Properties

Label 38.5
Level 38
Weight 5
Dimension 60
Nonzero newspaces 3
Newform subspaces 3
Sturm bound 450
Trace bound 1

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Defining parameters

Level: \( N \) = \( 38 = 2 \cdot 19 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 3 \)
Sturm bound: \(450\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(38))\).

Total New Old
Modular forms 198 60 138
Cusp forms 162 60 102
Eisenstein series 36 0 36

Trace form

\( 60q + O(q^{10}) \) \( 60q - 432q^{12} + 120q^{13} + 864q^{14} + 2268q^{15} + 594q^{17} - 1554q^{19} - 1296q^{20} - 4158q^{21} - 3024q^{22} - 1890q^{23} - 252q^{25} + 1728q^{26} + 1692q^{27} + 2640q^{28} - 864q^{29} + 2808q^{31} + 10800q^{33} + 4752q^{35} - 7992q^{39} - 4752q^{41} - 17274q^{43} - 6048q^{44} - 29646q^{45} - 2880q^{46} + 7398q^{47} + 2304q^{48} + 24342q^{49} + 27648q^{50} + 46494q^{51} + 2112q^{52} + 20952q^{53} + 11232q^{54} + 7848q^{55} - 10170q^{57} - 8064q^{58} - 29430q^{59} - 14976q^{60} - 41136q^{61} - 28512q^{62} - 43992q^{63} - 3072q^{64} - 34290q^{65} - 23040q^{66} + 14154q^{67} + 864q^{68} + 21762q^{69} + 28224q^{70} + 76302q^{71} + 16128q^{72} + 22254q^{73} - 46710q^{77} - 57600q^{78} - 60036q^{79} - 26964q^{81} + 8640q^{82} + 12042q^{83} + 36720q^{84} + 57672q^{85} + 31104q^{86} + 113040q^{87} + 45846q^{89} + 59040q^{90} + 65784q^{91} + 12960q^{92} + 41544q^{93} - 97038q^{95} - 65682q^{97} - 51840q^{98} - 122796q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(38))\)

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
38.5.b \(\chi_{38}(37, \cdot)\) 38.5.b.a 8 1
38.5.d \(\chi_{38}(27, \cdot)\) 38.5.d.a 16 2
38.5.f \(\chi_{38}(3, \cdot)\) 38.5.f.a 36 6

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(38))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(38)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 2}\)