Properties

Label 5220.2
Level 5220
Weight 2
Dimension 305044
Nonzero newspaces 80
Sturm bound 2903040

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Defining parameters

Level: \( N \) = \( 5220 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 80 \)
Sturm bound: \(2903040\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5220))\).

Total New Old
Modular forms 734720 307956 426764
Cusp forms 716801 305044 411757
Eisenstein series 17919 2912 15007

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5220))\)

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
5220.2.a \(\chi_{5220}(1, \cdot)\) 5220.2.a.a 1 1
5220.2.a.b 1
5220.2.a.c 1
5220.2.a.d 1
5220.2.a.e 1
5220.2.a.f 1
5220.2.a.g 1
5220.2.a.h 1
5220.2.a.i 1
5220.2.a.j 1
5220.2.a.k 1
5220.2.a.l 1
5220.2.a.m 1
5220.2.a.n 1
5220.2.a.o 1
5220.2.a.p 1
5220.2.a.q 2
5220.2.a.r 2
5220.2.a.s 2
5220.2.a.t 2
5220.2.a.u 2
5220.2.a.v 2
5220.2.a.w 3
5220.2.a.x 3
5220.2.a.y 7
5220.2.a.z 7
5220.2.b \(\chi_{5220}(289, \cdot)\) 5220.2.b.a 4 1
5220.2.b.b 4
5220.2.b.c 14
5220.2.b.d 14
5220.2.b.e 16
5220.2.b.f 24
5220.2.e \(\chi_{5220}(3131, \cdot)\) n/a 240 1
5220.2.g \(\chi_{5220}(2089, \cdot)\) 5220.2.g.a 2 1
5220.2.g.b 2
5220.2.g.c 4
5220.2.g.d 10
5220.2.g.e 12
5220.2.g.f 12
5220.2.g.g 14
5220.2.g.h 14
5220.2.h \(\chi_{5220}(4931, \cdot)\) n/a 224 1
5220.2.k \(\chi_{5220}(5219, \cdot)\) n/a 360 1
5220.2.l \(\chi_{5220}(3421, \cdot)\) 5220.2.l.a 2 1
5220.2.l.b 2
5220.2.l.c 2
5220.2.l.d 4
5220.2.l.e 4
5220.2.l.f 4
5220.2.l.g 4
5220.2.l.h 6
5220.2.l.i 6
5220.2.l.j 6
5220.2.l.k 10
5220.2.n \(\chi_{5220}(1799, \cdot)\) n/a 336 1
5220.2.q \(\chi_{5220}(1741, \cdot)\) n/a 224 2
5220.2.r \(\chi_{5220}(1351, \cdot)\) n/a 600 2
5220.2.u \(\chi_{5220}(3149, \cdot)\) n/a 120 2
5220.2.v \(\chi_{5220}(233, \cdot)\) n/a 112 2
5220.2.y \(\chi_{5220}(523, \cdot)\) n/a 840 2
5220.2.ba \(\chi_{5220}(2303, \cdot)\) n/a 720 2
5220.2.bc \(\chi_{5220}(1873, \cdot)\) n/a 150 2
5220.2.bd \(\chi_{5220}(2593, \cdot)\) n/a 150 2
5220.2.bf \(\chi_{5220}(1583, \cdot)\) n/a 720 2
5220.2.bh \(\chi_{5220}(3943, \cdot)\) n/a 892 2
5220.2.bk \(\chi_{5220}(3653, \cdot)\) n/a 120 2
5220.2.bl \(\chi_{5220}(1061, \cdot)\) 5220.2.bl.a 40 2
5220.2.bl.b 40
5220.2.bo \(\chi_{5220}(3439, \cdot)\) n/a 892 2
5220.2.bq \(\chi_{5220}(59, \cdot)\) n/a 2016 2
5220.2.bs \(\chi_{5220}(1681, \cdot)\) n/a 240 2
5220.2.bv \(\chi_{5220}(1739, \cdot)\) n/a 2144 2
5220.2.bw \(\chi_{5220}(1451, \cdot)\) n/a 1344 2
5220.2.bz \(\chi_{5220}(349, \cdot)\) n/a 336 2
5220.2.cb \(\chi_{5220}(1391, \cdot)\) n/a 1440 2
5220.2.cc \(\chi_{5220}(2029, \cdot)\) n/a 360 2
5220.2.ce \(\chi_{5220}(181, \cdot)\) n/a 300 6
5220.2.cf \(\chi_{5220}(679, \cdot)\) n/a 4288 4
5220.2.ci \(\chi_{5220}(41, \cdot)\) n/a 480 4
5220.2.ck \(\chi_{5220}(463, \cdot)\) n/a 4288 4
5220.2.cl \(\chi_{5220}(173, \cdot)\) n/a 720 4
5220.2.cn \(\chi_{5220}(563, \cdot)\) n/a 4288 4
5220.2.cp \(\chi_{5220}(133, \cdot)\) n/a 720 4
5220.2.cs \(\chi_{5220}(853, \cdot)\) n/a 720 4
5220.2.cu \(\chi_{5220}(1607, \cdot)\) n/a 4288 4
5220.2.cw \(\chi_{5220}(1973, \cdot)\) n/a 672 4
