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Properties

Label 100.1
Level 100
Weight 1
Dimension 4
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 600
Trace bound 0

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Defining parameters

Level: \( N \) = \( 100 = 2^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(600\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(100))\).

Total New Old
Modular forms 74 25 49
Cusp forms 4 4 0
Eisenstein series 70 21 49

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

\( 4 q - q^{2} - q^{4} - q^{5} - q^{8} - q^{9} + O(q^{10}) \) \( 4 q - q^{2} - q^{4} - q^{5} - q^{8} - q^{9} - q^{10} - 2 q^{13} - q^{16} - 2 q^{17} + 4 q^{18} + 4 q^{20} - q^{25} - 2 q^{26} - 2 q^{29} + 4 q^{32} + 3 q^{34} - q^{36} + 3 q^{37} - q^{40} - 2 q^{41} - q^{45} + 4 q^{49} - q^{50} - 2 q^{52} + 3 q^{53} - 2 q^{58} - 2 q^{61} - q^{64} + 3 q^{65} - 2 q^{68} - q^{72} - 2 q^{73} - 2 q^{74} - q^{80} - q^{81} - 2 q^{82} + 3 q^{85} + 3 q^{89} - q^{90} - 2 q^{97} - q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(100))\)

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
100.1.b \(\chi_{100}(51, \cdot)\) None 0 1
100.1.d \(\chi_{100}(99, \cdot)\) None 0 1
100.1.f \(\chi_{100}(57, \cdot)\) None 0 2
100.1.h \(\chi_{100}(19, \cdot)\) None 0 4
100.1.j \(\chi_{100}(11, \cdot)\) 100.1.j.a 4 4
100.1.k \(\chi_{100}(13, \cdot)\) None 0 8