↑

Properties

Label 4522.2
Level 4522
Weight 2
Dimension 196237
Nonzero newspaces 80
Sturm bound 2488320

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 4522 = 2 \cdot 7 \cdot 17 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 80 \)
Sturm bound: \(2488320\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4522))\).

Total New Old
Modular forms 628992 196237 432755
Cusp forms 615169 196237 418932
Eisenstein series 13823 0 13823

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4522))\)

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
4522.2.a \(\chi_{4522}(1, \cdot)\) 4522.2.a.a 1 1
4522.2.a.b 1
4522.2.a.c 1
4522.2.a.d 1
4522.2.a.e 1
4522.2.a.f 1
4522.2.a.g 1
4522.2.a.h 1
4522.2.a.i 1
4522.2.a.j 1
4522.2.a.k 2
4522.2.a.l 2
4522.2.a.m 2
4522.2.a.n 3
4522.2.a.o 3
4522.2.a.p 3
4522.2.a.q 3
4522.2.a.r 3
4522.2.a.s 4
4522.2.a.t 5
4522.2.a.u 6
4522.2.a.v 6
4522.2.a.w 6
4522.2.a.x 6
4522.2.a.y 7
4522.2.a.z 8
4522.2.a.ba 8
4522.2.a.bb 10
4522.2.a.bc 11
4522.2.a.bd 11
4522.2.a.be 11
4522.2.a.bf 15
4522.2.b \(\chi_{4522}(1597, \cdot)\) n/a 164 1
4522.2.d \(\chi_{4522}(4521, \cdot)\) n/a 240 1
4522.2.g \(\chi_{4522}(2925, \cdot)\) n/a 208 1
4522.2.i \(\chi_{4522}(2585, \cdot)\) n/a 384 2
4522.2.j \(\chi_{4522}(239, \cdot)\) n/a 320 2
4522.2.k \(\chi_{4522}(919, \cdot)\) n/a 432 2
4522.2.l \(\chi_{4522}(1565, \cdot)\) n/a 432 2
4522.2.o \(\chi_{4522}(2129, \cdot)\) n/a 328 2
4522.2.p \(\chi_{4522}(531, \cdot)\) n/a 480 2
4522.2.r \(\chi_{4522}(1699, \cdot)\) n/a 480 2
4522.2.t \(\chi_{4522}(3161, \cdot)\) n/a 480 2
4522.2.u \(\chi_{4522}(2007, \cdot)\) n/a 432 2
4522.2.z \(\chi_{4522}(341, \cdot)\) n/a 432 2
4522.2.bb \(\chi_{4522}(69, \cdot)\) n/a 416 2
4522.2.be \(\chi_{4522}(543, \cdot)\) n/a 480 2
4522.2.bf \(\chi_{4522}(1665, \cdot)\) n/a 480 2
4522.2.bh \(\chi_{4522}(1291, \cdot)\) n/a 480 2
4522.2.bj \(\chi_{4522}(1835, \cdot)\) n/a 360 2
4522.2.bl \(\chi_{4522}(305, \cdot)\) n/a 432 2
4522.2.bo \(\chi_{4522}(1053, \cdot)\) n/a 480 2
4522.2.bq \(\chi_{4522}(103, \cdot)\) n/a 432 2
4522.2.bs \(\chi_{4522}(2395, \cdot)\) n/a 640 4
4522.2.bt \(\chi_{4522}(797, \cdot)\) n/a 960 4
4522.2.bw \(\chi_{4522}(1429, \cdot)\) n/a 960 6
4522.2.bx \(\chi_{4522}(443, \cdot)\) n/a 1272 6
4522.2.by \(\chi_{4522}(137, \cdot)\) n/a 1272 6
4522.2.bz \(\chi_{4522}(829, \cdot)\) n/a 960 4
4522.2.ca \(\chi_{4522}(429, \cdot)\) n/a 960 4
4522.2.cf \(\chi_{4522}(1475, \cdot)\) n/a 960 4
4522.2.cg \(\chi_{4522}(293, \cdot)\) n/a 960 4
4522.2.ch \(\chi_{4522}(387, \cdot)\) n/a 960 4
4522.2.ci \(\chi_{4522}(463, \cdot)\) n/a 720 4
4522.2.cn \(\chi_{4522}(191, \cdot)\) n/a 864 4
4522.2.co \(\chi_{4522}(1823, \cdot)\) n/a 960 4
4522.2.cr \(\chi_{4522}(419, \cdot)\) n/a 1728 8
