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Properties

Label 8010.2
Level 8010
Weight 2
Dimension 413714
Nonzero newspaces 56
Sturm bound 6842880

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Defining parameters

Level: \( N \) = \( 8010 = 2 \cdot 3^{2} \cdot 5 \cdot 89 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 56 \)
Sturm bound: \(6842880\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8010))\).

Total New Old
Modular forms 1721984 413714 1308270
Cusp forms 1699457 413714 1285743
Eisenstein series 22527 0 22527

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8010))\)

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
8010.2.a \(\chi_{8010}(1, \cdot)\) 8010.2.a.a 1 1
8010.2.a.b 1
8010.2.a.c 1
8010.2.a.d 1
8010.2.a.e 1
8010.2.a.f 1
8010.2.a.g 1
8010.2.a.h 1
8010.2.a.i 1
8010.2.a.j 1
8010.2.a.k 1
8010.2.a.l 1
8010.2.a.m 1
8010.2.a.n 1
8010.2.a.o 2
8010.2.a.p 2
8010.2.a.q 2
8010.2.a.r 2
8010.2.a.s 2
8010.2.a.t 2
8010.2.a.u 2
8010.2.a.v 2
8010.2.a.w 2
8010.2.a.x 3
8010.2.a.y 3
8010.2.a.z 3
8010.2.a.ba 3
8010.2.a.bb 3
8010.2.a.bc 3
8010.2.a.bd 4
8010.2.a.be 4
8010.2.a.bf 5
8010.2.a.bg 5
8010.2.a.bh 5
8010.2.a.bi 5
8010.2.a.bj 5
8010.2.a.bk 6
8010.2.a.bl 6
8010.2.a.bm 6
8010.2.a.bn 7
8010.2.a.bo 8
8010.2.a.bp 8
8010.2.a.bq 10
8010.2.a.br 10
8010.2.d \(\chi_{8010}(6409, \cdot)\) n/a 220 1
8010.2.e \(\chi_{8010}(7831, \cdot)\) n/a 150 1
8010.2.h \(\chi_{8010}(6229, \cdot)\) n/a 224 1
8010.2.i \(\chi_{8010}(2671, \cdot)\) n/a 704 2
8010.2.j \(\chi_{8010}(233, \cdot)\) n/a 360 2
8010.2.m \(\chi_{8010}(3383, \cdot)\) n/a 352 2
8010.2.n \(\chi_{8010}(3203, \cdot)\) n/a 360 2
8010.2.p \(\chi_{8010}(2971, \cdot)\) n/a 300 2
8010.2.s \(\chi_{8010}(1369, \cdot)\) n/a 452 2
8010.2.t \(\chi_{8010}(3437, \cdot)\) n/a 360 2
8010.2.v \(\chi_{8010}(889, \cdot)\) n/a 1080 2
8010.2.y \(\chi_{8010}(1069, \cdot)\) n/a 1056 2
8010.2.z \(\chi_{8010}(2491, \cdot)\) n/a 720 2
8010.2.bc \(\chi_{8010}(3637, \cdot)\) n/a 900 4
8010.2.bf \(\chi_{8010}(37, \cdot)\) n/a 900 4
8010.2.bh \(\chi_{8010}(1169, \cdot)\) n/a 720 4
8010.2.bi \(\chi_{8010}(611, \cdot)\) n/a 480 4
8010.2.bk \(\chi_{8010}(91, \cdot)\) n/a 1500 10
8010.2.bm \(\chi_{8010}(767, \cdot)\) n/a 2160 4
8010.2.bn \(\chi_{8010}(301, \cdot)\) n/a 1440 4
8010.2.bq \(\chi_{8010}(589, \cdot)\) n/a 2160 4
8010.2.bs \(\chi_{8010}(713, \cdot)\) n/a 2112 4
8010.2.bt \(\chi_{8010}(533, \cdot)\) n/a 2160 4
8010.2.bw \(\chi_{8010}(2903, \cdot)\) n/a 2160 4
8010.2.bx \(\chi_{8010}(289, \cdot)\) n/a 2240 10
8010.2.ca \(\chi_{8010}(901, \cdot)\) n/a 1500 10
8010.2.cb \(\chi_{8010}(1189, \cdot)\) n/a 2240 10
8010.2.cf \(\chi_{8010}(101, \cdot)\) n/a 2880 8
8010.2.cg \(\chi_{8010}(749, \cdot)\) n/a 4320 8
8010.2.ci \(\chi_{8010}(457, \cdot)\) n/a 4320 8
8010.2.cl \(\chi_{8010}(2707, \cdot)\) n/a 4320 8
8010.2.cm \(\chi_{8010}(121, \cdot)\) n/a 7200 20
8010.2.co \(\chi_{8010}(53, \cdot)\) n/a 3600 20
8010.2.cp \(\chi_{8010}(109, \cdot)\) n/a 4520 20
8010.2.cs \(\chi_{8010}(361, \cdot)\) n/a 3000 20
8010.2.cu \(\chi_{8010}(413, \cdot)\) n/a 3600 20
8010.2.cv \(\chi_{8010}(1043, \cdot)\) n/a 3600 20
8010.2.cy \(\chi_{8010}(17, \cdot)\) n/a 3600 20
8010.2.db \(\chi_{8010}(1141, \cdot)\) n/a 7200 20
8010.2.dc \(\chi_{8010}(1159, \cdot)\) n/a 10800 20
8010.2.df \(\chi_{8010}(139, \cdot)\) n/a 10800 20
8010.2.dh \(\chi_{8010}(341, \cdot)\) n/a 4800 40
8010.2.di \(\chi_{8010}(359, \cdot)\) n/a 7200 40
8010.2.dk \(\chi_{8010}(127, \cdot)\) n/a 9000 40
8010.2.dn \(\chi_{8010}(163, \cdot)\) n/a 9000 40
8010.2.do \(\chi_{8010}(47, \cdot)\) n/a 21600 40
8010.2.dr \(\chi_{8010}(203, \cdot)\) n/a 21600 40
8010.2.ds \(\chi_{8010}(167, \cdot)\) n/a 21600 40
8010.2.du \(\chi_{8010}(49, \cdot)\) n/a 21600 40
8010.2.dx \(\chi_{8010}(481, \cdot)\) n/a 14400 40
8010.2.dy \(\chi_{8010}(227, \cdot)\) n/a 21600 40
8010.2.ea \(\chi_{8010}(43, \cdot)\) n/a 43200 80
8010.2.ed \(\chi_{8010}(7, \cdot)\) n/a 43200 80
8010.2.ef \(\chi_{8010}(29, \cdot)\) n/a 43200 80
8010.2.eg \(\chi_{8010}(41, \cdot)\) n/a 28800 80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8010))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8010)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(89))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(178))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(267))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(445))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(534))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(801))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(890))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1335))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1602))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2670))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4005))\)\(^{\oplus 2}\)