Properties

Label 38.8
Level 38
Weight 8
Dimension 103
Nonzero newspaces 3
Newform subspaces 9
Sturm bound 720
Trace bound 1

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Defining parameters

Level: \( N \) = \( 38 = 2 \cdot 19 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 9 \)
Sturm bound: \(720\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(38))\).

Total New Old
Modular forms 333 103 230
Cusp forms 297 103 194
Eisenstein series 36 0 36

Trace form

\( 103q + 16q^{2} - 24q^{3} - 128q^{4} + 420q^{5} + 192q^{6} - 2032q^{7} + 1024q^{8} + 4086q^{9} + O(q^{10}) \) \( 103q + 16q^{2} - 24q^{3} - 128q^{4} + 420q^{5} + 192q^{6} - 2032q^{7} + 1024q^{8} + 4086q^{9} - 3360q^{10} - 2184q^{11} - 11904q^{12} - 47092q^{13} + 56720q^{14} + 128484q^{15} - 8192q^{16} - 88146q^{17} - 190152q^{18} - 161114q^{19} + 28032q^{20} + 260250q^{21} + 334776q^{22} + 59370q^{23} + 12288q^{24} - 448586q^{25} - 487792q^{26} + 238581q^{27} + 160640q^{28} - 392838q^{29} - 40320q^{30} - 31006q^{31} + 65536q^{32} + 1618794q^{33} + 235296q^{34} - 156876q^{35} + 261504q^{36} - 1232806q^{37} - 319520q^{38} - 1430202q^{39} - 215040q^{40} + 771594q^{41} + 195072q^{42} + 7315082q^{43} - 35520q^{44} - 7155540q^{45} - 3499104q^{46} - 5451648q^{47} + 380928q^{48} + 2048454q^{49} + 9366832q^{50} + 15820695q^{51} + 162176q^{52} + 1697292q^{53} - 5765904q^{54} - 10233288q^{55} - 5281792q^{56} - 14459190q^{57} - 5923392q^{58} - 8932710q^{59} + 2370816q^{60} + 9358190q^{61} + 16431920q^{62} + 15379344q^{63} + 1048576q^{64} + 16772880q^{65} + 2089152q^{66} + 4173134q^{67} - 5334336q^{68} - 30139002q^{69} - 21293664q^{70} - 3690000q^{71} + 4870656q^{72} + 5856455q^{73} + 2568416q^{74} - 16902150q^{75} + 2556160q^{76} + 24529128q^{77} + 3456672q^{78} - 16747138q^{79} + 1720320q^{80} - 41281821q^{81} - 9100416q^{82} + 6859632q^{83} + 22247808q^{84} + 52273872q^{85} + 15283424q^{86} + 89110980q^{87} + 1118208q^{88} + 18620928q^{89} + 1239120q^{90} - 53284736q^{91} - 29777664q^{92} - 106636638q^{93} - 52239552q^{94} - 21696582q^{95} + 786432q^{96} - 94148962q^{97} - 6780336q^{98} - 24494085q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(38))\)

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
38.8.a \(\chi_{38}(1, \cdot)\) 38.8.a.a 1 1
38.8.a.b 2
38.8.a.c 2
38.8.a.d 2
38.8.a.e 4
38.8.c \(\chi_{38}(7, \cdot)\) 38.8.c.a 12 2
38.8.c.b 14
38.8.e \(\chi_{38}(5, \cdot)\) 38.8.e.a 30 6
38.8.e.b 36

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(38))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(38)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 2}\)