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Properties

Label 8550.2
Level 8550
Weight 2
Dimension 470189
Nonzero newspaces 96
Sturm bound 7776000

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Defining parameters

Level: \( N \) = \( 8550 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 96 \)
Sturm bound: \(7776000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8550))\).

Total New Old
Modular forms 1960128 470189 1489939
Cusp forms 1927873 470189 1457684
Eisenstein series 32255 0 32255

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8550))\)

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
8550.2.a \(\chi_{8550}(1, \cdot)\) 8550.2.a.a 1 1
8550.2.a.b 1
8550.2.a.c 1
8550.2.a.d 1
8550.2.a.e 1
8550.2.a.f 1
8550.2.a.g 1
8550.2.a.h 1
8550.2.a.i 1
8550.2.a.j 1
8550.2.a.k 1
8550.2.a.l 1
8550.2.a.m 1
8550.2.a.n 1
8550.2.a.o 1
8550.2.a.p 1
8550.2.a.q 1
8550.2.a.r 1
8550.2.a.s 1
8550.2.a.t 1
8550.2.a.u 1
8550.2.a.v 1
8550.2.a.w 1
8550.2.a.x 1
8550.2.a.y 1
8550.2.a.z 1
8550.2.a.ba 1
8550.2.a.bb 1
8550.2.a.bc 1
8550.2.a.bd 1
8550.2.a.be 1
8550.2.a.bf 1
8550.2.a.bg 1
8550.2.a.bh 1
8550.2.a.bi 1
8550.2.a.bj 1
8550.2.a.bk 1
8550.2.a.bl 1
8550.2.a.bm 1
8550.2.a.bn 2
8550.2.a.bo 2
8550.2.a.bp 2
8550.2.a.bq 2
8550.2.a.br 2
8550.2.a.bs 2
8550.2.a.bt 2
8550.2.a.bu 2
8550.2.a.bv 2
8550.2.a.bw 2
8550.2.a.bx 2
8550.2.a.by 2
8550.2.a.bz 2
8550.2.a.ca 2
8550.2.a.cb 2
8550.2.a.cc 3
8550.2.a.cd 3
8550.2.a.ce 3
8550.2.a.cf 3
8550.2.a.cg 3
8550.2.a.ch 3
8550.2.a.ci 3
8550.2.a.cj 3
8550.2.a.ck 3
8550.2.a.cl 3
8550.2.a.cm 3
8550.2.a.cn 3
8550.2.a.co 3
8550.2.a.cp 3
8550.2.a.cq 3
8550.2.a.cr 3
8550.2.a.cs 3
8550.2.a.ct 3
8550.2.a.cu 4
8550.2.a.cv 4
8550.2.a.cw 6
8550.2.a.cx 6
8550.2.c \(\chi_{8550}(8549, \cdot)\) n/a 120 1
8550.2.d \(\chi_{8550}(6499, \cdot)\) n/a 134 1
8550.2.f \(\chi_{8550}(2051, \cdot)\) n/a 124 1
8550.2.i \(\chi_{8550}(5251, \cdot)\) n/a 760 2
8550.2.j \(\chi_{8550}(2851, \cdot)\) n/a 684 2
8550.2.k \(\chi_{8550}(2101, \cdot)\) n/a 760 2
8550.2.l \(\chi_{8550}(4951, \cdot)\) n/a 314 2
8550.2.n \(\chi_{8550}(2357, \cdot)\) n/a 216 2
8550.2.p \(\chi_{8550}(3457, \cdot)\) n/a 300 2
8550.2.q \(\chi_{8550}(1711, \cdot)\) n/a 896 4
8550.2.r \(\chi_{8550}(449, \cdot)\) n/a 240 2
8550.2.u \(\chi_{8550}(2899, \cdot)\) n/a 300 2
8550.2.y \(\chi_{8550}(8201, \cdot)\) n/a 760 2
8550.2.bb \(\chi_{8550}(4901, \cdot)\) n/a 760 2
8550.2.bc \(\chi_{8550}(2801, \cdot)\) n/a 760 2
8550.2.be \(\chi_{8550}(49, \cdot)\) n/a 720 2
8550.2.bh \(\chi_{8550}(799, \cdot)\) n/a 648 2
8550.2.bi \(\chi_{8550}(3199, \cdot)\) n/a 720 2
8550.2.bl \(\chi_{8550}(749, \cdot)\) n/a 720 2
8550.2.bm \(\chi_{8550}(2849, \cdot)\) n/a 720 2
8550.2.bp \(\chi_{8550}(6149, \cdot)\) n/a 720 2
8550.2.br \(\chi_{8550}(2501, \cdot)\) n/a 248 2
8550.2.bt \(\chi_{8550}(2251, \cdot)\) n/a 954 6
8550.2.bu \(\chi_{8550}(301, \cdot)\) n/a 2280 6
8550.2.bv \(\chi_{8550}(1201, \cdot)\) n/a 2280 6
8550.2.bx \(\chi_{8550}(1369, \cdot)\) n/a 904 4
8550.2.by \(\chi_{8550}(1709, \cdot)\) n/a 800 4
8550.2.cc \(\chi_{8550}(341, \cdot)\) n/a 800 4
8550.2.cd \(\chi_{8550}(1493, \cdot)\) n/a 480 4
8550.2.cg \(\chi_{8550}(493, \cdot)\) n/a 1440 4
8550.2.ch \(\chi_{8550}(943, \cdot)\) n/a 1440 4
8550.2.ck \(\chi_{8550}(1057, \cdot)\) n/a 1440 4
8550.2.cm \(\chi_{8550}(2243, \cdot)\) n/a 1296 4
8550.2.cn \(\chi_{8550}(1607, \cdot)\) n/a 1440 4
8550.2.cq \(\chi_{8550}(4457, \cdot)\) n/a 1440 4
8550.2.cr \(\chi_{8550}(1243, \cdot)\) n/a 600 4
8550.2.ct \(\chi_{8550}(391, \cdot)\) n/a 4800 8
8550.2.cu \(\chi_{8550}(571, \cdot)\) n/a 4320 8
8550.2.cv \(\chi_{8550}(121, \cdot)\) n/a 4800 8
