↑

Properties

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

Downloads

Learn more

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

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

Display 100 coefficients 10 coefficients

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 available 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