Properties

 Label 5082.2 Level 5082 Weight 2 Dimension 164234 Nonzero newspaces 32 Sturm bound 2787840

Defining parameters

 Level: $$N$$ = $$5082 = 2 \cdot 3 \cdot 7 \cdot 11^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$32$$ Sturm bound: $$2787840$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(5082))$$.

Total New Old
Modular forms 704640 164234 540406
Cusp forms 689281 164234 525047
Eisenstein series 15359 0 15359

Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(5082))$$

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
5082.2.a $$\chi_{5082}(1, \cdot)$$ 5082.2.a.a 1 1
5082.2.a.b 1
5082.2.a.c 1
5082.2.a.d 1
5082.2.a.e 1
5082.2.a.f 1
5082.2.a.g 1
5082.2.a.h 1
5082.2.a.i 1
5082.2.a.j 1
5082.2.a.k 1
5082.2.a.l 1
5082.2.a.m 1
5082.2.a.n 1
5082.2.a.o 1
5082.2.a.p 1
5082.2.a.q 1
5082.2.a.r 1
5082.2.a.s 1
5082.2.a.t 1
5082.2.a.u 1
5082.2.a.v 1
5082.2.a.w 1
5082.2.a.x 1
5082.2.a.y 1
5082.2.a.z 1
5082.2.a.ba 1
5082.2.a.bb 1
5082.2.a.bc 2
5082.2.a.bd 2
5082.2.a.be 2
5082.2.a.bf 2
5082.2.a.bg 2
5082.2.a.bh 2
5082.2.a.bi 2
5082.2.a.bj 2
5082.2.a.bk 2
5082.2.a.bl 2
5082.2.a.bm 2
5082.2.a.bn 2
5082.2.a.bo 2
5082.2.a.bp 2
5082.2.a.bq 2
5082.2.a.br 2
5082.2.a.bs 2
5082.2.a.bt 2
5082.2.a.bu 2
5082.2.a.bv 2
5082.2.a.bw 2
5082.2.a.bx 4
5082.2.a.by 4
5082.2.a.bz 4
5082.2.a.ca 4
5082.2.a.cb 4
5082.2.a.cc 4
5082.2.a.cd 4
5082.2.a.ce 4
5082.2.a.cf 4
5082.2.a.cg 4
5082.2.c $$\chi_{5082}(4355, \cdot)$$ n/a 216 1
5082.2.e $$\chi_{5082}(1693, \cdot)$$ n/a 144 1
5082.2.g $$\chi_{5082}(4115, \cdot)$$ n/a 292 1
5082.2.i $$\chi_{5082}(1453, \cdot)$$ n/a 292 2
5082.2.j $$\chi_{5082}(1219, \cdot)$$ n/a 432 4
5082.2.k $$\chi_{5082}(1937, \cdot)$$ n/a 580 2
5082.2.n $$\chi_{5082}(725, \cdot)$$ n/a 576 2
5082.2.p $$\chi_{5082}(241, \cdot)$$ n/a 288 2
5082.2.s $$\chi_{5082}(251, \cdot)$$ n/a 1152 4
5082.2.u $$\chi_{5082}(475, \cdot)$$ n/a 576 4
5082.2.w $$\chi_{5082}(239, \cdot)$$ n/a 864 4
5082.2.y $$\chi_{5082}(463, \cdot)$$ n/a 1320 10
5082.2.z $$\chi_{5082}(487, \cdot)$$ n/a 1152 8
5082.2.bb $$\chi_{5082}(419, \cdot)$$ n/a 3520 10
5082.2.bd $$\chi_{5082}(307, \cdot)$$ n/a 1760 10
5082.2.bf $$\chi_{5082}(197, \cdot)$$ n/a 2640 10
5082.2.bi $$\chi_{5082}(481, \cdot)$$ n/a 1152 8
5082.2.bk $$\chi_{5082}(233, \cdot)$$ n/a 2304 8
5082.2.bn $$\chi_{5082}(269, \cdot)$$ n/a 2304 8
5082.2.bo $$\chi_{5082}(67, \cdot)$$ n/a 3520 20
5082.2.bp $$\chi_{5082}(169, \cdot)$$ n/a 5280 40
5082.2.br $$\chi_{5082}(439, \cdot)$$ n/a 3520 20
5082.2.bt $$\chi_{5082}(65, \cdot)$$ n/a 7040 20
5082.2.bw $$\chi_{5082}(89, \cdot)$$ n/a 7040 20
5082.2.by $$\chi_{5082}(29, \cdot)$$ n/a 10560 40
5082.2.ca $$\chi_{5082}(13, \cdot)$$ n/a 7040 40
5082.2.cc $$\chi_{5082}(125, \cdot)$$ n/a 14080 40
5082.2.ce $$\chi_{5082}(25, \cdot)$$ n/a 14080 80
5082.2.cf $$\chi_{5082}(5, \cdot)$$ n/a 28160 80
5082.2.ci $$\chi_{5082}(95, \cdot)$$ n/a 28160 80
5082.2.ck $$\chi_{5082}(19, \cdot)$$ n/a 14080 80

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

Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(5082))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(5082)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(66))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(77))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(121))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(154))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(231))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(242))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(363))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(462))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(726))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(847))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1694))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2541))$$$$^{\oplus 2}$$