Properties

Label 2003.1
Level 2003
Weight 1
Dimension 4
Nonzero newspaces 1
Newforms 2
Sturm bound 334334
Trace bound 0

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Defining parameters

Level: \( N \) = \( 2003 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newforms: \( 2 \)
Sturm bound: \(334334\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2003))\).

Total New Old
Modular forms 1005 1005 0
Cusp forms 4 4 0
Eisenstein series 1001 1001 0

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

\(4q \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut +\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut +\mathstrut 3q^{9} \) \(\mathstrut -\mathstrut q^{12} \) \(\mathstrut -\mathstrut q^{13} \) \(\mathstrut +\mathstrut 4q^{16} \) \(\mathstrut -\mathstrut q^{19} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut -\mathstrut 2q^{27} \) \(\mathstrut +\mathstrut 3q^{36} \) \(\mathstrut -\mathstrut 2q^{39} \) \(\mathstrut -\mathstrut q^{47} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut +\mathstrut 4q^{49} \) \(\mathstrut -\mathstrut q^{52} \) \(\mathstrut -\mathstrut q^{53} \) \(\mathstrut -\mathstrut 2q^{57} \) \(\mathstrut -\mathstrut q^{59} \) \(\mathstrut +\mathstrut 4q^{64} \) \(\mathstrut -\mathstrut q^{73} \) \(\mathstrut -\mathstrut q^{75} \) \(\mathstrut -\mathstrut q^{76} \) \(\mathstrut -\mathstrut q^{79} \) \(\mathstrut +\mathstrut 2q^{81} \) \(\mathstrut -\mathstrut q^{89} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2003))\)

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
2003.1.b \(\chi_{2003}(2002, \cdot)\) 2003.1.b.a 1 1
2003.1.b.b 3
2003.1.f \(\chi_{2003}(318, \cdot)\) None 0 6
2003.1.g \(\chi_{2003}(180, \cdot)\) None 0 10
2003.1.h \(\chi_{2003}(45, \cdot)\) None 0 12
2003.1.l \(\chi_{2003}(50, \cdot)\) None 0 60
2003.1.m \(\chi_{2003}(6, \cdot)\) None 0 72
2003.1.n \(\chi_{2003}(2, \cdot)\) None 0 120
2003.1.p \(\chi_{2003}(5, \cdot)\) None 0 720