Properties

Label 9800.2
Level 9800
Weight 2
Dimension 1400159
Nonzero newspaces 72
Sturm bound 11289600

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Defining parameters

Level: \( N \) = \( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 72 \)
Sturm bound: \(11289600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9800))\).

Total New Old
Modular forms 2842560 1408113 1434447
Cusp forms 2802241 1400159 1402082
Eisenstein series 40319 7954 32365

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9800))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
9800.2.a \(\chi_{9800}(1, \cdot)\) 9800.2.a.a 1 1
9800.2.a.b 1
9800.2.a.c 1
9800.2.a.d 1
9800.2.a.e 1
9800.2.a.f 1
9800.2.a.g 1
9800.2.a.h 1
9800.2.a.i 1
9800.2.a.j 1
9800.2.a.k 1
9800.2.a.l 1
9800.2.a.m 1
9800.2.a.n 1
9800.2.a.o 1
9800.2.a.p 1
9800.2.a.q 1
9800.2.a.r 1
9800.2.a.s 1
9800.2.a.t 1
9800.2.a.u 1
9800.2.a.v 1
9800.2.a.w 1
9800.2.a.x 1
9800.2.a.y 1
9800.2.a.z 1
9800.2.a.ba 1
9800.2.a.bb 1
9800.2.a.bc 1
9800.2.a.bd 1
9800.2.a.be 1
9800.2.a.bf 1
9800.2.a.bg 1
9800.2.a.bh 1
9800.2.a.bi 1
9800.2.a.bj 1
9800.2.a.bk 1
9800.2.a.bl 1
9800.2.a.bm 1
9800.2.a.bn 1
9800.2.a.bo 1
9800.2.a.bp 1
9800.2.a.bq 1
9800.2.a.br 2
9800.2.a.bs 2
9800.2.a.bt 2
9800.2.a.bu 2
9800.2.a.bv 2
9800.2.a.bw 2
9800.2.a.bx 2
9800.2.a.by 2
9800.2.a.bz 2
9800.2.a.ca 2
9800.2.a.cb 3
9800.2.a.cc 3
9800.2.a.cd 3
9800.2.a.ce 3
9800.2.a.cf 3
9800.2.a.cg 3
9800.2.a.ch 3
9800.2.a.ci 3
9800.2.a.cj 4
9800.2.a.ck 4
9800.2.a.cl 4
9800.2.a.cm 4
9800.2.a.cn 4
9800.2.a.co 4
9800.2.a.cp 4
9800.2.a.cq 4
9800.2.a.cr 4
9800.2.a.cs 4
9800.2.a.ct 4
9800.2.a.cu 4
9800.2.a.cv 6
9800.2.a.cw 6
9800.2.a.cx 6
9800.2.a.cy 6
9800.2.a.cz 8
9800.2.a.da 8
9800.2.a.db 10
9800.2.a.dc 10
9800.2.b \(\chi_{9800}(4901, \cdot)\) n/a 764 1
9800.2.e \(\chi_{9800}(9799, \cdot)\) None 0 1
9800.2.g \(\chi_{9800}(7449, \cdot)\) n/a 184 1
9800.2.h \(\chi_{9800}(7251, \cdot)\) n/a 748 1
9800.2.k \(\chi_{9800}(2351, \cdot)\) None 0 1
9800.2.l \(\chi_{9800}(2549, \cdot)\) n/a 728 1
9800.2.n \(\chi_{9800}(4899, \cdot)\) n/a 712 1
9800.2.q \(\chi_{9800}(8201, \cdot)\) n/a 380 2
9800.2.s \(\chi_{9800}(293, \cdot)\) n/a 1424 2
9800.2.t \(\chi_{9800}(4607, \cdot)\) None 0 2
9800.2.w \(\chi_{9800}(2843, \cdot)\) n/a 1456 2
9800.2.x \(\chi_{9800}(2057, \cdot)\) n/a 360 2
9800.2.z \(\chi_{9800}(1961, \cdot)\) n/a 1228 4
9800.2.bb \(\chi_{9800}(5899, \cdot)\) n/a 1424 2
9800.2.bd \(\chi_{9800}(3351, \cdot)\) None 0 2
9800.2.bg \(\chi_{9800}(949, \cdot)\) n/a 1424 2
9800.2.bh \(\chi_{9800}(5849, \cdot)\) n/a 360 2
9800.2.bk \(\chi_{9800}(8251, \cdot)\) n/a 1496 2
9800.2.bm \(\chi_{9800}(3301, \cdot)\) n/a 1496 2
9800.2.bn \(\chi_{9800}(999, \cdot)\) None 0 2
9800.2.bp \(\chi_{9800}(1401, \cdot)\) n/a 1596 6
9800.2.bs \(\chi_{9800}(979, \cdot)\) n/a 4768 4
9800.2.bu \(\chi_{9800}(589, \cdot)\) n/a 4880 4
9800.2.bv \(\chi_{9800}(391, \cdot)\) None 0 4
9800.2.by \(\chi_{9800}(1371, \cdot)\) n/a 4768 4
9800.2.bz \(\chi_{9800}(1569, \cdot)\) n/a 1232 4
9800.2.cb \(\chi_{9800}(1959, \cdot)\) None 0 4
9800.2.ce \(\chi_{9800}(981, \cdot)\) n/a 4880 4
9800.2.cf \(\chi_{9800}(3057, \cdot)\) n/a 720 4
9800.2.ci \(\chi_{9800}(1243, \cdot)\) n/a 2848 4
9800.2.cj \(\chi_{9800}(3007, \cdot)\) None 0 4
9800.2.cm \(\chi_{9800}(1293, \cdot)\) n/a 2848 4
9800.2.co \(\chi_{9800}(699, \cdot)\) n/a 6024 6
9800.2.cq \(\chi_{9800}(1149, \cdot)\) n/a 6024 6
9800.2.ct \(\chi_{9800}(951, \cdot)\) None 0 6
9800.2.cu \(\chi_{9800}(251, \cdot)\) n/a 6348 6
9800.2.cx \(\chi_{9800}(449, \cdot)\) n/a 1512 6
9800.2.cz \(\chi_{9800}(1399, \cdot)\) None 0 6
