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Properties

Label 9200.2
Level 9200
Weight 2
Dimension 1305077
Nonzero newspaces 56
Sturm bound 10137600

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Defining parameters

Level: \( N \) = \( 9200 = 2^{4} \cdot 5^{2} \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 56 \)
Sturm bound: \(10137600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9200))\).

Total New Old
Modular forms 2551648 1312825 1238823
Cusp forms 2517153 1305077 1212076
Eisenstein series 34495 7748 26747

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9200))\)

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
9200.2.a \(\chi_{9200}(1, \cdot)\) 9200.2.a.a 1 1
9200.2.a.b 1
9200.2.a.c 1
9200.2.a.d 1
9200.2.a.e 1
9200.2.a.f 1
9200.2.a.g 1
9200.2.a.h 1
9200.2.a.i 1
9200.2.a.j 1
9200.2.a.k 1
9200.2.a.l 1
9200.2.a.m 1
9200.2.a.n 1
9200.2.a.o 1
9200.2.a.p 1
9200.2.a.q 1
9200.2.a.r 1
9200.2.a.s 1
9200.2.a.t 1
9200.2.a.u 1
9200.2.a.v 1
9200.2.a.w 1
9200.2.a.x 1
9200.2.a.y 1
9200.2.a.z 1
9200.2.a.ba 1
9200.2.a.bb 1
9200.2.a.bc 1
9200.2.a.bd 1
9200.2.a.be 1
9200.2.a.bf 1
9200.2.a.bg 1
9200.2.a.bh 1
9200.2.a.bi 1
9200.2.a.bj 1
9200.2.a.bk 1
9200.2.a.bl 1
9200.2.a.bm 2
9200.2.a.bn 2
9200.2.a.bo 2
9200.2.a.bp 2
9200.2.a.bq 2
9200.2.a.br 2
9200.2.a.bs 2
9200.2.a.bt 2
9200.2.a.bu 2
9200.2.a.bv 2
9200.2.a.bw 2
9200.2.a.bx 2
9200.2.a.by 2
9200.2.a.bz 2
9200.2.a.ca 2
9200.2.a.cb 3
9200.2.a.cc 3
9200.2.a.cd 3
9200.2.a.ce 3
9200.2.a.cf 3
9200.2.a.cg 3
9200.2.a.ch 3
9200.2.a.ci 3
9200.2.a.cj 4
9200.2.a.ck 4
9200.2.a.cl 4
9200.2.a.cm 4
9200.2.a.cn 4
9200.2.a.co 4
9200.2.a.cp 4
9200.2.a.cq 4
9200.2.a.cr 4
9200.2.a.cs 5
9200.2.a.ct 5
9200.2.a.cu 5
9200.2.a.cv 5
9200.2.a.cw 5
9200.2.a.cx 6
9200.2.a.cy 6
9200.2.a.cz 7
9200.2.a.da 7
9200.2.a.db 7
9200.2.a.dc 7
9200.2.a.dd 8
9200.2.a.de 8
9200.2.b \(\chi_{9200}(4599, \cdot)\) None 0 1
9200.2.e \(\chi_{9200}(4049, \cdot)\) n/a 198 1
9200.2.f \(\chi_{9200}(4601, \cdot)\) None 0 1
9200.2.i \(\chi_{9200}(5151, \cdot)\) n/a 228 1
9200.2.j \(\chi_{9200}(8649, \cdot)\) None 0 1
9200.2.m \(\chi_{9200}(9199, \cdot)\) n/a 216 1
9200.2.n \(\chi_{9200}(551, \cdot)\) None 0 1
9200.2.r \(\chi_{9200}(4093, \cdot)\) n/a 1720 2
9200.2.t \(\chi_{9200}(1243, \cdot)\) n/a 1584 2
9200.2.u \(\chi_{9200}(2851, \cdot)\) n/a 1812 2
9200.2.x \(\chi_{9200}(2301, \cdot)\) n/a 1672 2
9200.2.y \(\chi_{9200}(1057, \cdot)\) n/a 428 2
9200.2.ba \(\chi_{9200}(7407, \cdot)\) n/a 396 2
9200.2.bd \(\chi_{9200}(2807, \cdot)\) None 0 2
9200.2.bf \(\chi_{9200}(5657, \cdot)\) None 0 2
9200.2.bg \(\chi_{9200}(1749, \cdot)\) n/a 1584 2
9200.2.bj \(\chi_{9200}(2299, \cdot)\) n/a 1720 2
9200.2.bk \(\chi_{9200}(507, \cdot)\) n/a 1584 2
9200.2.bm \(\chi_{9200}(3357, \cdot)\) n/a 1720 2
9200.2.bo \(\chi_{9200}(1841, \cdot)\) n/a 1320 4
9200.2.bp \(\chi_{9200}(1839, \cdot)\) n/a 1440 4
9200.2.bs \(\chi_{9200}(1289, \cdot)\) None 0 4
9200.2.bv \(\chi_{9200}(2391, \cdot)\) None 0 4
9200.2.bw \(\chi_{9200}(369, \cdot)\) n/a 1320 4
9200.2.bz \(\chi_{9200}(919, \cdot)\) None 0 4
9200.2.ca \(\chi_{9200}(1471, \cdot)\) n/a 1440 4
9200.2.cd \(\chi_{9200}(921, \cdot)\) None 0 4
9200.2.ce \(\chi_{9200}(2401, \cdot)\) n/a 2250 10
9200.2.cg \(\chi_{9200}(1333, \cdot)\) n/a 11488 8
