Properties

Label 19.10
Level 19
Weight 10
Dimension 126
Nonzero newspaces 3
Newform subspaces 4
Sturm bound 300
Trace bound 1

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Defining parameters

Level: \( N \) = \( 19 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 4 \)
Sturm bound: \(300\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(19))\).

Total New Old
Modular forms 144 142 2
Cusp forms 126 126 0
Eisenstein series 18 16 2

Trace form

\( 126q - 9q^{2} - 9q^{3} - 9q^{4} - 9q^{5} - 9q^{6} - 9q^{7} - 9q^{8} - 9q^{9} + O(q^{10}) \) \( 126q - 9q^{2} - 9q^{3} - 9q^{4} - 9q^{5} - 9q^{6} - 9q^{7} - 9q^{8} - 9q^{9} - 9q^{10} - 9q^{11} + 497655q^{12} - 389241q^{13} - 290601q^{14} + 895203q^{15} + 1575927q^{16} - 347481q^{17} - 2834370q^{18} - 1407303q^{19} + 2617326q^{20} + 4279707q^{21} + 4755015q^{22} - 652203q^{23} - 14183433q^{24} - 7559577q^{25} + 3441879q^{26} + 1968606q^{27} + 27218232q^{28} - 5964219q^{29} - 66276702q^{30} - 7845579q^{31} + 29375946q^{32} + 68195457q^{33} + 43354116q^{34} - 2311245q^{35} - 110906667q^{36} - 33734916q^{37} - 98142102q^{38} - 15579288q^{39} + 91569600q^{40} + 51418341q^{41} + 276833601q^{42} - 13729599q^{43} + 117224766q^{44} - 99194715q^{45} - 352679400q^{46} - 233699553q^{47} - 87164856q^{48} + 198963621q^{49} + 551201922q^{50} + 24202656q^{51} + 411028983q^{52} + 84938823q^{53} - 155718756q^{54} - 271147185q^{55} - 1062125586q^{56} - 393858369q^{57} - 154571346q^{58} + 109433241q^{59} + 306661266q^{60} + 1299787065q^{61} + 1715007384q^{62} + 196459839q^{63} - 1427440977q^{64} - 1746880479q^{65} - 2534287041q^{66} - 342606519q^{67} + 56164428q^{68} + 1948697883q^{69} + 3872950515q^{70} + 1874280069q^{71} - 77553576q^{72} - 1806359706q^{73} - 1873153665q^{74} - 2657812518q^{75} - 2615267259q^{76} - 2629124712q^{77} + 2129411097q^{78} + 2736862047q^{79} + 3376651311q^{80} + 2437341822q^{81} + 3902190750q^{82} - 340223319q^{83} - 2392813989q^{84} - 1666739745q^{85} - 2201222358q^{86} - 1163665953q^{87} + 648207855q^{88} - 323782767q^{89} + 4659311826q^{90} + 5009470767q^{91} + 3411376974q^{92} - 3788710551q^{93} - 19293664734q^{94} + 1034210493q^{95} + 4843415718q^{96} + 2961124011q^{97} + 108853290q^{98} - 1603896048q^{99} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(19))\)

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
19.10.a \(\chi_{19}(1, \cdot)\) 19.10.a.a 6 1
19.10.a.b 8
19.10.c \(\chi_{19}(7, \cdot)\) 19.10.c.a 28 2
19.10.e \(\chi_{19}(4, \cdot)\) 19.10.e.a 84 6