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Properties

Label 38.3
Level 38
Weight 3
Dimension 30
Nonzero newspaces 3
Newform subspaces 3
Sturm bound 270
Trace bound 1

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Defining parameters

Level: \( N \) = \( 38 = 2 \cdot 19 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 3 \)
Sturm bound: \(270\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(38))\).

Total New Old
Modular forms 108 30 78
Cusp forms 72 30 42
Eisenstein series 36 0 36

Trace form

\( 30 q + O(q^{10}) \) \( 30 q - 36 q^{12} - 120 q^{13} - 72 q^{14} - 108 q^{15} - 18 q^{17} + 42 q^{19} + 36 q^{20} + 126 q^{21} + 108 q^{22} + 90 q^{23} + 252 q^{25} + 144 q^{26} + 126 q^{27} + 60 q^{28} - 144 q^{29} - 108 q^{31} - 216 q^{33} - 72 q^{35} + 108 q^{39} + 72 q^{41} + 138 q^{43} - 108 q^{44} - 162 q^{45} - 360 q^{46} - 306 q^{47} - 72 q^{48} - 78 q^{49} - 432 q^{50} - 324 q^{51} - 24 q^{52} - 216 q^{53} - 108 q^{54} - 72 q^{55} + 90 q^{57} + 72 q^{58} + 270 q^{59} + 144 q^{60} + 276 q^{61} + 324 q^{62} + 216 q^{63} + 48 q^{64} + 630 q^{65} + 720 q^{66} + 174 q^{67} + 108 q^{68} + 702 q^{69} + 504 q^{70} + 738 q^{71} + 144 q^{72} + 48 q^{73} - 270 q^{77} - 576 q^{78} - 372 q^{79} - 774 q^{81} - 432 q^{82} - 450 q^{83} - 540 q^{84} - 648 q^{85} - 288 q^{86} - 576 q^{87} - 18 q^{89} - 360 q^{90} + 168 q^{91} - 72 q^{92} - 36 q^{93} - 594 q^{95} - 414 q^{97} + 288 q^{98} - 162 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(38))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
38.3.b \(\chi_{38}(37, \cdot)\) 38.3.b.a 2 1
38.3.d \(\chi_{38}(27, \cdot)\) 38.3.d.a 4 2
38.3.f \(\chi_{38}(3, \cdot)\) 38.3.f.a 24 6

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(38))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(38)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 2}\)