Properties

Label 8470.2
Level 8470
Weight 2
Dimension 602186
Nonzero newspaces 48
Sturm bound 8363520

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Defining parameters

Level: \( N \) = \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(8363520\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8470))\).

Total New Old
Modular forms 2106240 602186 1504054
Cusp forms 2075521 602186 1473335
Eisenstein series 30719 0 30719

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8470))\)

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
8470.2.a \(\chi_{8470}(1, \cdot)\) 8470.2.a.a 1 1
8470.2.a.b 1
8470.2.a.c 1
8470.2.a.d 1
8470.2.a.e 1
8470.2.a.f 1
8470.2.a.g 1
8470.2.a.h 1
8470.2.a.i 1
8470.2.a.j 1
8470.2.a.k 1
8470.2.a.l 1
8470.2.a.m 1
8470.2.a.n 1
8470.2.a.o 1
8470.2.a.p 1
8470.2.a.q 1
8470.2.a.r 1
8470.2.a.s 1
8470.2.a.t 1
8470.2.a.u 1
8470.2.a.v 1
8470.2.a.w 1
8470.2.a.x 1
8470.2.a.y 1
8470.2.a.z 1
8470.2.a.ba 1
8470.2.a.bb 1
8470.2.a.bc 1
8470.2.a.bd 1
8470.2.a.be 1
8470.2.a.bf 1
8470.2.a.bg 1
8470.2.a.bh 1
8470.2.a.bi 2
8470.2.a.bj 2
8470.2.a.bk 2
8470.2.a.bl 2
8470.2.a.bm 2
8470.2.a.bn 2
8470.2.a.bo 2
8470.2.a.bp 2
8470.2.a.bq 2
8470.2.a.br 2
8470.2.a.bs 2
8470.2.a.bt 2
8470.2.a.bu 2
8470.2.a.bv 2
8470.2.a.bw 2
8470.2.a.bx 2
8470.2.a.by 2
8470.2.a.bz 2
8470.2.a.ca 2
8470.2.a.cb 2
8470.2.a.cc 2
8470.2.a.cd 2
8470.2.a.ce 2
8470.2.a.cf 2
8470.2.a.cg 3
8470.2.a.ch 3
8470.2.a.ci 3
8470.2.a.cj 3
8470.2.a.ck 3
8470.2.a.cl 3
8470.2.a.cm 3
8470.2.a.cn 3
8470.2.a.co 4
8470.2.a.cp 4
8470.2.a.cq 4
8470.2.a.cr 4
8470.2.a.cs 4
8470.2.a.ct 4
8470.2.a.cu 6
8470.2.a.cv 6
8470.2.a.cw 6
8470.2.a.cx 6
8470.2.a.cy 6
8470.2.a.cz 6
8470.2.a.da 6
8470.2.a.db 6
8470.2.a.dc 6
8470.2.a.dd 6
8470.2.a.de 6
8470.2.a.df 6
8470.2.a.dg 8
8470.2.a.dh 8
8470.2.c \(\chi_{8470}(3389, \cdot)\) n/a 328 1
8470.2.e \(\chi_{8470}(5081, \cdot)\) n/a 288 1
8470.2.g \(\chi_{8470}(8469, \cdot)\) n/a 432 1
8470.2.i \(\chi_{8470}(4841, \cdot)\) n/a 584 2
8470.2.l \(\chi_{8470}(727, \cdot)\) n/a 872 2
8470.2.m \(\chi_{8470}(967, \cdot)\) n/a 648 2
8470.2.n \(\chi_{8470}(3711, \cdot)\) n/a 864 4
8470.2.o \(\chi_{8470}(1209, \cdot)\) n/a 864 2
8470.2.r \(\chi_{8470}(2179, \cdot)\) n/a 872 2
8470.2.t \(\chi_{8470}(241, \cdot)\) n/a 576 2
8470.2.w \(\chi_{8470}(699, \cdot)\) n/a 1728 4
8470.2.y \(\chi_{8470}(1371, \cdot)\) n/a 1152 4
8470.2.ba \(\chi_{8470}(729, \cdot)\) n/a 1296 4
8470.2.bc \(\chi_{8470}(771, \cdot)\) n/a 2640 10
8470.2.bd \(\chi_{8470}(243, \cdot)\) n/a 1744 4
8470.2.be \(\chi_{8470}(4113, \cdot)\) n/a 1728 4
8470.2.bh \(\chi_{8470}(81, \cdot)\) n/a 2304 8
8470.2.bi \(\chi_{8470}(1443, \cdot)\) n/a 2592 8
8470.2.bj \(\chi_{8470}(27, \cdot)\) n/a 3456 8
8470.2.bm \(\chi_{8470}(461, \cdot)\) n/a 3520 10
8470.2.bo \(\chi_{8470}(309, \cdot)\) n/a 3960 10
8470.2.br \(\chi_{8470}(769, \cdot)\) n/a 5280 10
8470.2.bu \(\chi_{8470}(481, \cdot)\) n/a 2304 8
8470.2.bw \(\chi_{8470}(9, \cdot)\) n/a 3456 8
8470.2.bz \(\chi_{8470}(1909, \cdot)\) n/a 3456 8
8470.2.ca \(\chi_{8470}(221, \cdot)\) n/a 7040 20
8470.2.cb \(\chi_{8470}(43, \cdot)\) n/a 7920 20
8470.2.cc \(\chi_{8470}(573, \cdot)\) n/a 10560 20
8470.2.cf \(\chi_{8470}(71, \cdot)\) n/a 10560 40
8470.2.ci \(\chi_{8470}(233, \cdot)\) n/a 6912 16
8470.2.cj \(\chi_{8470}(3, \cdot)\) n/a 6912 16
8470.2.cm \(\chi_{8470}(439, \cdot)\) n/a 10560 20
8470.2.co \(\chi_{8470}(131, \cdot)\) n/a 7040 20
8470.2.cq \(\chi_{8470}(529, \cdot)\) n/a 10560 20
8470.2.cs \(\chi_{8470}(139, \cdot)\) n/a 21120 40
8470.2.cv \(\chi_{8470}(169, \cdot)\) n/a 15840 40
8470.2.cx \(\chi_{8470}(41, \cdot)\) n/a 14080 40
8470.2.da \(\chi_{8470}(263, \cdot)\) n/a 21120 40
8470.2.db \(\chi_{8470}(353, \cdot)\) n/a 21120 40
8470.2.dc \(\chi_{8470}(191, \cdot)\) n/a 28160 80
8470.2.df \(\chi_{8470}(97, \cdot)\) n/a 42240 80
8470.2.dg \(\chi_{8470}(57, \cdot)\) n/a 31680 80
8470.2.dh \(\chi_{8470}(179, \cdot)\) n/a 42240 80
8470.2.dj \(\chi_{8470}(61, \cdot)\) n/a 28160 80
8470.2.dl \(\chi_{8470}(19, \cdot)\) n/a 42240 80
8470.2.do \(\chi_{8470}(47, \cdot)\) n/a 84480 160
8470.2.dp \(\chi_{8470}(107, \cdot)\) n/a 84480 160

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8470))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8470)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(385))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(605))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(770))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(847))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1210))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1694))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4235))\)\(^{\oplus 2}\)