Properties

Label 13.3
Level 13
Weight 3
Dimension 8
Nonzero newspaces 2
Newforms 2
Sturm bound 42
Trace bound 2

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Defining parameters

Level: \( N \) = \( 13 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 2 \)
Sturm bound: \(42\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(13))\).

Total New Old
Modular forms 20 20 0
Cusp forms 8 8 0
Eisenstein series 12 12 0

Trace form

\(8q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut 6q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut 6q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut 24q^{10} \) \(\mathstrut -\mathstrut 18q^{13} \) \(\mathstrut -\mathstrut 36q^{14} \) \(\mathstrut -\mathstrut 42q^{15} \) \(\mathstrut -\mathstrut 86q^{16} \) \(\mathstrut -\mathstrut 12q^{17} \) \(\mathstrut +\mathstrut 30q^{18} \) \(\mathstrut +\mathstrut 10q^{19} \) \(\mathstrut +\mathstrut 42q^{20} \) \(\mathstrut +\mathstrut 72q^{21} \) \(\mathstrut +\mathstrut 84q^{22} \) \(\mathstrut +\mathstrut 18q^{23} \) \(\mathstrut +\mathstrut 66q^{24} \) \(\mathstrut -\mathstrut 36q^{26} \) \(\mathstrut -\mathstrut 84q^{27} \) \(\mathstrut -\mathstrut 40q^{28} \) \(\mathstrut +\mathstrut 42q^{29} \) \(\mathstrut -\mathstrut 54q^{30} \) \(\mathstrut +\mathstrut 20q^{31} \) \(\mathstrut -\mathstrut 108q^{33} \) \(\mathstrut -\mathstrut 126q^{34} \) \(\mathstrut -\mathstrut 36q^{35} \) \(\mathstrut -\mathstrut 54q^{36} \) \(\mathstrut -\mathstrut 28q^{37} \) \(\mathstrut +\mathstrut 66q^{39} \) \(\mathstrut +\mathstrut 156q^{40} \) \(\mathstrut +\mathstrut 132q^{41} \) \(\mathstrut +\mathstrut 120q^{42} \) \(\mathstrut +\mathstrut 180q^{43} \) \(\mathstrut -\mathstrut 84q^{44} \) \(\mathstrut +\mathstrut 54q^{45} \) \(\mathstrut +\mathstrut 102q^{46} \) \(\mathstrut -\mathstrut 72q^{47} \) \(\mathstrut -\mathstrut 126q^{48} \) \(\mathstrut -\mathstrut 72q^{49} \) \(\mathstrut -\mathstrut 174q^{50} \) \(\mathstrut +\mathstrut 80q^{52} \) \(\mathstrut +\mathstrut 48q^{53} \) \(\mathstrut +\mathstrut 168q^{54} \) \(\mathstrut -\mathstrut 36q^{55} \) \(\mathstrut -\mathstrut 84q^{56} \) \(\mathstrut -\mathstrut 60q^{57} \) \(\mathstrut -\mathstrut 180q^{58} \) \(\mathstrut -\mathstrut 108q^{59} \) \(\mathstrut -\mathstrut 108q^{60} \) \(\mathstrut -\mathstrut 420q^{61} \) \(\mathstrut +\mathstrut 6q^{62} \) \(\mathstrut -\mathstrut 12q^{63} \) \(\mathstrut +\mathstrut 108q^{65} \) \(\mathstrut +\mathstrut 192q^{66} \) \(\mathstrut +\mathstrut 34q^{67} \) \(\mathstrut +\mathstrut 516q^{68} \) \(\mathstrut +\mathstrut 72q^{69} \) \(\mathstrut +\mathstrut 132q^{70} \) \(\mathstrut +\mathstrut 198q^{71} \) \(\mathstrut +\mathstrut 24q^{72} \) \(\mathstrut +\mathstrut 58q^{73} \) \(\mathstrut +\mathstrut 168q^{74} \) \(\mathstrut +\mathstrut 48q^{75} \) \(\mathstrut +\mathstrut 94q^{76} \) \(\mathstrut -\mathstrut 336q^{78} \) \(\mathstrut +\mathstrut 24q^{79} \) \(\mathstrut -\mathstrut 228q^{80} \) \(\mathstrut -\mathstrut 222q^{81} \) \(\mathstrut +\mathstrut 24q^{82} \) \(\mathstrut -\mathstrut 240q^{83} \) \(\mathstrut -\mathstrut 180q^{84} \) \(\mathstrut -\mathstrut 48q^{85} \) \(\mathstrut -\mathstrut 204q^{86} \) \(\mathstrut +\mathstrut 198q^{87} \) \(\mathstrut -\mathstrut 204q^{88} \) \(\mathstrut +\mathstrut 90q^{89} \) \(\mathstrut +\mathstrut 208q^{91} \) \(\mathstrut -\mathstrut 612q^{92} \) \(\mathstrut +\mathstrut 60q^{93} \) \(\mathstrut -\mathstrut 426q^{94} \) \(\mathstrut -\mathstrut 78q^{95} \) \(\mathstrut +\mathstrut 360q^{96} \) \(\mathstrut +\mathstrut 110q^{97} \) \(\mathstrut +\mathstrut 210q^{98} \) \(\mathstrut +\mathstrut 360q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(13))\)

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
13.3.d \(\chi_{13}(5, \cdot)\) 13.3.d.a 4 2
13.3.f \(\chi_{13}(2, \cdot)\) 13.3.f.a 4 4