# Properties

 Label 8018.2 Level 8018 Weight 2 Dimension 664063 Nonzero newspaces 64 Sturm bound 8.0136e+06

## Defining parameters

 Level: $$N$$ = $$8018 = 2 \cdot 19 \cdot 211$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$64$$ Sturm bound: $$8013600$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(8018))$$.

Total New Old
Modular forms 2010960 664063 1346897
Cusp forms 1995841 664063 1331778
Eisenstein series 15119 0 15119

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(8018))$$

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
8018.2.a $$\chi_{8018}(1, \cdot)$$ 8018.2.a.a 1 1
8018.2.a.b 2
8018.2.a.c 2
8018.2.a.d 30
8018.2.a.e 32
8018.2.a.f 34
8018.2.a.g 34
8018.2.a.h 41
8018.2.a.i 43
8018.2.a.j 47
8018.2.a.k 49
8018.2.d $$\chi_{8018}(8017, \cdot)$$ n/a 356 1
8018.2.e $$\chi_{8018}(5711, \cdot)$$ n/a 704 2
8018.2.f $$\chi_{8018}(4643, \cdot)$$ n/a 700 2
8018.2.g $$\chi_{8018}(647, \cdot)$$ n/a 636 2
8018.2.h $$\chi_{8018}(5289, \cdot)$$ n/a 704 2
8018.2.i $$\chi_{8018}(951, \cdot)$$ n/a 1272 4
8018.2.l $$\chi_{8018}(2953, \cdot)$$ n/a 712 2
8018.2.m $$\chi_{8018}(1703, \cdot)$$ n/a 704 2
8018.2.n $$\chi_{8018}(6345, \cdot)$$ n/a 704 2
8018.2.u $$\chi_{8018}(1281, \cdot)$$ n/a 704 2
8018.2.v $$\chi_{8018}(2281, \cdot)$$ n/a 1908 6
8018.2.w $$\chi_{8018}(1251, \cdot)$$ n/a 2124 6
8018.2.x $$\chi_{8018}(423, \cdot)$$ n/a 2100 6
8018.2.y $$\chi_{8018}(225, \cdot)$$ n/a 2124 6
8018.2.z $$\chi_{8018}(1633, \cdot)$$ n/a 1424 4
8018.2.bc $$\chi_{8018}(645, \cdot)$$ n/a 2136 6
8018.2.bf $$\chi_{8018}(201, \cdot)$$ n/a 2816 8
8018.2.bg $$\chi_{8018}(1825, \cdot)$$ n/a 2544 8
8018.2.bh $$\chi_{8018}(1337, \cdot)$$ n/a 2848 8
8018.2.bi $$\chi_{8018}(83, \cdot)$$ n/a 2816 8
8018.2.bj $$\chi_{8018}(15, \cdot)$$ n/a 2124 6
8018.2.bn $$\chi_{8018}(421, \cdot)$$ n/a 2112 6
8018.2.bo $$\chi_{8018}(1041, \cdot)$$ n/a 2124 6
8018.2.bs $$\chi_{8018}(391, \cdot)$$ n/a 4224 12
8018.2.bt $$\chi_{8018}(495, \cdot)$$ n/a 3816 12
8018.2.bu $$\chi_{8018}(691, \cdot)$$ n/a 4272 12
8018.2.bv $$\chi_{8018}(961, \cdot)$$ n/a 4224 12
8018.2.bw $$\chi_{8018}(825, \cdot)$$ n/a 2816 8
8018.2.cd $$\chi_{8018}(2089, \cdot)$$ n/a 2816 8
8018.2.ce $$\chi_{8018}(221, \cdot)$$ n/a 2816 8
8018.2.cf $$\chi_{8018}(445, \cdot)$$ n/a 2848 8
8018.2.ci $$\chi_{8018}(1027, \cdot)$$ n/a 7632 24
8018.2.cj $$\chi_{8018}(1931, \cdot)$$ n/a 4224 12
8018.2.cq $$\chi_{8018}(379, \cdot)$$ n/a 4224 12
8018.2.cr $$\chi_{8018}(31, \cdot)$$ n/a 4224 12
8018.2.cs $$\chi_{8018}(673, \cdot)$$ n/a 4272 12
8018.2.cv $$\chi_{8018}(441, \cdot)$$ n/a 8496 24
8018.2.cw $$\chi_{8018}(55, \cdot)$$ n/a 8448 24
8018.2.cx $$\chi_{8018}(137, \cdot)$$ n/a 8496 24
8018.2.cy $$\chi_{8018}(43, \cdot)$$ n/a 12744 36
8018.2.cz $$\chi_{8018}(123, \cdot)$$ n/a 12672 36
8018.2.da $$\chi_{8018}(465, \cdot)$$ n/a 12744 36
8018.2.dd $$\chi_{8018}(417, \cdot)$$ n/a 8544 24
8018.2.dh $$\chi_{8018}(1245, \cdot)$$ n/a 8496 24
8018.2.di $$\chi_{8018}(737, \cdot)$$ n/a 8448 24
8018.2.dm $$\chi_{8018}(401, \cdot)$$ n/a 8496 24
8018.2.dn $$\chi_{8018}(49, \cdot)$$ n/a 16896 48
8018.2.do $$\chi_{8018}(11, \cdot)$$ n/a 17088 48
8018.2.dp $$\chi_{8018}(267, \cdot)$$ n/a 15264 48
8018.2.dq $$\chi_{8018}(45, \cdot)$$ n/a 16896 48
8018.2.du $$\chi_{8018}(33, \cdot)$$ n/a 12744 36
8018.2.dv $$\chi_{8018}(67, \cdot)$$ n/a 12672 36
8018.2.dz $$\chi_{8018}(249, \cdot)$$ n/a 12744 36
8018.2.ec $$\chi_{8018}(27, \cdot)$$ n/a 17088 48
8018.2.ed $$\chi_{8018}(141, \cdot)$$ n/a 16896 48
8018.2.ee $$\chi_{8018}(75, \cdot)$$ n/a 16896 48
8018.2.el $$\chi_{8018}(145, \cdot)$$ n/a 16896 48
8018.2.em $$\chi_{8018}(9, \cdot)$$ n/a 50976 144
8018.2.en $$\chi_{8018}(5, \cdot)$$ n/a 50688 144
8018.2.eo $$\chi_{8018}(47, \cdot)$$ n/a 50976 144
8018.2.ep $$\chi_{8018}(41, \cdot)$$ n/a 50976 144
8018.2.et $$\chi_{8018}(89, \cdot)$$ n/a 50688 144
8018.2.eu $$\chi_{8018}(3, \cdot)$$ n/a 50976 144

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(8018))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(8018)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(211))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(422))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4009))$$$$^{\oplus 2}$$