# Properties

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

## 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

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