# Properties

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

## 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

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