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Properties

Label 9680.2
Level 9680
Weight 2
Dimension 1410026
Nonzero newspaces 56
Sturm bound 11151360

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Defining parameters

Level: \( N \) = \( 9680 = 2^{4} \cdot 5 \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 56 \)
Sturm bound: \(11151360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9680))\).

Total New Old
Modular forms 2805760 1417612 1388148
Cusp forms 2769921 1410026 1359895
Eisenstein series 35839 7586 28253

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9680))\)

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
9680.2.a \(\chi_{9680}(1, \cdot)\) 9680.2.a.a 1 1
9680.2.a.b 1
9680.2.a.c 1
9680.2.a.d 1
9680.2.a.e 1
9680.2.a.f 1
9680.2.a.g 1
9680.2.a.h 1
9680.2.a.i 1
9680.2.a.j 1
9680.2.a.k 1
9680.2.a.l 1
9680.2.a.m 1
9680.2.a.n 1
9680.2.a.o 1
9680.2.a.p 1
9680.2.a.q 1
9680.2.a.r 1
9680.2.a.s 1
9680.2.a.t 1
9680.2.a.u 1
9680.2.a.v 1
9680.2.a.w 1
9680.2.a.x 1
9680.2.a.y 1
9680.2.a.z 1
9680.2.a.ba 1
9680.2.a.bb 1
9680.2.a.bc 1
9680.2.a.bd 1
9680.2.a.be 1
9680.2.a.bf 1
9680.2.a.bg 2
9680.2.a.bh 2
9680.2.a.bi 2
9680.2.a.bj 2
9680.2.a.bk 2
9680.2.a.bl 2
9680.2.a.bm 2
9680.2.a.bn 2
9680.2.a.bo 2
9680.2.a.bp 2
9680.2.a.bq 2
9680.2.a.br 2
9680.2.a.bs 2
9680.2.a.bt 2
9680.2.a.bu 2
9680.2.a.bv 2
9680.2.a.bw 2
9680.2.a.bx 2
9680.2.a.by 3
9680.2.a.bz 3
9680.2.a.ca 3
9680.2.a.cb 3
9680.2.a.cc 3
9680.2.a.cd 3
9680.2.a.ce 3
9680.2.a.cf 3
9680.2.a.cg 3
9680.2.a.ch 3
9680.2.a.ci 4
9680.2.a.cj 4
9680.2.a.ck 4
9680.2.a.cl 4
9680.2.a.cm 4
9680.2.a.cn 4
9680.2.a.co 4
9680.2.a.cp 4
9680.2.a.cq 4
9680.2.a.cr 4
9680.2.a.cs 4
9680.2.a.ct 4
9680.2.a.cu 4
9680.2.a.cv 4
9680.2.a.cw 6
9680.2.a.cx 6
9680.2.a.cy 6
9680.2.a.cz 6
9680.2.a.da 6
9680.2.a.db 6
9680.2.a.dc 6
9680.2.a.dd 6
9680.2.a.de 8
9680.2.a.df 8
9680.2.b \(\chi_{9680}(5809, \cdot)\) n/a 318 1
9680.2.c \(\chi_{9680}(4839, \cdot)\) None 0 1
9680.2.f \(\chi_{9680}(3871, \cdot)\) n/a 216 1
9680.2.g \(\chi_{9680}(4841, \cdot)\) None 0 1
9680.2.l \(\chi_{9680}(969, \cdot)\) None 0 1
9680.2.m \(\chi_{9680}(9679, \cdot)\) n/a 324 1
9680.2.p \(\chi_{9680}(8711, \cdot)\) None 0 1
9680.2.s \(\chi_{9680}(5083, \cdot)\) n/a 2580 2
9680.2.t \(\chi_{9680}(1693, \cdot)\) n/a 2560 2
9680.2.v \(\chi_{9680}(1451, \cdot)\) n/a 1728 2
9680.2.w \(\chi_{9680}(2421, \cdot)\) n/a 1744 2
9680.2.z \(\chi_{9680}(727, \cdot)\) None 0 2
9680.2.bb \(\chi_{9680}(7017, \cdot)\) None 0 2
9680.2.bd \(\chi_{9680}(2177, \cdot)\) n/a 632 2
9680.2.bf \(\chi_{9680}(5567, \cdot)\) n/a 654 2
9680.2.bh \(\chi_{9680}(3389, \cdot)\) n/a 2580 2
9680.2.bi \(\chi_{9680}(2419, \cdot)\) n/a 2560 2
9680.2.bk \(\chi_{9680}(243, \cdot)\) n/a 2580 2
9680.2.bl \(\chi_{9680}(6533, \cdot)\) n/a 2560 2
9680.2.bo \(\chi_{9680}(81, \cdot)\) n/a 864 4
9680.2.bp \(\chi_{9680}(2151, \cdot)\) None 0 4
9680.2.bs \(\chi_{9680}(239, \cdot)\) n/a 1296 4
9680.2.bt \(\chi_{9680}(9, \cdot)\) None 0 4
9680.2.by \(\chi_{9680}(1721, \cdot)\) None 0 4
9680.2.bz \(\chi_{9680}(3791, \cdot)\) n/a 864 4
9680.2.cc \(\chi_{9680}(4759, \cdot)\) None 0 4
9680.2.cd \(\chi_{9680}(2689, \cdot)\) n/a 1264 4
9680.2.ce \(\chi_{9680}(881, \cdot)\) n/a 2640 10
9680.2.ch \(\chi_{9680}(717, \cdot)\) n/a 10240 8
