Properties

Label 38.2
Level 38
Weight 2
Dimension 14
Nonzero newspaces 3
Newforms 5
Sturm bound 180
Trace bound 2

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Defining parameters

Level: \( N \) = \( 38 = 2 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 3 \)
Newforms: \( 5 \)
Sturm bound: \(180\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(38))\).

Total New Old
Modular forms 63 14 49
Cusp forms 28 14 14
Eisenstein series 35 0 35

Trace form

\(14q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut q^{8} \) \(\mathstrut -\mathstrut 13q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(14q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut q^{8} \) \(\mathstrut -\mathstrut 13q^{9} \) \(\mathstrut -\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 12q^{11} \) \(\mathstrut +\mathstrut 2q^{12} \) \(\mathstrut +\mathstrut 10q^{13} \) \(\mathstrut +\mathstrut 10q^{14} \) \(\mathstrut +\mathstrut 12q^{15} \) \(\mathstrut -\mathstrut q^{16} \) \(\mathstrut +\mathstrut 14q^{18} \) \(\mathstrut +\mathstrut 23q^{19} \) \(\mathstrut +\mathstrut 12q^{20} \) \(\mathstrut +\mathstrut 10q^{21} \) \(\mathstrut +\mathstrut 15q^{22} \) \(\mathstrut -\mathstrut 6q^{23} \) \(\mathstrut -\mathstrut 4q^{24} \) \(\mathstrut +\mathstrut 5q^{25} \) \(\mathstrut +\mathstrut 4q^{26} \) \(\mathstrut -\mathstrut 7q^{27} \) \(\mathstrut -\mathstrut 2q^{28} \) \(\mathstrut -\mathstrut 12q^{29} \) \(\mathstrut -\mathstrut 24q^{30} \) \(\mathstrut -\mathstrut 14q^{31} \) \(\mathstrut -\mathstrut q^{32} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut -\mathstrut 18q^{34} \) \(\mathstrut -\mathstrut 12q^{35} \) \(\mathstrut -\mathstrut 13q^{36} \) \(\mathstrut -\mathstrut 20q^{37} \) \(\mathstrut -\mathstrut 19q^{38} \) \(\mathstrut -\mathstrut 2q^{39} \) \(\mathstrut -\mathstrut 6q^{40} \) \(\mathstrut -\mathstrut 24q^{41} \) \(\mathstrut -\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 2q^{43} \) \(\mathstrut -\mathstrut 3q^{44} \) \(\mathstrut +\mathstrut 30q^{45} \) \(\mathstrut +\mathstrut 12q^{46} \) \(\mathstrut +\mathstrut 24q^{47} \) \(\mathstrut +\mathstrut 5q^{48} \) \(\mathstrut +\mathstrut 3q^{49} \) \(\mathstrut +\mathstrut 41q^{50} \) \(\mathstrut +\mathstrut 27q^{51} \) \(\mathstrut -\mathstrut 8q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 14q^{54} \) \(\mathstrut +\mathstrut 28q^{56} \) \(\mathstrut +\mathstrut 14q^{57} \) \(\mathstrut +\mathstrut 6q^{58} \) \(\mathstrut +\mathstrut 30q^{59} \) \(\mathstrut +\mathstrut 12q^{60} \) \(\mathstrut +\mathstrut 16q^{61} \) \(\mathstrut +\mathstrut 22q^{62} \) \(\mathstrut -\mathstrut 8q^{63} \) \(\mathstrut +\mathstrut 5q^{64} \) \(\mathstrut +\mathstrut 24q^{65} \) \(\mathstrut +\mathstrut 24q^{66} \) \(\mathstrut +\mathstrut 10q^{67} \) \(\mathstrut -\mathstrut 9q^{68} \) \(\mathstrut -\mathstrut 42q^{69} \) \(\mathstrut -\mathstrut 12q^{70} \) \(\mathstrut -\mathstrut 4q^{72} \) \(\mathstrut -\mathstrut 41q^{73} \) \(\mathstrut -\mathstrut 38q^{74} \) \(\mathstrut -\mathstrut 82q^{75} \) \(\mathstrut -\mathstrut 19q^{76} \) \(\mathstrut -\mathstrut 60q^{77} \) \(\mathstrut -\mathstrut 20q^{78} \) \(\mathstrut -\mathstrut 2q^{79} \) \(\mathstrut -\mathstrut 6q^{80} \) \(\mathstrut -\mathstrut 22q^{81} \) \(\mathstrut -\mathstrut 6q^{82} \) \(\mathstrut -\mathstrut 12q^{83} \) \(\mathstrut +\mathstrut 22q^{84} \) \(\mathstrut -\mathstrut 36q^{85} \) \(\mathstrut -\mathstrut 8q^{86} \) \(\mathstrut +\mathstrut 60q^{87} \) \(\mathstrut -\mathstrut 12q^{88} \) \(\mathstrut -\mathstrut 18q^{89} \) \(\mathstrut +\mathstrut 12q^{90} \) \(\mathstrut -\mathstrut 16q^{91} \) \(\mathstrut +\mathstrut 12q^{92} \) \(\mathstrut +\mathstrut 22q^{93} \) \(\mathstrut +\mathstrut 24q^{94} \) \(\mathstrut -\mathstrut 24q^{95} \) \(\mathstrut -\mathstrut 4q^{96} \) \(\mathstrut -\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut 15q^{98} \) \(\mathstrut +\mathstrut 51q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)

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
38.2.a \(\chi_{38}(1, \cdot)\) 38.2.a.a 1 1
38.2.a.b 1
38.2.c \(\chi_{38}(7, \cdot)\) 38.2.c.a 2 2
38.2.c.b 4
38.2.e \(\chi_{38}(5, \cdot)\) 38.2.e.a 6 6

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(38))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(38)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 2}\)