Properties

Label 200.1
Level 200
Weight 1
Dimension 4
Nonzero newspaces 2
Newforms 3
Sturm bound 2400
Trace bound 4

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Defining parameters

Level: \( N \) = \( 200 = 2^{3} \cdot 5^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 3 \)
Sturm bound: \(2400\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(200))\).

Total New Old
Modular forms 180 45 135
Cusp forms 12 4 8
Eisenstein series 168 41 127

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\(4q \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut +\mathstrut 4q^{16} \) \(\mathstrut -\mathstrut 4q^{41} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut +\mathstrut 4q^{66} \) \(\mathstrut -\mathstrut 4q^{76} \) \(\mathstrut -\mathstrut 4q^{81} \) \(\mathstrut +\mathstrut 8q^{86} \) \(\mathstrut -\mathstrut 4q^{96} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(200))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
200.1.b \(\chi_{200}(151, \cdot)\) None 0 1
200.1.e \(\chi_{200}(99, \cdot)\) 200.1.e.a 2 1
200.1.g \(\chi_{200}(51, \cdot)\) 200.1.g.a 1 1
200.1.g.b 1
200.1.h \(\chi_{200}(199, \cdot)\) None 0 1
200.1.i \(\chi_{200}(93, \cdot)\) None 0 2
200.1.l \(\chi_{200}(57, \cdot)\) None 0 2
200.1.n \(\chi_{200}(11, \cdot)\) None 0 4
200.1.p \(\chi_{200}(39, \cdot)\) None 0 4
200.1.r \(\chi_{200}(31, \cdot)\) None 0 4
200.1.s \(\chi_{200}(19, \cdot)\) None 0 4
200.1.u \(\chi_{200}(17, \cdot)\) None 0 8
200.1.x \(\chi_{200}(13, \cdot)\) None 0 8

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(200))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(200)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 2}\)