Properties

Label 5610.2
Level 5610
Weight 2
Dimension 185623
Nonzero newspaces 72
Sturm bound 3317760

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Defining parameters

Level: \( N \) = \( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 72 \)
Sturm bound: \(3317760\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5610))\).

Total New Old
Modular forms 839680 185623 654057
Cusp forms 819201 185623 633578
Eisenstein series 20479 0 20479

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5610))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
5610.2.a \(\chi_{5610}(1, \cdot)\) 5610.2.a.a 1 1
5610.2.a.b 1
5610.2.a.c 1
5610.2.a.d 1
5610.2.a.e 1
5610.2.a.f 1
5610.2.a.g 1
5610.2.a.h 1
5610.2.a.i 1
5610.2.a.j 1
5610.2.a.k 1
5610.2.a.l 1
5610.2.a.m 1
5610.2.a.n 1
5610.2.a.o 1
5610.2.a.p 1
5610.2.a.q 1
5610.2.a.r 1
5610.2.a.s 1
5610.2.a.t 1
5610.2.a.u 1
5610.2.a.v 1
5610.2.a.w 1
5610.2.a.x 1
5610.2.a.y 1
5610.2.a.z 1
5610.2.a.ba 1
5610.2.a.bb 1
5610.2.a.bc 1
5610.2.a.bd 1
5610.2.a.be 1
5610.2.a.bf 1
5610.2.a.bg 1
5610.2.a.bh 1
5610.2.a.bi 1
5610.2.a.bj 1
5610.2.a.bk 1
5610.2.a.bl 1
5610.2.a.bm 2
5610.2.a.bn 2
5610.2.a.bo 2
5610.2.a.bp 2
5610.2.a.bq 2
5610.2.a.br 2
5610.2.a.bs 2
5610.2.a.bt 2
5610.2.a.bu 2
5610.2.a.bv 2
5610.2.a.bw 2
5610.2.a.bx 2
5610.2.a.by 3
5610.2.a.bz 3
5610.2.a.ca 3
5610.2.a.cb 3
5610.2.a.cc 3
5610.2.a.cd 3
5610.2.a.ce 4
5610.2.a.cf 4
5610.2.a.cg 4
5610.2.a.ch 4
5610.2.a.ci 5
5610.2.a.cj 5
5610.2.a.ck 5
5610.2.b \(\chi_{5610}(4421, \cdot)\) n/a 256 1
5610.2.d \(\chi_{5610}(4489, \cdot)\) n/a 160 1
5610.2.f \(\chi_{5610}(5609, \cdot)\) n/a 432 1
5610.2.h \(\chi_{5610}(2311, \cdot)\) n/a 120 1
5610.2.k \(\chi_{5610}(1121, \cdot)\) n/a 288 1
5610.2.m \(\chi_{5610}(1189, \cdot)\) n/a 176 1
5610.2.o \(\chi_{5610}(3299, \cdot)\) n/a 384 1
5610.2.q \(\chi_{5610}(3013, \cdot)\) n/a 432 2
5610.2.s \(\chi_{5610}(353, \cdot)\) n/a 720 2
5610.2.u \(\chi_{5610}(1849, \cdot)\) n/a 352 2
5610.2.w \(\chi_{5610}(1781, \cdot)\) n/a 576 2
5610.2.y \(\chi_{5610}(1937, \cdot)\) n/a 720 2
5610.2.bb \(\chi_{5610}(2993, \cdot)\) n/a 640 2
5610.2.bc \(\chi_{5610}(373, \cdot)\) n/a 432 2
5610.2.bf \(\chi_{5610}(307, \cdot)\) n/a 384 2
5610.2.bh \(\chi_{5610}(2971, \cdot)\) n/a 240 2
5610.2.bj \(\chi_{5610}(659, \cdot)\) n/a 864 2
5610.2.bl \(\chi_{5610}(1033, \cdot)\) n/a 432 2
5610.2.bn \(\chi_{5610}(2333, \cdot)\) n/a 720 2
5610.2.bo \(\chi_{5610}(511, \cdot)\) n/a 512 4
5610.2.bp \(\chi_{5610}(3629, \cdot)\) n/a 1728 4
5610.2.bq \(\chi_{5610}(331, \cdot)\) n/a 480 4
5610.2.bt \(\chi_{5610}(287, \cdot)\) n/a 1440 4
5610.2.bu \(\chi_{5610}(637, \cdot)\) n/a 864 4
5610.2.bz \(\chi_{5610}(43, \cdot)\) n/a 864 4
5610.2.ca \(\chi_{5610}(1607, \cdot)\) n/a 1440 4
5610.2.cd \(\chi_{5610}(529, \cdot)\) n/a 736 4
5610.2.ce \(\chi_{5610}(461, \cdot)\) n/a 1152 4
5610.2.ch \(\chi_{5610}(239, \cdot)\) n/a 1536 4