9680.2.ci \(\chi_{9680}(3, \cdot)\) n/a 10240 8
9680.2.cj \(\chi_{9680}(699, \cdot)\) n/a 10240 8
9680.2.cm \(\chi_{9680}(269, \cdot)\) n/a 10240 8
9680.2.cn \(\chi_{9680}(2097, \cdot)\) n/a 2528 8
9680.2.cp \(\chi_{9680}(2447, \cdot)\) n/a 2592 8
9680.2.cr \(\chi_{9680}(487, \cdot)\) None 0 8
9680.2.ct \(\chi_{9680}(233, \cdot)\) None 0 8
9680.2.cv \(\chi_{9680}(1461, \cdot)\) n/a 6912 8
9680.2.cy \(\chi_{9680}(1371, \cdot)\) n/a 6912 8
9680.2.cz \(\chi_{9680}(1613, \cdot)\) n/a 10240 8
9680.2.da \(\chi_{9680}(1963, \cdot)\) n/a 10240 8
9680.2.df \(\chi_{9680}(441, \cdot)\) None 0 10
9680.2.dg \(\chi_{9680}(351, \cdot)\) n/a 2640 10
9680.2.dj \(\chi_{9680}(439, \cdot)\) None 0 10
9680.2.dk \(\chi_{9680}(529, \cdot)\) n/a 3940 10
9680.2.dl \(\chi_{9680}(791, \cdot)\) None 0 10
9680.2.do \(\chi_{9680}(879, \cdot)\) n/a 3960 10
9680.2.dp \(\chi_{9680}(89, \cdot)\) None 0 10
9680.2.ds \(\chi_{9680}(197, \cdot)\) n/a 31600 20
9680.2.dt \(\chi_{9680}(67, \cdot)\) n/a 31600 20
9680.2.dx \(\chi_{9680}(219, \cdot)\) n/a 31600 20
9680.2.dy \(\chi_{9680}(309, \cdot)\) n/a 31600 20
9680.2.ea \(\chi_{9680}(287, \cdot)\) n/a 7920 20
9680.2.ec \(\chi_{9680}(417, \cdot)\) n/a 7880 20
9680.2.ee \(\chi_{9680}(153, \cdot)\) None 0 20
9680.2.eg \(\chi_{9680}(23, \cdot)\) None 0 20
9680.2.ej \(\chi_{9680}(221, \cdot)\) n/a 21120 20
9680.2.ek \(\chi_{9680}(131, \cdot)\) n/a 21120 20
9680.2.eo \(\chi_{9680}(373, \cdot)\) n/a 31600 20
9680.2.ep \(\chi_{9680}(507, \cdot)\) n/a 31600 20
9680.2.eq \(\chi_{9680}(401, \cdot)\) n/a 10560 40
9680.2.et \(\chi_{9680}(169, \cdot)\) None 0 40
9680.2.eu \(\chi_{9680}(79, \cdot)\) n/a 15840 40
9680.2.ex \(\chi_{9680}(151, \cdot)\) None 0 40
9680.2.ey \(\chi_{9680}(49, \cdot)\) n/a 15760 40
9680.2.ez \(\chi_{9680}(39, \cdot)\) None 0 40
9680.2.fc \(\chi_{9680}(271, \cdot)\) n/a 10560 40
9680.2.fd \(\chi_{9680}(201, \cdot)\) None 0 40
9680.2.fg \(\chi_{9680}(163, \cdot)\) n/a 126400 80
9680.2.fh \(\chi_{9680}(237, \cdot)\) n/a 126400 80
9680.2.fk \(\chi_{9680}(51, \cdot)\) n/a 84480 80
9680.2.fn \(\chi_{9680}(141, \cdot)\) n/a 84480 80
9680.2.fp \(\chi_{9680}(57, \cdot)\) None 0 80
9680.2.fr \(\chi_{9680}(103, \cdot)\) None 0 80
9680.2.ft \(\chi_{9680}(47, \cdot)\) n/a 31680 80
9680.2.fv \(\chi_{9680}(17, \cdot)\) n/a 31520 80
9680.2.fw \(\chi_{9680}(69, \cdot)\) n/a 126400 80
9680.2.fz \(\chi_{9680}(19, \cdot)\) n/a 126400 80
9680.2.gc \(\chi_{9680}(147, \cdot)\) n/a 126400 80
9680.2.gd \(\chi_{9680}(13, \cdot)\) n/a 126400 80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9680))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9680)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(220))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(440))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(484))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(605))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(880))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(968))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1210))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1936))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2420))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4840))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9680))\)\(^{\oplus 1}\)