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Properties

Label 5550.2
Level 5550
Weight 2
Dimension 188852
Nonzero newspaces 60
Sturm bound 3283200

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Defining parameters

Level: \( N \) = \( 5550 = 2 \cdot 3 \cdot 5^{2} \cdot 37 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(3283200\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5550))\).

Total New Old
Modular forms 828864 188852 640012
Cusp forms 812737 188852 623885
Eisenstein series 16127 0 16127

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5550))\)

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
5550.2.a \(\chi_{5550}(1, \cdot)\) 5550.2.a.a 1 1
5550.2.a.b 1
5550.2.a.c 1
5550.2.a.d 1
5550.2.a.e 1
5550.2.a.f 1
5550.2.a.g 1
5550.2.a.h 1
5550.2.a.i 1
5550.2.a.j 1
5550.2.a.k 1
5550.2.a.l 1
5550.2.a.m 1
5550.2.a.n 1
5550.2.a.o 1
5550.2.a.p 1
5550.2.a.q 1
5550.2.a.r 1
5550.2.a.s 1
5550.2.a.t 1
5550.2.a.u 1
5550.2.a.v 1
5550.2.a.w 1
5550.2.a.x 1
5550.2.a.y 1
5550.2.a.z 1
5550.2.a.ba 1
5550.2.a.bb 1
5550.2.a.bc 1
5550.2.a.bd 1
5550.2.a.be 1
5550.2.a.bf 1
5550.2.a.bg 1
5550.2.a.bh 1
5550.2.a.bi 1
5550.2.a.bj 1
5550.2.a.bk 1
5550.2.a.bl 1
5550.2.a.bm 1
5550.2.a.bn 1
5550.2.a.bo 1
5550.2.a.bp 1
5550.2.a.bq 1
5550.2.a.br 1
5550.2.a.bs 2
5550.2.a.bt 2
5550.2.a.bu 2
5550.2.a.bv 2
5550.2.a.bw 2
5550.2.a.bx 2
5550.2.a.by 2
5550.2.a.bz 2
5550.2.a.ca 2
5550.2.a.cb 2
5550.2.a.cc 2
5550.2.a.cd 3
5550.2.a.ce 3
5550.2.a.cf 3
5550.2.a.cg 3
5550.2.a.ch 3
5550.2.a.ci 3
5550.2.a.cj 4
5550.2.a.ck 4
5550.2.a.cl 4
5550.2.a.cm 4
5550.2.a.cn 4
5550.2.a.co 5
5550.2.a.cp 5
5550.2.d \(\chi_{5550}(1999, \cdot)\) n/a 108 1
5550.2.e \(\chi_{5550}(1849, \cdot)\) n/a 116 1
5550.2.h \(\chi_{5550}(5401, \cdot)\) n/a 118 1
5550.2.i \(\chi_{5550}(3451, \cdot)\) n/a 240 2
5550.2.k \(\chi_{5550}(2399, \cdot)\) n/a 456 2
5550.2.l \(\chi_{5550}(43, \cdot)\) n/a 228 2
5550.2.m \(\chi_{5550}(593, \cdot)\) n/a 432 2
5550.2.n \(\chi_{5550}(443, \cdot)\) n/a 456 2
5550.2.o \(\chi_{5550}(2707, \cdot)\) n/a 228 2
5550.2.u \(\chi_{5550}(401, \cdot)\) n/a 484 2
5550.2.v \(\chi_{5550}(1111, \cdot)\) n/a 720 4
5550.2.y \(\chi_{5550}(751, \cdot)\) n/a 236 2
5550.2.bb \(\chi_{5550}(2749, \cdot)\) n/a 232 2
5550.2.bc \(\chi_{5550}(1099, \cdot)\) n/a 224 2
5550.2.bd \(\chi_{5550}(451, \cdot)\) n/a 732 6
5550.2.be \(\chi_{5550}(739, \cdot)\) n/a 752 4
5550.2.bf \(\chi_{5550}(889, \cdot)\) n/a 720 4
5550.2.bi \(\chi_{5550}(961, \cdot)\) n/a 768 4
5550.2.bm \(\chi_{5550}(251, \cdot)\) n/a 968 4
5550.2.bn \(\chi_{5550}(643, \cdot)\) n/a 456 4
