Properties

Label 13.2
Level 13
Weight 2
Dimension 2
Nonzero newspaces 1
Newforms 1
Sturm bound 28
Trace bound 0

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Defining parameters

Level: \( N \) = \( 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 1 \)
Newforms: \( 1 \)
Sturm bound: \(28\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(13))\).

Total New Old
Modular forms 13 13 0
Cusp forms 2 2 0
Eisenstein series 11 11 0

Trace form

\(2q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut q^{4} \) \(\mathstrut +\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut q^{4} \) \(\mathstrut +\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut q^{9} \) \(\mathstrut -\mathstrut 3q^{10} \) \(\mathstrut -\mathstrut 4q^{12} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut +\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 5q^{16} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut -\mathstrut 6q^{19} \) \(\mathstrut +\mathstrut 3q^{20} \) \(\mathstrut +\mathstrut 6q^{23} \) \(\mathstrut -\mathstrut 6q^{24} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut +\mathstrut 3q^{26} \) \(\mathstrut -\mathstrut 8q^{27} \) \(\mathstrut -\mathstrut 3q^{29} \) \(\mathstrut -\mathstrut 6q^{30} \) \(\mathstrut -\mathstrut 9q^{32} \) \(\mathstrut +\mathstrut q^{36} \) \(\mathstrut +\mathstrut 15q^{37} \) \(\mathstrut +\mathstrut 12q^{38} \) \(\mathstrut +\mathstrut 14q^{39} \) \(\mathstrut +\mathstrut 6q^{40} \) \(\mathstrut -\mathstrut 9q^{41} \) \(\mathstrut -\mathstrut 8q^{43} \) \(\mathstrut -\mathstrut 3q^{45} \) \(\mathstrut -\mathstrut 18q^{46} \) \(\mathstrut +\mathstrut 10q^{48} \) \(\mathstrut -\mathstrut 7q^{49} \) \(\mathstrut -\mathstrut 6q^{50} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut +\mathstrut 2q^{52} \) \(\mathstrut -\mathstrut 6q^{53} \) \(\mathstrut +\mathstrut 12q^{54} \) \(\mathstrut +\mathstrut 9q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut q^{61} \) \(\mathstrut +\mathstrut 6q^{62} \) \(\mathstrut -\mathstrut 2q^{64} \) \(\mathstrut -\mathstrut 9q^{65} \) \(\mathstrut +\mathstrut 6q^{67} \) \(\mathstrut -\mathstrut 3q^{68} \) \(\mathstrut +\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 6q^{71} \) \(\mathstrut +\mathstrut 3q^{72} \) \(\mathstrut -\mathstrut 15q^{74} \) \(\mathstrut -\mathstrut 4q^{75} \) \(\mathstrut -\mathstrut 6q^{76} \) \(\mathstrut -\mathstrut 24q^{78} \) \(\mathstrut +\mathstrut 8q^{79} \) \(\mathstrut -\mathstrut 15q^{80} \) \(\mathstrut +\mathstrut 11q^{81} \) \(\mathstrut +\mathstrut 9q^{82} \) \(\mathstrut +\mathstrut 9q^{85} \) \(\mathstrut -\mathstrut 6q^{87} \) \(\mathstrut -\mathstrut 12q^{89} \) \(\mathstrut +\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 12q^{92} \) \(\mathstrut -\mathstrut 12q^{93} \) \(\mathstrut -\mathstrut 6q^{94} \) \(\mathstrut +\mathstrut 6q^{95} \) \(\mathstrut +\mathstrut 12q^{97} \) \(\mathstrut +\mathstrut 21q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)

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
13.2.a \(\chi_{13}(1, \cdot)\) None 0 1
13.2.b \(\chi_{13}(12, \cdot)\) None 0 1
13.2.c \(\chi_{13}(3, \cdot)\) None 0 2
13.2.e \(\chi_{13}(4, \cdot)\) 13.2.e.a 2 2