Properties

Label 6422.2
Level 6422
Weight 2
Dimension 418515
Nonzero newspaces 48
Sturm bound 5110560

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 6422 = 2 \cdot 13^{2} \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(5110560\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6422))\).

Total New Old
Modular forms 1285848 418515 867333
Cusp forms 1269433 418515 850918
Eisenstein series 16415 0 16415

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6422))\)

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
6422.2.a \(\chi_{6422}(1, \cdot)\) 6422.2.a.a 1 1
6422.2.a.b 1
6422.2.a.c 1
6422.2.a.d 1
6422.2.a.e 1
6422.2.a.f 1
6422.2.a.g 1
6422.2.a.h 1
6422.2.a.i 1
6422.2.a.j 1
6422.2.a.k 3
6422.2.a.l 3
6422.2.a.m 3
6422.2.a.n 3
6422.2.a.o 3
6422.2.a.p 3
6422.2.a.q 3
6422.2.a.r 3
6422.2.a.s 3
6422.2.a.t 3
6422.2.a.u 3
6422.2.a.v 3
6422.2.a.w 3
6422.2.a.x 3
6422.2.a.y 3
6422.2.a.z 4
6422.2.a.ba 4
6422.2.a.bb 4
6422.2.a.bc 6
6422.2.a.bd 6
6422.2.a.be 7
6422.2.a.bf 7
6422.2.a.bg 8
6422.2.a.bh 8
6422.2.a.bi 9
6422.2.a.bj 9
6422.2.a.bk 9
6422.2.a.bl 9
6422.2.a.bm 14
6422.2.a.bn 14
6422.2.a.bo 15
6422.2.a.bp 15
6422.2.a.bq 15
6422.2.a.br 15
6422.2.d \(\chi_{6422}(3041, \cdot)\) n/a 230 1
6422.2.e \(\chi_{6422}(653, \cdot)\) n/a 516 2
6422.2.f \(\chi_{6422}(2367, \cdot)\) n/a 514 2
6422.2.g \(\chi_{6422}(191, \cdot)\) n/a 464 2
6422.2.h \(\chi_{6422}(315, \cdot)\) n/a 516 2
6422.2.i \(\chi_{6422}(1253, \cdot)\) n/a 508 2
6422.2.m \(\chi_{6422}(2851, \cdot)\) n/a 460 2
6422.2.n \(\chi_{6422}(5407, \cdot)\) n/a 508 2
6422.2.o \(\chi_{6422}(1375, \cdot)\) n/a 516 2
6422.2.v \(\chi_{6422}(1037, \cdot)\) n/a 516 2
6422.2.w \(\chi_{6422}(529, \cdot)\) n/a 1536 6
6422.2.x \(\chi_{6422}(339, \cdot)\) n/a 1554 6
6422.2.y \(\chi_{6422}(1543, \cdot)\) n/a 1536 6
6422.2.z \(\chi_{6422}(2117, \cdot)\) n/a 1032 4
6422.2.bd \(\chi_{6422}(1779, \cdot)\) n/a 1032 4
6422.2.be \(\chi_{6422}(1671, \cdot)\) n/a 1032 4
6422.2.bf \(\chi_{6422}(4971, \cdot)\) n/a 1016 4
6422.2.bh \(\chi_{6422}(495, \cdot)\) n/a 3264 12
6422.2.bi \(\chi_{6422}(823, \cdot)\) n/a 1536 6
6422.2.bm \(\chi_{6422}(1013, \cdot)\) n/a 1548 6
6422.2.bn \(\chi_{6422}(23, \cdot)\) n/a 1536 6
6422.2.br \(\chi_{6422}(77, \cdot)\) n/a 3288 12
6422.2.bx \(\chi_{6422}(249, \cdot)\) n/a 3072 12
6422.2.by \(\chi_{6422}(89, \cdot)\) n/a 3072 12
6422.2.bz \(\chi_{6422}(775, \cdot)\) n/a 3096 12
6422.2.ca \(\chi_{6422}(425, \cdot)\) n/a 7248 24
6422.2.cb \(\chi_{6422}(419, \cdot)\) n/a 6528 24
6422.2.cc \(\chi_{6422}(235, \cdot)\) n/a 7344 24
6422.2.cd \(\chi_{6422}(87, \cdot)\) n/a 7248 24
6422.2.cf \(\chi_{6422}(151, \cdot)\) n/a 7344 24
6422.2.cg \(\chi_{6422}(49, \cdot)\) n/a 7248 24
6422.2.cn \(\chi_{6422}(277, \cdot)\) n/a 7248 24
6422.2.co \(\chi_{6422}(311, \cdot)\) n/a 7344 24
6422.2.cp \(\chi_{6422}(153, \cdot)\) n/a 6576 24
6422.2.cs \(\chi_{6422}(9, \cdot)\) n/a 21888 72
6422.2.ct \(\chi_{6422}(131, \cdot)\) n/a 21744 72
6422.2.cu \(\chi_{6422}(35, \cdot)\) n/a 21888 72
6422.2.cw \(\chi_{6422}(31, \cdot)\) n/a 14688 48
6422.2.cx \(\chi_{6422}(37, \cdot)\) n/a 14496 48
6422.2.cy \(\chi_{6422}(145, \cdot)\) n/a 14496 48
6422.2.dc \(\chi_{6422}(141, \cdot)\) n/a 14496 48
6422.2.dg \(\chi_{6422}(17, \cdot)\) n/a 21888 72
6422.2.dh \(\chi_{6422}(25, \cdot)\) n/a 21744 72
6422.2.dl \(\chi_{6422}(199, \cdot)\) n/a 21888 72
6422.2.dm \(\chi_{6422}(21, \cdot)\) n/a 43488 144
6422.2.dn \(\chi_{6422}(15, \cdot)\) n/a 43776 144
6422.2.do \(\chi_{6422}(41, \cdot)\) n/a 43776 144

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6422))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6422)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(247))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(338))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(494))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3211))\)\(^{\oplus 2}\)