4522.2.cs \(\chi_{4522}(113, \cdot)\) n/a 1440 8
4522.2.cv \(\chi_{4522}(33, \cdot)\) n/a 1440 6
4522.2.cw \(\chi_{4522}(1563, \cdot)\) n/a 1440 6
4522.2.cx \(\chi_{4522}(307, \cdot)\) n/a 1296 6
4522.2.cy \(\chi_{4522}(1055, \cdot)\) n/a 1272 6
4522.2.dh \(\chi_{4522}(509, \cdot)\) n/a 1440 6
4522.2.di \(\chi_{4522}(1087, \cdot)\) n/a 1440 6
4522.2.dj \(\chi_{4522}(169, \cdot)\) n/a 1080 6
4522.2.dk \(\chi_{4522}(713, \cdot)\) n/a 1440 6
4522.2.dl \(\chi_{4522}(409, \cdot)\) n/a 1272 6
4522.2.do \(\chi_{4522}(2089, \cdot)\) n/a 1920 8
4522.2.dp \(\chi_{4522}(457, \cdot)\) n/a 1728 8
4522.2.dw \(\chi_{4522}(501, \cdot)\) n/a 1920 8
4522.2.dx \(\chi_{4522}(559, \cdot)\) n/a 1920 8
4522.2.dy \(\chi_{4522}(729, \cdot)\) n/a 1440 8
4522.2.dz \(\chi_{4522}(297, \cdot)\) n/a 1920 8
4522.2.ea \(\chi_{4522}(145, \cdot)\) n/a 1920 8
4522.2.eb \(\chi_{4522}(121, \cdot)\) n/a 1920 8
4522.2.ee \(\chi_{4522}(13, \cdot)\) n/a 2880 12
4522.2.ef \(\chi_{4522}(89, \cdot)\) n/a 2880 12
4522.2.eg \(\chi_{4522}(395, \cdot)\) n/a 2880 12
4522.2.eh \(\chi_{4522}(123, \cdot)\) n/a 2880 12
4522.2.ei \(\chi_{4522}(225, \cdot)\) n/a 2160 12
4522.2.ej \(\chi_{4522}(81, \cdot)\) n/a 2880 12
4522.2.es \(\chi_{4522}(141, \cdot)\) n/a 2880 16
4522.2.et \(\chi_{4522}(37, \cdot)\) n/a 3840 16
4522.2.eu \(\chi_{4522}(65, \cdot)\) n/a 3840 16
4522.2.ev \(\chi_{4522}(125, \cdot)\) n/a 3840 16
4522.2.ew \(\chi_{4522}(381, \cdot)\) n/a 3456 16
4522.2.ex \(\chi_{4522}(45, \cdot)\) n/a 3840 16
4522.2.fe \(\chi_{4522}(159, \cdot)\) n/a 3840 16
4522.2.ff \(\chi_{4522}(107, \cdot)\) n/a 3840 16
4522.2.fg \(\chi_{4522}(43, \cdot)\) n/a 4320 24
4522.2.fh \(\chi_{4522}(117, \cdot)\) n/a 5760 24
4522.2.fi \(\chi_{4522}(25, \cdot)\) n/a 5760 24
4522.2.fj \(\chi_{4522}(223, \cdot)\) n/a 5760 24
4522.2.fk \(\chi_{4522}(59, \cdot)\) n/a 5760 24
4522.2.fl \(\chi_{4522}(9, \cdot)\) n/a 5760 24
4522.2.fy \(\chi_{4522}(109, \cdot)\) n/a 11520 48
4522.2.fz \(\chi_{4522}(61, \cdot)\) n/a 11520 48
4522.2.ga \(\chi_{4522}(29, \cdot)\) n/a 8640 48
4522.2.gb \(\chi_{4522}(139, \cdot)\) n/a 11520 48
4522.2.gc \(\chi_{4522}(5, \cdot)\) n/a 11520 48
4522.2.gd \(\chi_{4522}(79, \cdot)\) n/a 11520 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4522))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4522)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(133))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(238))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(266))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(323))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(646))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2261))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4522))\)\(^{\oplus 1}\)