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Properties

Label 2000.1
Level 2000
Weight 1
Dimension 40
Nonzero newspaces 5
Newform subspaces 5
Sturm bound 240000
Trace bound 9

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Defining parameters

Level: \( N \) = \( 2000 = 2^{4} \cdot 5^{3} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 5 \)
Newform subspaces: \( 5 \)
Sturm bound: \(240000\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2000))\).

Total New Old
Modular forms 2749 616 2133
Cusp forms 229 40 189
Eisenstein series 2520 576 1944

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 40 0 0 0

Trace form

\( 40 q - q^{9} + 2 q^{29} + 10 q^{37} + 10 q^{41} + 9 q^{49} + 10 q^{53} + 10 q^{61} + 5 q^{65} + 5 q^{81} - 5 q^{85} - 8 q^{89}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2000))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
2000.1.b \(\chi_{2000}(751, \cdot)\) 2000.1.b.a 4 1
2000.1.e \(\chi_{2000}(999, \cdot)\) None 0 1
2000.1.g \(\chi_{2000}(1751, \cdot)\) None 0 1
2000.1.h \(\chi_{2000}(1999, \cdot)\) 2000.1.h.a 4 1
2000.1.i \(\chi_{2000}(1557, \cdot)\) None 0 2
2000.1.k \(\chi_{2000}(499, \cdot)\) None 0 2
2000.1.m \(\chi_{2000}(57, \cdot)\) None 0 2
2000.1.p \(\chi_{2000}(193, \cdot)\) None 0 2
2000.1.r \(\chi_{2000}(251, \cdot)\) None 0 2
2000.1.t \(\chi_{2000}(557, \cdot)\) None 0 2
2000.1.v \(\chi_{2000}(151, \cdot)\) None 0 4
2000.1.x \(\chi_{2000}(399, \cdot)\) 2000.1.x.a 4 4
2000.1.z \(\chi_{2000}(351, \cdot)\) 2000.1.z.a 8 4
2000.1.ba \(\chi_{2000}(199, \cdot)\) None 0 4
2000.1.bc \(\chi_{2000}(157, \cdot)\) None 0 8
2000.1.bf \(\chi_{2000}(99, \cdot)\) None 0 8
2000.1.bg \(\chi_{2000}(257, \cdot)\) None 0 8
2000.1.bj \(\chi_{2000}(393, \cdot)\) None 0 8
2000.1.bk \(\chi_{2000}(51, \cdot)\) None 0 8
2000.1.bn \(\chi_{2000}(93, \cdot)\) None 0 8
2000.1.bp \(\chi_{2000}(79, \cdot)\) 2000.1.bp.a 20 20
2000.1.bq \(\chi_{2000}(39, \cdot)\) None 0 20
2000.1.bs \(\chi_{2000}(71, \cdot)\) None 0 20
2000.1.bv \(\chi_{2000}(31, \cdot)\) None 0 20
2000.1.bw \(\chi_{2000}(11, \cdot)\) None 0 40
2000.1.bz \(\chi_{2000}(13, \cdot)\) None 0 40
2000.1.ca \(\chi_{2000}(17, \cdot)\) None 0 40
2000.1.cd \(\chi_{2000}(73, \cdot)\) None 0 40
2000.1.ce \(\chi_{2000}(53, \cdot)\) None 0 40
2000.1.ch \(\chi_{2000}(19, \cdot)\) None 0 40

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2000))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2000)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 15}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(125))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(250))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(400))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(500))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1000))\)\(^{\oplus 2}\)