5610.2.cj \(\chi_{5610}(169, \cdot)\) n/a 864 4
5610.2.cl \(\chi_{5610}(101, \cdot)\) n/a 1152 4
5610.2.cm \(\chi_{5610}(1291, \cdot)\) n/a 576 4
5610.2.co \(\chi_{5610}(1019, \cdot)\) n/a 1728 4
5610.2.cq \(\chi_{5610}(1939, \cdot)\) n/a 768 4
5610.2.cs \(\chi_{5610}(1361, \cdot)\) n/a 1024 4
5610.2.cw \(\chi_{5610}(133, \cdot)\) n/a 1440 8
5610.2.cx \(\chi_{5610}(1187, \cdot)\) n/a 3456 8
5610.2.da \(\chi_{5610}(551, \cdot)\) n/a 1920 8
5610.2.db \(\chi_{5610}(241, \cdot)\) n/a 1152 8
5610.2.de \(\chi_{5610}(109, \cdot)\) n/a 1728 8
5610.2.df \(\chi_{5610}(419, \cdot)\) n/a 2880 8
5610.2.dg \(\chi_{5610}(197, \cdot)\) n/a 3456 8
5610.2.dh \(\chi_{5610}(793, \cdot)\) n/a 1440 8
5610.2.dl \(\chi_{5610}(47, \cdot)\) n/a 3456 8
5610.2.dn \(\chi_{5610}(13, \cdot)\) n/a 1728 8
5610.2.do \(\chi_{5610}(149, \cdot)\) n/a 3456 8
5610.2.dq \(\chi_{5610}(361, \cdot)\) n/a 1152 8
5610.2.ds \(\chi_{5610}(613, \cdot)\) n/a 1536 8
5610.2.dv \(\chi_{5610}(1393, \cdot)\) n/a 1728 8
5610.2.dw \(\chi_{5610}(137, \cdot)\) n/a 3072 8
5610.2.dz \(\chi_{5610}(203, \cdot)\) n/a 3456 8
5610.2.eb \(\chi_{5610}(701, \cdot)\) n/a 2304 8
5610.2.ed \(\chi_{5610}(829, \cdot)\) n/a 1728 8
5610.2.ee \(\chi_{5610}(863, \cdot)\) n/a 3456 8
5610.2.eg \(\chi_{5610}(217, \cdot)\) n/a 1728 8
5610.2.ei \(\chi_{5610}(49, \cdot)\) n/a 3456 16
5610.2.ej \(\chi_{5610}(161, \cdot)\) n/a 4608 16
5610.2.eo \(\chi_{5610}(127, \cdot)\) n/a 3456 16
5610.2.ep \(\chi_{5610}(257, \cdot)\) n/a 6912 16
5610.2.eq \(\chi_{5610}(53, \cdot)\) n/a 6912 16
5610.2.er \(\chi_{5610}(457, \cdot)\) n/a 3456 16
5610.2.ew \(\chi_{5610}(359, \cdot)\) n/a 6912 16
5610.2.ex \(\chi_{5610}(631, \cdot)\) n/a 2304 16
5610.2.fa \(\chi_{5610}(37, \cdot)\) n/a 6912 32
5610.2.fb \(\chi_{5610}(173, \cdot)\) n/a 13824 32
5610.2.fc \(\chi_{5610}(61, \cdot)\) n/a 4608 32
5610.2.fd \(\chi_{5610}(71, \cdot)\) n/a 9216 32
5610.2.fg \(\chi_{5610}(269, \cdot)\) n/a 13824 32
5610.2.fh \(\chi_{5610}(79, \cdot)\) n/a 6912 32
5610.2.fk \(\chi_{5610}(107, \cdot)\) n/a 13824 32
5610.2.fl \(\chi_{5610}(367, \cdot)\) n/a 6912 32

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5610))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5610)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(170))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(187))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(255))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(330))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(374))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(510))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(561))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(935))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1122))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1870))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2805))\)\(^{\oplus 2}\)