Properties

Label 8018.2
Level 8018
Weight 2
Dimension 664063
Nonzero newspaces 64
Sturm bound 8013600

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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

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