Properties

Label 4009.2
Level 4009
Weight 2
Dimension 660505
Nonzero newspaces 64
Sturm bound 2671200

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Defining parameters

Level: \( N \) = \( 4009 = 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 64 \)
Sturm bound: \(2671200\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4009))\).

Total New Old
Modular forms 671580 667613 3967
Cusp forms 664021 660505 3516
Eisenstein series 7559 7108 451

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4009))\)

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
4009.2.a \(\chi_{4009}(1, \cdot)\) 4009.2.a.a 1 1
4009.2.a.b 3
4009.2.a.c 71
4009.2.a.d 75
4009.2.a.e 82
4009.2.a.f 83
4009.2.d \(\chi_{4009}(4008, \cdot)\) n/a 350 1
4009.2.e \(\chi_{4009}(1702, \cdot)\) n/a 704 2
4009.2.f \(\chi_{4009}(634, \cdot)\) n/a 700 2
4009.2.g \(\chi_{4009}(647, \cdot)\) n/a 636 2
4009.2.h \(\chi_{4009}(1280, \cdot)\) n/a 704 2
4009.2.i \(\chi_{4009}(704, \cdot)\) n/a 1272 4
4009.2.l \(\chi_{4009}(2953, \cdot)\) n/a 700 2
4009.2.m \(\chi_{4009}(1703, \cdot)\) n/a 704 2
4009.2.n \(\chi_{4009}(2336, \cdot)\) n/a 704 2
4009.2.u \(\chi_{4009}(1281, \cdot)\) n/a 704 2
4009.2.v \(\chi_{4009}(58, \cdot)\) n/a 1908 6
4009.2.w \(\chi_{4009}(1251, \cdot)\) n/a 2106 6
4009.2.x \(\chi_{4009}(423, \cdot)\) n/a 2100 6
4009.2.y \(\chi_{4009}(196, \cdot)\) n/a 2106 6
4009.2.z \(\chi_{4009}(1500, \cdot)\) n/a 1400 4
4009.2.bc \(\chi_{4009}(645, \cdot)\) n/a 2100 6
4009.2.bf \(\chi_{4009}(201, \cdot)\) n/a 2816 8
4009.2.bg \(\chi_{4009}(134, \cdot)\) n/a 2544 8
4009.2.bh \(\chi_{4009}(1337, \cdot)\) n/a 2800 8
4009.2.bi \(\chi_{4009}(83, \cdot)\) n/a 2816 8
4009.2.bj \(\chi_{4009}(15, \cdot)\) n/a 2106 6
4009.2.bn \(\chi_{4009}(648, \cdot)\) n/a 2106 6
4009.2.bo \(\chi_{4009}(421, \cdot)\) n/a 2112 6
4009.2.bs \(\chi_{4009}(254, \cdot)\) n/a 4224 12
4009.2.bt \(\chi_{4009}(476, \cdot)\) n/a 3816 12
4009.2.bu \(\chi_{4009}(144, \cdot)\) n/a 4200 12
4009.2.bv \(\chi_{4009}(178, \cdot)\) n/a 4224 12
4009.2.bw \(\chi_{4009}(825, \cdot)\) n/a 2816 8
4009.2.cd \(\chi_{4009}(322, \cdot)\) n/a 2816 8
4009.2.ce \(\chi_{4009}(221, \cdot)\) n/a 2816 8
4009.2.cf \(\chi_{4009}(445, \cdot)\) n/a 2800 8
4009.2.ci \(\chi_{4009}(96, \cdot)\) n/a 7632 24
4009.2.cj \(\chi_{4009}(810, \cdot)\) n/a 4224 12
4009.2.cq \(\chi_{4009}(94, \cdot)\) n/a 4224 12
4009.2.cr \(\chi_{4009}(31, \cdot)\) n/a 4224 12
4009.2.cs \(\chi_{4009}(12, \cdot)\) n/a 4200 12
4009.2.cv \(\chi_{4009}(100, \cdot)\) n/a 8424 24
4009.2.cw \(\chi_{4009}(55, \cdot)\) n/a 8448 24
4009.2.cx \(\chi_{4009}(137, \cdot)\) n/a 8424 24
4009.2.cy \(\chi_{4009}(43, \cdot)\) n/a 12636 36
4009.2.cz \(\chi_{4009}(123, \cdot)\) n/a 12672 36
4009.2.da \(\chi_{4009}(54, \cdot)\) n/a 12636 36
4009.2.dd \(\chi_{4009}(18, \cdot)\) n/a 8400 24
4009.2.dh \(\chi_{4009}(526, \cdot)\) n/a 8448 24
4009.2.di \(\chi_{4009}(128, \cdot)\) n/a 8424 24
4009.2.dm \(\chi_{4009}(10, \cdot)\) n/a 8424 24
4009.2.dn \(\chi_{4009}(30, \cdot)\) n/a 16896 48
4009.2.do \(\chi_{4009}(11, \cdot)\) n/a 16800 48
4009.2.dp \(\chi_{4009}(20, \cdot)\) n/a 15264 48
4009.2.dq \(\chi_{4009}(45, \cdot)\) n/a 16896 48
4009.2.du \(\chi_{4009}(40, \cdot)\) n/a 12672 36
4009.2.dv \(\chi_{4009}(32, \cdot)\) n/a 12636 36
4009.2.dz \(\chi_{4009}(110, \cdot)\) n/a 12636 36
4009.2.ec \(\chi_{4009}(8, \cdot)\) n/a 16800 48
4009.2.ed \(\chi_{4009}(141, \cdot)\) n/a 16896 48
4009.2.ee \(\chi_{4009}(75, \cdot)\) n/a 16896 48
4009.2.el \(\chi_{4009}(145, \cdot)\) n/a 16896 48
4009.2.em \(\chi_{4009}(4, \cdot)\) n/a 50544 144
4009.2.en \(\chi_{4009}(5, \cdot)\) n/a 50688 144
4009.2.eo \(\chi_{4009}(47, \cdot)\) n/a 50544 144
4009.2.ep \(\chi_{4009}(41, \cdot)\) n/a 50544 144
4009.2.et \(\chi_{4009}(2, \cdot)\) n/a 50544 144
4009.2.eu \(\chi_{4009}(60, \cdot)\) n/a 50688 144

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4009))\) into lower level spaces

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