9200.2.ci \(\chi_{9200}(323, \cdot)\) n/a 10560 8
9200.2.cj \(\chi_{9200}(461, \cdot)\) n/a 10560 8
9200.2.cm \(\chi_{9200}(91, \cdot)\) n/a 11488 8
9200.2.cn \(\chi_{9200}(137, \cdot)\) None 0 8
9200.2.cp \(\chi_{9200}(967, \cdot)\) None 0 8
9200.2.cs \(\chi_{9200}(47, \cdot)\) n/a 2640 8
9200.2.cu \(\chi_{9200}(2897, \cdot)\) n/a 2864 8
9200.2.cv \(\chi_{9200}(459, \cdot)\) n/a 11488 8
9200.2.cy \(\chi_{9200}(829, \cdot)\) n/a 10560 8
9200.2.cz \(\chi_{9200}(1427, \cdot)\) n/a 10560 8
9200.2.db \(\chi_{9200}(413, \cdot)\) n/a 11488 8
9200.2.df \(\chi_{9200}(1351, \cdot)\) None 0 10
9200.2.dg \(\chi_{9200}(799, \cdot)\) n/a 2160 10
9200.2.dj \(\chi_{9200}(1849, \cdot)\) None 0 10
9200.2.dk \(\chi_{9200}(751, \cdot)\) n/a 2280 10
9200.2.dn \(\chi_{9200}(601, \cdot)\) None 0 10
9200.2.do \(\chi_{9200}(49, \cdot)\) n/a 2140 10
9200.2.dr \(\chi_{9200}(199, \cdot)\) None 0 10
9200.2.dt \(\chi_{9200}(157, \cdot)\) n/a 17200 20
9200.2.dv \(\chi_{9200}(243, \cdot)\) n/a 17200 20
9200.2.dx \(\chi_{9200}(99, \cdot)\) n/a 17200 20
9200.2.dy \(\chi_{9200}(349, \cdot)\) n/a 17200 20
9200.2.ea \(\chi_{9200}(57, \cdot)\) None 0 20
9200.2.ec \(\chi_{9200}(407, \cdot)\) None 0 20
9200.2.ef \(\chi_{9200}(607, \cdot)\) n/a 4320 20
9200.2.eh \(\chi_{9200}(1857, \cdot)\) n/a 4280 20
9200.2.ej \(\chi_{9200}(101, \cdot)\) n/a 18120 20
9200.2.ek \(\chi_{9200}(51, \cdot)\) n/a 18120 20
9200.2.em \(\chi_{9200}(307, \cdot)\) n/a 17200 20
9200.2.eo \(\chi_{9200}(493, \cdot)\) n/a 17200 20
9200.2.eq \(\chi_{9200}(81, \cdot)\) n/a 14320 40
9200.2.er \(\chi_{9200}(41, \cdot)\) None 0 40
9200.2.eu \(\chi_{9200}(111, \cdot)\) n/a 14400 40
9200.2.ev \(\chi_{9200}(359, \cdot)\) None 0 40
9200.2.ey \(\chi_{9200}(209, \cdot)\) n/a 14320 40
9200.2.ez \(\chi_{9200}(471, \cdot)\) None 0 40
9200.2.fc \(\chi_{9200}(9, \cdot)\) None 0 40
9200.2.ff \(\chi_{9200}(79, \cdot)\) n/a 14400 40
9200.2.fh \(\chi_{9200}(37, \cdot)\) n/a 114880 80
9200.2.fj \(\chi_{9200}(123, \cdot)\) n/a 114880 80
9200.2.fl \(\chi_{9200}(29, \cdot)\) n/a 114880 80
9200.2.fm \(\chi_{9200}(19, \cdot)\) n/a 114880 80
9200.2.fo \(\chi_{9200}(17, \cdot)\) n/a 28640 80
9200.2.fq \(\chi_{9200}(127, \cdot)\) n/a 28800 80
9200.2.ft \(\chi_{9200}(87, \cdot)\) None 0 80
9200.2.fv \(\chi_{9200}(153, \cdot)\) None 0 80
9200.2.fx \(\chi_{9200}(11, \cdot)\) n/a 114880 80
9200.2.fy \(\chi_{9200}(141, \cdot)\) n/a 114880 80
9200.2.ga \(\chi_{9200}(3, \cdot)\) n/a 114880 80
9200.2.gc \(\chi_{9200}(53, \cdot)\) n/a 114880 80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9200))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9200)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(230))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(368))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(400))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(460))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(575))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(920))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1150))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1840))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2300))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4600))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9200))\)\(^{\oplus 1}\)