5550.2.bo \(\chi_{5550}(1343, \cdot)\) n/a 912 4
5550.2.bp \(\chi_{5550}(1157, \cdot)\) n/a 912 4
5550.2.bq \(\chi_{5550}(193, \cdot)\) n/a 456 4
5550.2.bw \(\chi_{5550}(1799, \cdot)\) n/a 912 4
5550.2.bx \(\chi_{5550}(121, \cdot)\) n/a 1504 8
5550.2.by \(\chi_{5550}(1249, \cdot)\) n/a 696 6
5550.2.bz \(\chi_{5550}(49, \cdot)\) n/a 672 6
5550.2.ca \(\chi_{5550}(151, \cdot)\) n/a 720 6
5550.2.cf \(\chi_{5550}(179, \cdot)\) n/a 3040 8
5550.2.cl \(\chi_{5550}(253, \cdot)\) n/a 1520 8
5550.2.cm \(\chi_{5550}(887, \cdot)\) n/a 3040 8
5550.2.cn \(\chi_{5550}(1037, \cdot)\) n/a 2880 8
5550.2.co \(\chi_{5550}(697, \cdot)\) n/a 1520 8
5550.2.cp \(\chi_{5550}(191, \cdot)\) n/a 3040 8
5550.2.cr \(\chi_{5550}(841, \cdot)\) n/a 1536 8
5550.2.cu \(\chi_{5550}(1009, \cdot)\) n/a 1536 8
5550.2.cv \(\chi_{5550}(529, \cdot)\) n/a 1504 8
5550.2.da \(\chi_{5550}(449, \cdot)\) n/a 2736 12
5550.2.db \(\chi_{5550}(701, \cdot)\) n/a 2880 12
5550.2.de \(\chi_{5550}(457, \cdot)\) n/a 1368 12
5550.2.df \(\chi_{5550}(107, \cdot)\) n/a 2736 12
5550.2.di \(\chi_{5550}(707, \cdot)\) n/a 2736 12
5550.2.dj \(\chi_{5550}(607, \cdot)\) n/a 1368 12
5550.2.dk \(\chi_{5550}(181, \cdot)\) n/a 4512 24
5550.2.dl \(\chi_{5550}(341, \cdot)\) n/a 6080 16
5550.2.dr \(\chi_{5550}(547, \cdot)\) n/a 3040 16
5550.2.ds \(\chi_{5550}(47, \cdot)\) n/a 6080 16
5550.2.dt \(\chi_{5550}(233, \cdot)\) n/a 6080 16
5550.2.du \(\chi_{5550}(97, \cdot)\) n/a 3040 16
5550.2.dv \(\chi_{5550}(29, \cdot)\) n/a 6080 16
5550.2.eb \(\chi_{5550}(361, \cdot)\) n/a 4608 24
5550.2.ec \(\chi_{5550}(229, \cdot)\) n/a 4608 24
5550.2.ed \(\chi_{5550}(139, \cdot)\) n/a 4512 24
5550.2.ee \(\chi_{5550}(13, \cdot)\) n/a 9120 48
5550.2.ef \(\chi_{5550}(77, \cdot)\) n/a 18240 48
5550.2.ei \(\chi_{5550}(53, \cdot)\) n/a 18240 48
5550.2.ej \(\chi_{5550}(163, \cdot)\) n/a 9120 48
5550.2.em \(\chi_{5550}(131, \cdot)\) n/a 18240 48
5550.2.en \(\chi_{5550}(59, \cdot)\) n/a 18240 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5550))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5550)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(111))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(185))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(222))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(370))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(555))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(925))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1110))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1850))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2775))\)\(^{\oplus 2}\)