Properties

Label 38.10
Level 38
Weight 10
Dimension 133
Nonzero newspaces 3
Newform subspaces 9
Sturm bound 900
Trace bound 1

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Defining parameters

Level: \( N \) = \( 38 = 2 \cdot 19 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 9 \)
Sturm bound: \(900\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(38))\).

Total New Old
Modular forms 423 133 290
Cusp forms 387 133 254
Eisenstein series 36 0 36

Trace form

\( 133q - 32q^{2} + 312q^{3} - 512q^{4} - 1740q^{5} + 4992q^{6} + 1904q^{7} - 8192q^{8} - 9306q^{9} + O(q^{10}) \) \( 133q - 32q^{2} + 312q^{3} - 512q^{4} - 1740q^{5} + 4992q^{6} + 1904q^{7} - 8192q^{8} - 9306q^{9} - 27840q^{10} + 112296q^{11} - 168960q^{12} + 422276q^{13} + 321056q^{14} - 1518984q^{15} - 131072q^{16} + 1190268q^{17} + 2685456q^{18} + 2499208q^{19} - 1754112q^{20} - 8856456q^{21} - 2958288q^{22} + 895380q^{23} + 1277952q^{24} + 17511586q^{25} - 9140896q^{26} - 19412559q^{27} + 2063360q^{28} + 13645110q^{29} + 4343040q^{30} + 10464386q^{31} - 2097152q^{32} - 85713642q^{33} + 7925184q^{34} + 3967716q^{35} - 2382336q^{36} + 25120742q^{37} - 5046080q^{38} + 71144598q^{39} - 7127040q^{40} - 54442434q^{41} - 4752384q^{42} + 18545936q^{43} - 29255424q^{44} - 47224782q^{45} + 84948288q^{46} + 427240974q^{47} + 63504384q^{48} - 120069024q^{49} - 307319648q^{50} - 425503539q^{51} - 128550400q^{52} - 203110092q^{53} + 80511840q^{54} + 639991872q^{55} + 361840640q^{56} + 836916000q^{57} + 277465728q^{58} - 443336700q^{59} - 270019584q^{60} - 1119962182q^{61} - 760726432q^{62} - 626397480q^{63} - 33554432q^{64} + 1206071130q^{65} + 1366978176q^{66} + 1219704296q^{67} + 266317056q^{68} - 392348952q^{69} - 1355089344q^{70} - 2193006690q^{71} + 22081536q^{72} + 1200889391q^{73} - 137826496q^{74} + 955684050q^{75} - 80737280q^{76} + 2189912154q^{77} - 1357907136q^{78} - 4168473646q^{79} - 114032640q^{80} + 2182598721q^{81} + 2064890112q^{82} + 3255984030q^{83} + 1408051200q^{84} - 98478648q^{85} - 2481396544q^{86} - 6951949740q^{87} + 459964416q^{88} - 2014750674q^{89} - 2149224480q^{90} - 1606357016q^{91} + 1424652288q^{92} + 9018243606q^{93} + 5959986816q^{94} + 662721720q^{95} + 327155712q^{96} - 1146090064q^{97} - 481444512q^{98} - 2558506401q^{99} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(38))\)

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
38.10.a \(\chi_{38}(1, \cdot)\) 38.10.a.a 1 1
38.10.a.b 1
38.10.a.c 3
38.10.a.d 4
38.10.a.e 4
38.10.c \(\chi_{38}(7, \cdot)\) 38.10.c.a 14 2
38.10.c.b 16
38.10.e \(\chi_{38}(5, \cdot)\) 38.10.e.a 42 6
38.10.e.b 48

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(38))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(38)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 2}\)