# Properties

 Label 8034.2 Level 8034 Weight 2 Dimension 440145 Nonzero newspaces 60 Sturm bound 7128576

## Defining parameters

 Level: $$N$$ = $$8034 = 2 \cdot 3 \cdot 13 \cdot 103$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$60$$ Sturm bound: $$7128576$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(8034))$$.

Total New Old
Modular forms 1791936 440145 1351791
Cusp forms 1772353 440145 1332208
Eisenstein series 19583 0 19583

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(8034))$$

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
8034.2.a $$\chi_{8034}(1, \cdot)$$ 8034.2.a.a 1 1
8034.2.a.b 1
8034.2.a.c 1
8034.2.a.d 1
8034.2.a.e 1
8034.2.a.f 1
8034.2.a.g 1
8034.2.a.h 1
8034.2.a.i 1
8034.2.a.j 1
8034.2.a.k 1
8034.2.a.l 2
8034.2.a.m 2
8034.2.a.n 4
8034.2.a.o 7
8034.2.a.p 8
8034.2.a.q 8
8034.2.a.r 9
8034.2.a.s 10
8034.2.a.t 11
8034.2.a.u 11
8034.2.a.v 11
8034.2.a.w 12
8034.2.a.x 13
8034.2.a.y 13
8034.2.a.z 14
8034.2.a.ba 14
8034.2.a.bb 14
8034.2.a.bc 15
8034.2.a.bd 16
8034.2.b $$\chi_{8034}(8033, \cdot)$$ n/a 488 1
8034.2.c $$\chi_{8034}(5563, \cdot)$$ n/a 236 1
8034.2.h $$\chi_{8034}(2471, \cdot)$$ n/a 416 1
8034.2.i $$\chi_{8034}(3043, \cdot)$$ n/a 416 2
8034.2.j $$\chi_{8034}(4897, \cdot)$$ n/a 484 2
8034.2.k $$\chi_{8034}(5515, \cdot)$$ n/a 484 2
8034.2.l $$\chi_{8034}(1855, \cdot)$$ n/a 480 2
8034.2.m $$\chi_{8034}(2059, \cdot)$$ n/a 480 2
8034.2.o $$\chi_{8034}(2267, \cdot)$$ n/a 952 2
8034.2.s $$\chi_{8034}(3091, \cdot)$$ n/a 472 2
8034.2.t $$\chi_{8034}(5561, \cdot)$$ n/a 968 2
8034.2.w $$\chi_{8034}(5825, \cdot)$$ n/a 832 2
8034.2.x $$\chi_{8034}(263, \cdot)$$ n/a 972 2
8034.2.bc $$\chi_{8034}(1901, \cdot)$$ n/a 972 2
8034.2.bd $$\chi_{8034}(1499, \cdot)$$ n/a 972 2
8034.2.be $$\chi_{8034}(355, \cdot)$$ n/a 484 2
8034.2.bj $$\chi_{8034}(6751, \cdot)$$ n/a 484 2
8034.2.bk $$\chi_{8034}(881, \cdot)$$ n/a 972 2
8034.2.bl $$\chi_{8034}(571, \cdot)$$ n/a 488 2
8034.2.bm $$\chi_{8034}(3353, \cdot)$$ n/a 968 2
8034.2.bp $$\chi_{8034}(4325, \cdot)$$ n/a 968 2
8034.2.bt $$\chi_{8034}(3343, \cdot)$$ n/a 968 4
8034.2.bv $$\chi_{8034}(1649, \cdot)$$ n/a 1904 4
8034.2.bw $$\chi_{8034}(3239, \cdot)$$ n/a 1944 4
8034.2.bz $$\chi_{8034}(983, \cdot)$$ n/a 1936 4
8034.2.cb $$\chi_{8034}(1087, \cdot)$$ n/a 976 4
8034.2.cd $$\chi_{8034}(1441, \cdot)$$ n/a 976 4
8034.2.ce $$\chi_{8034}(253, \cdot)$$ n/a 968 4
8034.2.ch $$\chi_{8034}(149, \cdot)$$ n/a 1944 4
8034.2.ci $$\chi_{8034}(79, \cdot)$$ n/a 3328 16
8034.2.cj $$\chi_{8034}(209, \cdot)$$ n/a 6656 16
8034.2.co $$\chi_{8034}(493, \cdot)$$ n/a 3840 16
8034.2.cp $$\chi_{8034}(233, \cdot)$$ n/a 7808 16
8034.2.cq $$\chi_{8034}(61, \cdot)$$ n/a 7808 32
8034.2.cr $$\chi_{8034}(367, \cdot)$$ n/a 7744 32
8034.2.cs $$\chi_{8034}(55, \cdot)$$ n/a 7744 32
8034.2.ct $$\chi_{8034}(235, \cdot)$$ n/a 6656 32
8034.2.cv $$\chi_{8034}(203, \cdot)$$ n/a 15616 32
8034.2.cx $$\chi_{8034}(31, \cdot)$$ n/a 7680 32
8034.2.da $$\chi_{8034}(113, \cdot)$$ n/a 15488 32
8034.2.dd $$\chi_{8034}(77, \cdot)$$ n/a 15488 32
8034.2.de $$\chi_{8034}(25, \cdot)$$ n/a 7808 32
8034.2.df $$\chi_{8034}(101, \cdot)$$ n/a 15552 32
8034.2.dg $$\chi_{8034}(49, \cdot)$$ n/a 7744 32
8034.2.dl $$\chi_{8034}(121, \cdot)$$ n/a 7744 32
8034.2.dm $$\chi_{8034}(257, \cdot)$$ n/a 15552 32
8034.2.dn $$\chi_{8034}(35, \cdot)$$ n/a 15552 32
8034.2.ds $$\chi_{8034}(191, \cdot)$$ n/a 15552 32
8034.2.dt $$\chi_{8034}(53, \cdot)$$ n/a 13312 32
8034.2.dw $$\chi_{8034}(95, \cdot)$$ n/a 15488 32
8034.2.dx $$\chi_{8034}(751, \cdot)$$ n/a 7808 32
8034.2.ea $$\chi_{8034}(59, \cdot)$$ n/a 31104 64
8034.2.ed $$\chi_{8034}(397, \cdot)$$ n/a 15488 64
8034.2.ee $$\chi_{8034}(37, \cdot)$$ n/a 15616 64
8034.2.eg $$\chi_{8034}(109, \cdot)$$ n/a 15616 64
8034.2.ei $$\chi_{8034}(83, \cdot)$$ n/a 30976 64
8034.2.el $$\chi_{8034}(41, \cdot)$$ n/a 31104 64
8034.2.em $$\chi_{8034}(137, \cdot)$$ n/a 30976 64
8034.2.eo $$\chi_{8034}(67, \cdot)$$ n/a 15488 64

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(8034))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(8034)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(78))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(103))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(206))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(309))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(618))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1339))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2678))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4017))$$$$^{\oplus 2}$$