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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

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

Display 100 coefficients 10 coefficients

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 available 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

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