# Properties

 Label 6272.2 Level 6272 Weight 2 Dimension 647688 Nonzero newspaces 40 Sturm bound 4816896

# Learn more

## Defining parameters

 Level: $$N$$ = $$6272 = 2^{7} \cdot 7^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$40$$ Sturm bound: $$4816896$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(6272))$$.

Total New Old
Modular forms 1213824 652344 561480
Cusp forms 1194625 647688 546937
Eisenstein series 19199 4656 14543

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(6272))$$

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
6272.2.a $$\chi_{6272}(1, \cdot)$$ 6272.2.a.a 1 1
6272.2.a.b 1
6272.2.a.c 1
6272.2.a.d 1
6272.2.a.e 1
6272.2.a.f 1
6272.2.a.g 1
6272.2.a.h 1
6272.2.a.i 2
6272.2.a.j 2
6272.2.a.k 2
6272.2.a.l 2
6272.2.a.m 2
6272.2.a.n 2
6272.2.a.o 2
6272.2.a.p 2
6272.2.a.q 2
6272.2.a.r 2
6272.2.a.s 2
6272.2.a.t 2
6272.2.a.u 3
6272.2.a.v 3
6272.2.a.w 3
6272.2.a.x 3
6272.2.a.y 4
6272.2.a.z 4
6272.2.a.ba 4
6272.2.a.bb 4
6272.2.a.bc 4
6272.2.a.bd 4
6272.2.a.be 4
6272.2.a.bf 4
6272.2.a.bg 4
6272.2.a.bh 4
6272.2.a.bi 4
6272.2.a.bj 4
6272.2.a.bk 4
6272.2.a.bl 4
6272.2.a.bm 4
6272.2.a.bn 4
6272.2.a.bo 4
6272.2.a.bp 4
6272.2.a.bq 4
6272.2.a.br 4
6272.2.a.bs 4
6272.2.a.bt 4
6272.2.a.bu 4
6272.2.a.bv 4
6272.2.a.bw 6
6272.2.a.bx 6
6272.2.a.by 6
6272.2.a.bz 6
6272.2.b $$\chi_{6272}(3137, \cdot)$$ n/a 164 1
6272.2.e $$\chi_{6272}(3135, \cdot)$$ n/a 160 1
6272.2.f $$\chi_{6272}(6271, \cdot)$$ n/a 160 1
6272.2.i $$\chi_{6272}(1537, \cdot)$$ n/a 320 2
6272.2.j $$\chi_{6272}(1567, \cdot)$$ n/a 304 2
6272.2.m $$\chi_{6272}(1569, \cdot)$$ n/a 308 2
6272.2.p $$\chi_{6272}(2175, \cdot)$$ n/a 320 2
6272.2.q $$\chi_{6272}(1599, \cdot)$$ n/a 320 2
6272.2.t $$\chi_{6272}(961, \cdot)$$ n/a 320 2
6272.2.u $$\chi_{6272}(897, \cdot)$$ n/a 1344 6
6272.2.v $$\chi_{6272}(785, \cdot)$$ n/a 636 4
6272.2.y $$\chi_{6272}(783, \cdot)$$ n/a 624 4
6272.2.ba $$\chi_{6272}(31, \cdot)$$ n/a 608 4
6272.2.bb $$\chi_{6272}(2529, \cdot)$$ n/a 608 4
6272.2.bf $$\chi_{6272}(895, \cdot)$$ n/a 1344 6
6272.2.bg $$\chi_{6272}(447, \cdot)$$ n/a 1344 6
6272.2.bj $$\chi_{6272}(449, \cdot)$$ n/a 1344 6
6272.2.bk $$\chi_{6272}(393, \cdot)$$ None 0 8
6272.2.bl $$\chi_{6272}(391, \cdot)$$ None 0 8
6272.2.bo $$\chi_{6272}(513, \cdot)$$ n/a 2688 12
6272.2.bq $$\chi_{6272}(177, \cdot)$$ n/a 1248 8
6272.2.br $$\chi_{6272}(815, \cdot)$$ n/a 1248 8
6272.2.bt $$\chi_{6272}(225, \cdot)$$ n/a 2640 12
6272.2.bw $$\chi_{6272}(223, \cdot)$$ n/a 2640 12
6272.2.bx $$\chi_{6272}(195, \cdot)$$ n/a 10176 16
6272.2.ca $$\chi_{6272}(197, \cdot)$$ n/a 10416 16
6272.2.cb $$\chi_{6272}(65, \cdot)$$ n/a 2688 12
6272.2.ce $$\chi_{6272}(703, \cdot)$$ n/a 2688 12
6272.2.cf $$\chi_{6272}(255, \cdot)$$ n/a 2688 12
6272.2.ck $$\chi_{6272}(215, \cdot)$$ None 0 16
6272.2.cl $$\chi_{6272}(361, \cdot)$$ None 0 16
6272.2.cm $$\chi_{6272}(111, \cdot)$$ n/a 5328 24
6272.2.cp $$\chi_{6272}(113, \cdot)$$ n/a 5328 24
6272.2.cr $$\chi_{6272}(289, \cdot)$$ n/a 5280 24
6272.2.cs $$\chi_{6272}(159, \cdot)$$ n/a 5280 24
6272.2.cv $$\chi_{6272}(19, \cdot)$$ n/a 20352 32
6272.2.cw $$\chi_{6272}(165, \cdot)$$ n/a 20352 32
6272.2.cy $$\chi_{6272}(55, \cdot)$$ None 0 48
6272.2.cz $$\chi_{6272}(57, \cdot)$$ None 0 48
6272.2.dd $$\chi_{6272}(47, \cdot)$$ n/a 10656 48
6272.2.de $$\chi_{6272}(81, \cdot)$$ n/a 10656 48
6272.2.dh $$\chi_{6272}(29, \cdot)$$ n/a 85824 96
6272.2.di $$\chi_{6272}(27, \cdot)$$ n/a 85824 96
6272.2.dm $$\chi_{6272}(9, \cdot)$$ None 0 96
6272.2.dn $$\chi_{6272}(87, \cdot)$$ None 0 96
6272.2.do $$\chi_{6272}(37, \cdot)$$ n/a 171648 192
6272.2.dr $$\chi_{6272}(3, \cdot)$$ n/a 171648 192

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(6272))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(6272)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 14}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(98))$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(112))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(128))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(196))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(224))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(392))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(448))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(784))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(896))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1568))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3136))$$$$^{\oplus 2}$$