8624
Weight 2
Dimension 1194539
Nonzero newspaces 64
Sturm bound 9031680

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Defining parameters

Level: \( N \) = \( 8624 = 2^{4} \cdot 7^{2} \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 64 \)
Sturm bound: \(9031680\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8624))\).

Total New Old
Modular forms 2274720 1202395 1072325
Cusp forms 2241121 1194539 1046582
Eisenstein series 33599 7856 25743

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8624))\)

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
8624.2.a \(\chi_{8624}(1, \cdot)\) 8624.2.a.a 1 1
8624.2.a.b 1
8624.2.a.c 1
8624.2.a.d 1
8624.2.a.e 1
8624.2.a.f 1
8624.2.a.g 1
8624.2.a.h 1
8624.2.a.i 1
8624.2.a.j 1
8624.2.a.k 1
8624.2.a.l 1
8624.2.a.m 1
8624.2.a.n 1
8624.2.a.o 1
8624.2.a.p 1
8624.2.a.q 1
8624.2.a.r 1
8624.2.a.s 1
8624.2.a.t 1
8624.2.a.u 1
8624.2.a.v 1
8624.2.a.w 1
8624.2.a.x 1
8624.2.a.y 1
8624.2.a.z 1
8624.2.a.ba 1
8624.2.a.bb 1
8624.2.a.bc 1
8624.2.a.bd 1
8624.2.a.be 1
8624.2.a.bf 2
8624.2.a.bg 2
8624.2.a.bh 2
8624.2.a.bi 2
8624.2.a.bj 2
8624.2.a.bk 2
8624.2.a.bl 2
8624.2.a.bm 2
8624.2.a.bn 2
8624.2.a.bo 2
8624.2.a.bp 2
8624.2.a.bq 2
8624.2.a.br 2
8624.2.a.bs 2
8624.2.a.bt 2
8624.2.a.bu 2
8624.2.a.bv 2
8624.2.a.bw 2
8624.2.a.bx 2
8624.2.a.by 2
8624.2.a.bz 2
8624.2.a.ca 2
8624.2.a.cb 2
8624.2.a.cc 2
8624.2.a.cd 2
8624.2.a.ce 2
8624.2.a.cf 3
8624.2.a.cg 3
8624.2.a.ch 3
8624.2.a.ci 3
8624.2.a.cj 3
8624.2.a.ck 3
8624.2.a.cl 3
8624.2.a.cm 3
8624.2.a.cn 3
8624.2.a.co 3
8624.2.a.cp 3
8624.2.a.cq 3
8624.2.a.cr 4
8624.2.a.cs 4
8624.2.a.ct 4
8624.2.a.cu 4
8624.2.a.cv 4
8624.2.a.cw 4
8624.2.a.cx 4
8624.2.a.cy 4
8624.2.a.cz 4
8624.2.a.da 5
8624.2.a.db 5
8624.2.a.dc 5
8624.2.a.dd 5
8624.2.a.de 8
8624.2.a.df 10
8624.2.a.dg 12
8624.2.c \(\chi_{8624}(4313, \cdot)\) None 0 1
8624.2.e \(\chi_{8624}(3233, \cdot)\) n/a 236 1
8624.2.f \(\chi_{8624}(7743, \cdot)\) n/a 246 1
8624.2.h \(\chi_{8624}(1959, \cdot)\) None 0 1
8624.2.j \(\chi_{8624}(6271, \cdot)\) n/a 200 1
8624.2.l \(\chi_{8624}(3431, \cdot)\) None 0 1
8624.2.o \(\chi_{8624}(7545, \cdot)\) None 0 1
8624.2.q \(\chi_{8624}(177, \cdot)\) n/a 400 2
8624.2.r \(\chi_{8624}(1275, \cdot)\) n/a 1948 2
8624.2.s \(\chi_{8624}(4115, \cdot)\) n/a 1600 2
8624.2.x \(\chi_{8624}(1077, \cdot)\) n/a 1904 2
8624.2.y \(\chi_{8624}(2157, \cdot)\) n/a 1640 2
8624.2.z \(\chi_{8624}(785, \cdot)\) n/a 964 4
8624.2.ba \(\chi_{8624}(2089, \cdot)\) None 0 2
8624.2.be \(\chi_{8624}(815, \cdot)\) n/a 400 2
8624.2.bg \(\chi_{8624}(263, \cdot)\) None 0 2
8624.2.bi \(\chi_{8624}(4575, \cdot)\) n/a 480 2
8624.2.bk \(\chi_{8624}(1783, \cdot)\) None 0 2
8624.2.bl \(\chi_{8624}(1145, \cdot)\) None 0 2
8624.2.bn \(\chi_{8624}(3057, \cdot)\) n/a 472 2
8624.2.bp \(\chi_{8624}(1233, \cdot)\) n/a 1680 6
8624.2.br \(\chi_{8624}(1273, \cdot)\) None 0 4
8624.2.bu \(\chi_{8624}(2647, \cdot)\) None 0 4
8624.2.bw \(\chi_{8624}(1567, \cdot)\) n/a 960 4
8624.2.by \(\chi_{8624}(1175, \cdot)\) None 0 4
8624.2.ca \(\chi_{8624}(1471, \cdot)\) n/a 984 4
8624.2.cb \(\chi_{8624}(2449, \cdot)\) n/a 944 4
8624.2.cd \(\chi_{8624}(1961, \cdot)\) None 0 4
8624.2.ch \(\chi_{8624}(2971, \cdot)\) n/a 3200 4
8624.2.ci \(\chi_{8624}(1451, \cdot)\) n/a 3808 4
8624.2.cj \(\chi_{8624}(2333, \cdot)\) n/a 3200 4
8624.2.ck \(\chi_{8624}(901, \cdot)\) n/a 3808 4
8624.2.co \(\chi_{8624}(153, \cdot)\) None 0 6
8624.2.cr \(\chi_{8624}(967, \cdot)\) None 0 6
8624.2.ct \(\chi_{8624}(111, \cdot)\) n/a 1680 6
8624.2.cv \(\chi_{8624}(727, \cdot)\) None 0 6
8624.2.cx \(\chi_{8624}(351, \cdot)\) n/a 2016 6