9800.2.da \(\chi_{9800}(701, \cdot)\) n/a 6348 6
9800.2.dc \(\chi_{9800}(361, \cdot)\) n/a 2400 8
9800.2.de \(\chi_{9800}(97, \cdot)\) n/a 2400 8
9800.2.df \(\chi_{9800}(883, \cdot)\) n/a 9760 8
9800.2.di \(\chi_{9800}(687, \cdot)\) None 0 8
9800.2.dj \(\chi_{9800}(1077, \cdot)\) n/a 9536 8
9800.2.dl \(\chi_{9800}(401, \cdot)\) n/a 3192 12
9800.2.dm \(\chi_{9800}(43, \cdot)\) n/a 12048 12
9800.2.dp \(\chi_{9800}(657, \cdot)\) n/a 3024 12
9800.2.dq \(\chi_{9800}(1357, \cdot)\) n/a 12048 12
9800.2.dt \(\chi_{9800}(407, \cdot)\) None 0 12
9800.2.dv \(\chi_{9800}(2959, \cdot)\) None 0 8
9800.2.dw \(\chi_{9800}(1341, \cdot)\) n/a 9536 8
9800.2.dy \(\chi_{9800}(411, \cdot)\) n/a 9536 8
9800.2.eb \(\chi_{9800}(569, \cdot)\) n/a 2400 8
9800.2.ec \(\chi_{9800}(2909, \cdot)\) n/a 9536 8
9800.2.ef \(\chi_{9800}(31, \cdot)\) None 0 8
9800.2.eh \(\chi_{9800}(19, \cdot)\) n/a 9536 8
9800.2.ej \(\chi_{9800}(281, \cdot)\) n/a 10080 24
9800.2.ek \(\chi_{9800}(199, \cdot)\) None 0 12
9800.2.en \(\chi_{9800}(501, \cdot)\) n/a 12696 12
9800.2.ep \(\chi_{9800}(451, \cdot)\) n/a 12696 12
9800.2.eq \(\chi_{9800}(249, \cdot)\) n/a 3024 12
9800.2.et \(\chi_{9800}(149, \cdot)\) n/a 12048 12
9800.2.eu \(\chi_{9800}(551, \cdot)\) None 0 12
9800.2.ey \(\chi_{9800}(299, \cdot)\) n/a 12048 12
9800.2.ez \(\chi_{9800}(117, \cdot)\) n/a 19072 16
9800.2.fc \(\chi_{9800}(263, \cdot)\) None 0 16
9800.2.fd \(\chi_{9800}(67, \cdot)\) n/a 19072 16
9800.2.fg \(\chi_{9800}(313, \cdot)\) n/a 4800 16
9800.2.fi \(\chi_{9800}(141, \cdot)\) n/a 40224 24
9800.2.fj \(\chi_{9800}(279, \cdot)\) None 0 24
9800.2.fl \(\chi_{9800}(169, \cdot)\) n/a 10080 24
9800.2.fo \(\chi_{9800}(531, \cdot)\) n/a 40224 24
9800.2.fp \(\chi_{9800}(111, \cdot)\) None 0 24
9800.2.fs \(\chi_{9800}(29, \cdot)\) n/a 40224 24
9800.2.fu \(\chi_{9800}(139, \cdot)\) n/a 40224 24
9800.2.fx \(\chi_{9800}(207, \cdot)\) None 0 24
9800.2.fy \(\chi_{9800}(157, \cdot)\) n/a 24096 24
9800.2.gb \(\chi_{9800}(257, \cdot)\) n/a 6048 24
9800.2.gc \(\chi_{9800}(107, \cdot)\) n/a 24096 24
9800.2.ge \(\chi_{9800}(81, \cdot)\) n/a 20160 48
9800.2.gf \(\chi_{9800}(127, \cdot)\) None 0 48
9800.2.gi \(\chi_{9800}(13, \cdot)\) n/a 80448 48
9800.2.gj \(\chi_{9800}(153, \cdot)\) n/a 20160 48
9800.2.gm \(\chi_{9800}(267, \cdot)\) n/a 80448 48
9800.2.gn \(\chi_{9800}(59, \cdot)\) n/a 80448 48
9800.2.gr \(\chi_{9800}(271, \cdot)\) None 0 48
9800.2.gs \(\chi_{9800}(109, \cdot)\) n/a 80448 48
9800.2.gv \(\chi_{9800}(9, \cdot)\) n/a 20160 48
9800.2.gw \(\chi_{9800}(131, \cdot)\) n/a 80448 48
9800.2.gy \(\chi_{9800}(221, \cdot)\) n/a 80448 48
9800.2.hb \(\chi_{9800}(159, \cdot)\) None 0 48
9800.2.hd \(\chi_{9800}(123, \cdot)\) n/a 160896 96
9800.2.he \(\chi_{9800}(17, \cdot)\) n/a 40320 96
9800.2.hh \(\chi_{9800}(173, \cdot)\) n/a 160896 96
9800.2.hi \(\chi_{9800}(23, \cdot)\) None 0 96

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9800))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9800)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(280))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(350))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(392))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(490))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(700))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(980))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1225))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1400))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1960))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2450))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4900))\)\(^{\oplus 2}\)