Properties

Label 19.2
Level 19
Weight 2
Dimension 7
Nonzero newspaces 2
Newforms 2
Sturm bound 60
Trace bound 1

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Defining parameters

Level: \( N \) = \( 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 2 \)
Sturm bound: \(60\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(19))\).

Total New Old
Modular forms 24 24 0
Cusp forms 7 7 0
Eisenstein series 17 17 0

Trace form

\(7q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(7q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut 9q^{10} \) \(\mathstrut +\mathstrut 3q^{11} \) \(\mathstrut +\mathstrut 7q^{12} \) \(\mathstrut -\mathstrut 7q^{13} \) \(\mathstrut -\mathstrut 3q^{14} \) \(\mathstrut -\mathstrut 3q^{15} \) \(\mathstrut -\mathstrut 14q^{16} \) \(\mathstrut -\mathstrut 6q^{18} \) \(\mathstrut -\mathstrut 11q^{19} \) \(\mathstrut -\mathstrut 12q^{20} \) \(\mathstrut +\mathstrut 2q^{21} \) \(\mathstrut +\mathstrut 6q^{23} \) \(\mathstrut +\mathstrut 15q^{24} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut +\mathstrut 15q^{26} \) \(\mathstrut +\mathstrut 10q^{27} \) \(\mathstrut +\mathstrut 8q^{28} \) \(\mathstrut +\mathstrut 3q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut +\mathstrut 9q^{32} \) \(\mathstrut -\mathstrut 15q^{33} \) \(\mathstrut +\mathstrut 3q^{35} \) \(\mathstrut -\mathstrut 26q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 15q^{38} \) \(\mathstrut -\mathstrut 16q^{39} \) \(\mathstrut +\mathstrut 15q^{41} \) \(\mathstrut -\mathstrut 3q^{42} \) \(\mathstrut -\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 3q^{44} \) \(\mathstrut -\mathstrut 12q^{45} \) \(\mathstrut -\mathstrut 18q^{46} \) \(\mathstrut -\mathstrut 6q^{47} \) \(\mathstrut -\mathstrut 11q^{48} \) \(\mathstrut +\mathstrut 9q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut +\mathstrut 9q^{51} \) \(\mathstrut +\mathstrut 23q^{52} \) \(\mathstrut +\mathstrut 9q^{53} \) \(\mathstrut +\mathstrut 30q^{54} \) \(\mathstrut +\mathstrut 27q^{55} \) \(\mathstrut -\mathstrut 6q^{56} \) \(\mathstrut +\mathstrut 22q^{57} \) \(\mathstrut +\mathstrut 36q^{58} \) \(\mathstrut +\mathstrut 6q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 13q^{61} \) \(\mathstrut -\mathstrut 12q^{62} \) \(\mathstrut +\mathstrut 11q^{63} \) \(\mathstrut -\mathstrut 20q^{64} \) \(\mathstrut -\mathstrut 24q^{65} \) \(\mathstrut -\mathstrut 9q^{66} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut -\mathstrut 9q^{68} \) \(\mathstrut -\mathstrut 12q^{69} \) \(\mathstrut -\mathstrut 9q^{70} \) \(\mathstrut -\mathstrut 12q^{72} \) \(\mathstrut -\mathstrut 19q^{73} \) \(\mathstrut +\mathstrut 15q^{74} \) \(\mathstrut +\mathstrut 22q^{75} \) \(\mathstrut +\mathstrut 34q^{76} \) \(\mathstrut -\mathstrut 21q^{77} \) \(\mathstrut +\mathstrut 15q^{78} \) \(\mathstrut -\mathstrut 31q^{79} \) \(\mathstrut +\mathstrut 15q^{80} \) \(\mathstrut -\mathstrut 5q^{81} \) \(\mathstrut -\mathstrut 54q^{82} \) \(\mathstrut +\mathstrut 12q^{83} \) \(\mathstrut -\mathstrut q^{84} \) \(\mathstrut -\mathstrut 9q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut -\mathstrut 33q^{87} \) \(\mathstrut +\mathstrut 9q^{88} \) \(\mathstrut +\mathstrut 18q^{90} \) \(\mathstrut +\mathstrut 19q^{91} \) \(\mathstrut +\mathstrut 42q^{92} \) \(\mathstrut +\mathstrut 17q^{93} \) \(\mathstrut +\mathstrut 18q^{94} \) \(\mathstrut +\mathstrut 42q^{95} \) \(\mathstrut +\mathstrut 18q^{96} \) \(\mathstrut +\mathstrut 26q^{97} \) \(\mathstrut -\mathstrut 9q^{98} \) \(\mathstrut +\mathstrut 12q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)

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
19.2.a \(\chi_{19}(1, \cdot)\) 19.2.a.a 1 1
19.2.c \(\chi_{19}(7, \cdot)\) None 0 2
19.2.e \(\chi_{19}(4, \cdot)\) 19.2.e.a 6 6