8624.2.cy \(\chi_{8624}(769, \cdot)\) n/a 2004 6
8624.2.da \(\chi_{8624}(617, \cdot)\) None 0 6
8624.2.dc \(\chi_{8624}(753, \cdot)\) n/a 1888 8
8624.2.dd \(\chi_{8624}(1373, \cdot)\) n/a 7792 8
8624.2.de \(\chi_{8624}(293, \cdot)\) n/a 7616 8
8624.2.dj \(\chi_{8624}(587, \cdot)\) n/a 7616 8
8624.2.dk \(\chi_{8624}(491, \cdot)\) n/a 7792 8
8624.2.dl \(\chi_{8624}(529, \cdot)\) n/a 3360 12
8624.2.dm \(\chi_{8624}(461, \cdot)\) n/a 16080 12
8624.2.dn \(\chi_{8624}(309, \cdot)\) n/a 13440 12
8624.2.ds \(\chi_{8624}(43, \cdot)\) n/a 16080 12
8624.2.dt \(\chi_{8624}(419, \cdot)\) n/a 13440 12
8624.2.dv \(\chi_{8624}(129, \cdot)\) n/a 1888 8
8624.2.dx \(\chi_{8624}(361, \cdot)\) None 0 8
8624.2.dy \(\chi_{8624}(423, \cdot)\) None 0 8
8624.2.ea \(\chi_{8624}(79, \cdot)\) n/a 1920 8
8624.2.ec \(\chi_{8624}(1047, \cdot)\) None 0 8
8624.2.ee \(\chi_{8624}(31, \cdot)\) n/a 1920 8
8624.2.ei \(\chi_{8624}(1097, \cdot)\) None 0 8
8624.2.ej \(\chi_{8624}(113, \cdot)\) n/a 8016 24
8624.2.el \(\chi_{8624}(241, \cdot)\) n/a 4008 12
8624.2.en \(\chi_{8624}(793, \cdot)\) None 0 12
8624.2.eo \(\chi_{8624}(199, \cdot)\) None 0 12
8624.2.eq \(\chi_{8624}(527, \cdot)\) n/a 4032 12
8624.2.es \(\chi_{8624}(1143, \cdot)\) None 0 12
8624.2.eu \(\chi_{8624}(1167, \cdot)\) n/a 3360 12
8624.2.ey \(\chi_{8624}(857, \cdot)\) None 0 12
8624.2.fb \(\chi_{8624}(117, \cdot)\) n/a 15232 16
8624.2.fc \(\chi_{8624}(949, \cdot)\) n/a 15232 16
8624.2.fd \(\chi_{8624}(459, \cdot)\) n/a 15232 16
8624.2.fe \(\chi_{8624}(411, \cdot)\) n/a 15232 16
8624.2.fi \(\chi_{8624}(169, \cdot)\) None 0 24
8624.2.fk \(\chi_{8624}(321, \cdot)\) n/a 8016 24
8624.2.fl \(\chi_{8624}(127, \cdot)\) n/a 8064 24
8624.2.fn \(\chi_{8624}(279, \cdot)\) None 0 24
8624.2.fp \(\chi_{8624}(223, \cdot)\) n/a 8064 24
8624.2.fr \(\chi_{8624}(183, \cdot)\) None 0 24
8624.2.fu \(\chi_{8624}(41, \cdot)\) None 0 24
8624.2.fy \(\chi_{8624}(221, \cdot)\) n/a 26880 24
8624.2.fz \(\chi_{8624}(285, \cdot)\) n/a 32160 24
8624.2.ga \(\chi_{8624}(243, \cdot)\) n/a 26880 24
8624.2.gb \(\chi_{8624}(219, \cdot)\) n/a 32160 24
8624.2.ge \(\chi_{8624}(81, \cdot)\) n/a 16032 48
8624.2.gf \(\chi_{8624}(27, \cdot)\) n/a 64320 48
8624.2.gg \(\chi_{8624}(211, \cdot)\) n/a 64320 48
8624.2.gl \(\chi_{8624}(141, \cdot)\) n/a 64320 48
8624.2.gm \(\chi_{8624}(13, \cdot)\) n/a 64320 48
8624.2.gn \(\chi_{8624}(73, \cdot)\) None 0 48
8624.2.gr \(\chi_{8624}(47, \cdot)\) n/a 16128 48
8624.2.gt \(\chi_{8624}(39, \cdot)\) None 0 48
8624.2.gv \(\chi_{8624}(95, \cdot)\) n/a 16128 48
8624.2.gx \(\chi_{8624}(103, \cdot)\) None 0 48
8624.2.gy \(\chi_{8624}(9, \cdot)\) None 0 48
8624.2.ha \(\chi_{8624}(17, \cdot)\) n/a 16032 48
8624.2.he \(\chi_{8624}(51, \cdot)\) n/a 128640 96
8624.2.hf \(\chi_{8624}(3, \cdot)\) n/a 128640 96
8624.2.hg \(\chi_{8624}(61, \cdot)\) n/a 128640 96
8624.2.hh \(\chi_{8624}(37, \cdot)\) n/a 128640 96

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8624))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8624)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(308))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(392))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(539))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(616))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(784))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1078))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1232))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2156))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4312))\)\(^{\oplus 2}\)