5220.2.cx \(\chi_{5220}(2263, \cdot)\) n/a 4032 4
5220.2.cz \(\chi_{5220}(389, \cdot)\) n/a 720 4
5220.2.dc \(\chi_{5220}(331, \cdot)\) n/a 2880 4
5220.2.df \(\chi_{5220}(719, \cdot)\) n/a 2160 6
5220.2.dh \(\chi_{5220}(361, \cdot)\) n/a 300 6
5220.2.di \(\chi_{5220}(179, \cdot)\) n/a 2160 6
5220.2.dl \(\chi_{5220}(431, \cdot)\) n/a 1440 6
5220.2.dm \(\chi_{5220}(1009, \cdot)\) n/a 444 6
5220.2.do \(\chi_{5220}(71, \cdot)\) n/a 1440 6
5220.2.dr \(\chi_{5220}(109, \cdot)\) n/a 456 6
5220.2.ds \(\chi_{5220}(661, \cdot)\) n/a 1440 12
5220.2.dt \(\chi_{5220}(19, \cdot)\) n/a 5352 12
5220.2.dw \(\chi_{5220}(881, \cdot)\) n/a 480 12
5220.2.dy \(\chi_{5220}(557, \cdot)\) n/a 720 12
5220.2.dz \(\chi_{5220}(847, \cdot)\) n/a 5352 12
5220.2.eb \(\chi_{5220}(37, \cdot)\) n/a 900 12
5220.2.ed \(\chi_{5220}(143, \cdot)\) n/a 4320 12
5220.2.eg \(\chi_{5220}(287, \cdot)\) n/a 4320 12
5220.2.ei \(\chi_{5220}(73, \cdot)\) n/a 900 12
5220.2.ek \(\chi_{5220}(343, \cdot)\) n/a 5352 12
5220.2.el \(\chi_{5220}(53, \cdot)\) n/a 720 12
5220.2.en \(\chi_{5220}(89, \cdot)\) n/a 720 12
5220.2.eq \(\chi_{5220}(271, \cdot)\) n/a 3600 12
5220.2.es \(\chi_{5220}(589, \cdot)\) n/a 2160 12
5220.2.et \(\chi_{5220}(671, \cdot)\) n/a 8640 12
5220.2.ev \(\chi_{5220}(49, \cdot)\) n/a 2160 12
5220.2.ey \(\chi_{5220}(371, \cdot)\) n/a 8640 12
5220.2.ez \(\chi_{5220}(299, \cdot)\) n/a 12864 12
5220.2.fc \(\chi_{5220}(121, \cdot)\) n/a 1440 12
5220.2.fe \(\chi_{5220}(239, \cdot)\) n/a 12864 12
5220.2.fg \(\chi_{5220}(31, \cdot)\) n/a 17280 24
5220.2.fj \(\chi_{5220}(329, \cdot)\) n/a 4320 24
5220.2.fk \(\chi_{5220}(7, \cdot)\) n/a 25728 24
5220.2.fn \(\chi_{5220}(257, \cdot)\) n/a 4320 24
5220.2.fp \(\chi_{5220}(97, \cdot)\) n/a 4320 24
5220.2.fr \(\chi_{5220}(443, \cdot)\) n/a 25728 24
5220.2.fs \(\chi_{5220}(47, \cdot)\) n/a 25728 24
5220.2.fu \(\chi_{5220}(733, \cdot)\) n/a 4320 24
5220.2.fw \(\chi_{5220}(353, \cdot)\) n/a 4320 24
5220.2.fz \(\chi_{5220}(67, \cdot)\) n/a 25728 24
5220.2.ga \(\chi_{5220}(101, \cdot)\) n/a 2880 24
5220.2.gd \(\chi_{5220}(79, \cdot)\) n/a 25728 24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5220))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5220)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(116))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(145))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(174))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(261))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(290))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(348))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(435))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(522))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(580))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(870))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1044))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1305))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1740))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2610))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5220))\)\(^{\oplus 1}\)