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

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

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

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