# Properties

 Label 8036.2 Level 8036 Weight 2 Dimension 1.10083e+06 Nonzero newspaces 64 Sturm bound 7.90272e+06

## Defining parameters

 Level: $$N$$ = $$8036 = 2^{2} \cdot 7^{2} \cdot 41$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$64$$ Sturm bound: $$7902720$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(8036))$$.

Total New Old
Modular forms 1987680 1108398 879282
Cusp forms 1963681 1100830 862851
Eisenstein series 23999 7568 16431

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(8036))$$

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
8036.2.a $$\chi_{8036}(1, \cdot)$$ 8036.2.a.a 1 1
8036.2.a.b 1
8036.2.a.c 1
8036.2.a.d 1
8036.2.a.e 1
8036.2.a.f 1
8036.2.a.g 2
8036.2.a.h 3
8036.2.a.i 4
8036.2.a.j 5
8036.2.a.k 5
8036.2.a.l 5
8036.2.a.m 8
8036.2.a.n 8
8036.2.a.o 10
8036.2.a.p 10
8036.2.a.q 15
8036.2.a.r 15
8036.2.a.s 20
8036.2.a.t 20
8036.2.c $$\chi_{8036}(8035, \cdot)$$ n/a 832 1
8036.2.d $$\chi_{8036}(4509, \cdot)$$ n/a 144 1
8036.2.f $$\chi_{8036}(3527, \cdot)$$ n/a 800 1
8036.2.i $$\chi_{8036}(165, \cdot)$$ n/a 268 2
8036.2.k $$\chi_{8036}(6077, \cdot)$$ n/a 286 2
8036.2.l $$\chi_{8036}(1567, \cdot)$$ n/a 1664 2
8036.2.n $$\chi_{8036}(2353, \cdot)$$ n/a 576 4
8036.2.p $$\chi_{8036}(411, \cdot)$$ n/a 1600 2
8036.2.r $$\chi_{8036}(4673, \cdot)$$ n/a 280 2
8036.2.u $$\chi_{8036}(4919, \cdot)$$ n/a 1664 2
8036.2.v $$\chi_{8036}(1149, \cdot)$$ n/a 1128 6
8036.2.x $$\chi_{8036}(489, \cdot)$$ n/a 560 4
8036.2.z $$\chi_{8036}(1667, \cdot)$$ n/a 3404 4
8036.2.bb $$\chi_{8036}(2157, \cdot)$$ n/a 576 4
8036.2.bc $$\chi_{8036}(195, \cdot)$$ n/a 3328 4
8036.2.bg $$\chi_{8036}(1371, \cdot)$$ n/a 3328 4
8036.2.bi $$\chi_{8036}(1403, \cdot)$$ n/a 3328 4
8036.2.bj $$\chi_{8036}(1157, \cdot)$$ n/a 560 4
8036.2.bn $$\chi_{8036}(83, \cdot)$$ n/a 6720 6
8036.2.bp $$\chi_{8036}(1065, \cdot)$$ n/a 1176 6
8036.2.bq $$\chi_{8036}(1147, \cdot)$$ n/a 7032 6
8036.2.bs $$\chi_{8036}(961, \cdot)$$ n/a 1120 8
8036.2.bu $$\chi_{8036}(979, \cdot)$$ n/a 6656 8
8036.2.bv $$\chi_{8036}(197, \cdot)$$ n/a 1144 8
8036.2.bx $$\chi_{8036}(821, \cdot)$$ n/a 2232 12
8036.2.by $$\chi_{8036}(79, \cdot)$$ n/a 6656 8
8036.2.ca $$\chi_{8036}(325, \cdot)$$ n/a 1120 8
8036.2.cd $$\chi_{8036}(419, \cdot)$$ n/a 14064 12
8036.2.ce $$\chi_{8036}(337, \cdot)$$ n/a 2352 12
8036.2.ch $$\chi_{8036}(215, \cdot)$$ n/a 6656 8
8036.2.cj $$\chi_{8036}(31, \cdot)$$ n/a 6656 8
8036.2.cm $$\chi_{8036}(373, \cdot)$$ n/a 1120 8
8036.2.cn $$\chi_{8036}(57, \cdot)$$ n/a 4704 24
8036.2.co $$\chi_{8036}(99, \cdot)$$ n/a 13616 16
8036.2.cq $$\chi_{8036}(97, \cdot)$$ n/a 2240 16
8036.2.cs $$\chi_{8036}(327, \cdot)$$ n/a 14064 12
8036.2.cv $$\chi_{8036}(81, \cdot)$$ n/a 2352 12
8036.2.cx $$\chi_{8036}(1067, \cdot)$$ n/a 13440 12
8036.2.da $$\chi_{8036}(407, \cdot)$$ n/a 28128 24
8036.2.dc $$\chi_{8036}(601, \cdot)$$ n/a 4704 24
8036.2.de $$\chi_{8036}(361, \cdot)$$ n/a 2240 16
8036.2.df $$\chi_{8036}(607, \cdot)$$ n/a 13312 16
8036.2.dh $$\chi_{8036}(139, \cdot)$$ n/a 28128 24
8036.2.dl $$\chi_{8036}(1007, \cdot)$$ n/a 28128 24
8036.2.dm $$\chi_{8036}(113, \cdot)$$ n/a 4704 24
8036.2.dp $$\chi_{8036}(9, \cdot)$$ n/a 4704 24
8036.2.dq $$\chi_{8036}(255, \cdot)$$ n/a 28128 24
8036.2.ds $$\chi_{8036}(37, \cdot)$$ n/a 9408 48
8036.2.du $$\chi_{8036}(117, \cdot)$$ n/a 4480 32
8036.2.dw $$\chi_{8036}(67, \cdot)$$ n/a 26624 32
8036.2.dy $$\chi_{8036}(169, \cdot)$$ n/a 9408 48
8036.2.dz $$\chi_{8036}(251, \cdot)$$ n/a 56256 48
8036.2.eb $$\chi_{8036}(437, \cdot)$$ n/a 9408 48
8036.2.ed $$\chi_{8036}(191, \cdot)$$ n/a 56256 48
8036.2.ef $$\chi_{8036}(25, \cdot)$$ n/a 9408 48
8036.2.ei $$\chi_{8036}(187, \cdot)$$ n/a 56256 48
8036.2.ek $$\chi_{8036}(59, \cdot)$$ n/a 56256 48
8036.2.em $$\chi_{8036}(13, \cdot)$$ n/a 18816 96
8036.2.eo $$\chi_{8036}(15, \cdot)$$ n/a 112512 96
8036.2.er $$\chi_{8036}(87, \cdot)$$ n/a 112512 96
8036.2.es $$\chi_{8036}(121, \cdot)$$ n/a 18816 96
8036.2.ev $$\chi_{8036}(11, \cdot)$$ n/a 225024 192
8036.2.ex $$\chi_{8036}(17, \cdot)$$ n/a 37632 192

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(8036))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(8036)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(41))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(82))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(98))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(164))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(196))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(287))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(574))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1148))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2009))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4018))$$$$^{\oplus 2}$$