8550.2.cw \(\chi_{8550}(1261, \cdot)\) n/a 2000 8
8550.2.cx \(\chi_{8550}(1849, \cdot)\) n/a 2160 6
8550.2.da \(\chi_{8550}(299, \cdot)\) n/a 2160 6
8550.2.db \(\chi_{8550}(401, \cdot)\) n/a 2280 6
8550.2.df \(\chi_{8550}(3851, \cdot)\) n/a 768 6
8550.2.dh \(\chi_{8550}(1649, \cdot)\) n/a 2160 6
8550.2.dj \(\chi_{8550}(199, \cdot)\) n/a 900 6
8550.2.dm \(\chi_{8550}(1799, \cdot)\) n/a 720 6
8550.2.do \(\chi_{8550}(499, \cdot)\) n/a 2160 6
8550.2.dr \(\chi_{8550}(851, \cdot)\) n/a 2280 6
8550.2.ds \(\chi_{8550}(37, \cdot)\) n/a 2000 8
8550.2.du \(\chi_{8550}(647, \cdot)\) n/a 1440 8
8550.2.dw \(\chi_{8550}(919, \cdot)\) n/a 2000 8
8550.2.dz \(\chi_{8550}(179, \cdot)\) n/a 1600 8
8550.2.eb \(\chi_{8550}(221, \cdot)\) n/a 4800 8
8550.2.ec \(\chi_{8550}(911, \cdot)\) n/a 4800 8
8550.2.ef \(\chi_{8550}(1361, \cdot)\) n/a 4800 8
8550.2.ej \(\chi_{8550}(1019, \cdot)\) n/a 4800 8
8550.2.em \(\chi_{8550}(569, \cdot)\) n/a 4800 8
8550.2.en \(\chi_{8550}(1589, \cdot)\) n/a 4800 8
8550.2.eq \(\chi_{8550}(619, \cdot)\) n/a 4800 8
8550.2.er \(\chi_{8550}(229, \cdot)\) n/a 4320 8
8550.2.eu \(\chi_{8550}(1759, \cdot)\) n/a 4800 8
8550.2.ew \(\chi_{8550}(521, \cdot)\) n/a 1600 8
8550.2.ez \(\chi_{8550}(443, \cdot)\) n/a 4320 12
8550.2.fc \(\chi_{8550}(907, \cdot)\) n/a 4320 12
8550.2.fd \(\chi_{8550}(307, \cdot)\) n/a 1800 12
8550.2.fe \(\chi_{8550}(707, \cdot)\) n/a 4320 12
8550.2.ff \(\chi_{8550}(557, \cdot)\) n/a 1440 12
8550.2.fi \(\chi_{8550}(193, \cdot)\) n/a 4320 12
8550.2.fk \(\chi_{8550}(61, \cdot)\) n/a 14400 24
8550.2.fl \(\chi_{8550}(271, \cdot)\) n/a 6000 24
8550.2.fm \(\chi_{8550}(481, \cdot)\) n/a 14400 24
8550.2.fo \(\chi_{8550}(217, \cdot)\) n/a 4000 16
8550.2.fp \(\chi_{8550}(353, \cdot)\) n/a 9600 16
8550.2.fs \(\chi_{8550}(83, \cdot)\) n/a 9600 16
8550.2.ft \(\chi_{8550}(77, \cdot)\) n/a 8640 16
8550.2.fv \(\chi_{8550}(373, \cdot)\) n/a 9600 16
8550.2.fy \(\chi_{8550}(103, \cdot)\) n/a 9600 16
8550.2.fz \(\chi_{8550}(1177, \cdot)\) n/a 9600 16
8550.2.gc \(\chi_{8550}(197, \cdot)\) n/a 3200 16
8550.2.gd \(\chi_{8550}(509, \cdot)\) n/a 14400 24
8550.2.gg \(\chi_{8550}(139, \cdot)\) n/a 14400 24
8550.2.gi \(\chi_{8550}(71, \cdot)\) n/a 4800 24
8550.2.gm \(\chi_{8550}(41, \cdot)\) n/a 14400 24
8550.2.gn \(\chi_{8550}(709, \cdot)\) n/a 14400 24
8550.2.gp \(\chi_{8550}(89, \cdot)\) n/a 4800 24
8550.2.gs \(\chi_{8550}(289, \cdot)\) n/a 6000 24
8550.2.gu \(\chi_{8550}(29, \cdot)\) n/a 14400 24
8550.2.gv \(\chi_{8550}(641, \cdot)\) n/a 14400 24
8550.2.gz \(\chi_{8550}(337, \cdot)\) n/a 28800 48
8550.2.hc \(\chi_{8550}(23, \cdot)\) n/a 28800 48
8550.2.hd \(\chi_{8550}(17, \cdot)\) n/a 9600 48
8550.2.he \(\chi_{8550}(13, \cdot)\) n/a 28800 48
8550.2.hf \(\chi_{8550}(127, \cdot)\) n/a 12000 48
8550.2.hi \(\chi_{8550}(47, \cdot)\) n/a 28800 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8550))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8550)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(190))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(285))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(342))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(450))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(475))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(570))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(855))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(950))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1425))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1710))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2850))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4275))\)\(^{\oplus 2}\)