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Properties

Label 19.6
Level 19
Weight 6
Dimension 66
Nonzero newspaces 3
Newform subspaces 6
Sturm bound 180
Trace bound 1

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Defining parameters

Level: \( N \) = \( 19 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 6 \)
Sturm bound: \(180\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(19))\).

Total New Old
Modular forms 84 82 2
Cusp forms 66 66 0
Eisenstein series 18 16 2

Trace form

\( 66 q - 9 q^{2} - 9 q^{3} - 9 q^{4} - 9 q^{5} - 9 q^{6} - 9 q^{7} - 9 q^{8} - 9 q^{9} + O(q^{10}) \) \( 66 q - 9 q^{2} - 9 q^{3} - 9 q^{4} - 9 q^{5} - 9 q^{6} - 9 q^{7} - 9 q^{8} - 9 q^{9} - 9 q^{10} - 9 q^{11} - 1737 q^{12} + 2163 q^{13} + 3951 q^{14} + 1773 q^{15} - 2889 q^{16} - 2160 q^{17} - 8766 q^{18} - 6414 q^{19} - 6354 q^{20} + 936 q^{21} + 8523 q^{22} + 5130 q^{23} + 25911 q^{24} + 11673 q^{25} + 3951 q^{26} - 32418 q^{27} - 43224 q^{28} + 11349 q^{29} + 69858 q^{30} + 19629 q^{31} + 33786 q^{32} + 12897 q^{33} - 14364 q^{34} - 29565 q^{35} - 107307 q^{36} - 24660 q^{37} - 83862 q^{38} - 57744 q^{39} - 38160 q^{40} + 549 q^{41} + 68481 q^{42} + 28128 q^{43} - 3042 q^{44} + 127080 q^{45} + 173160 q^{46} + 105606 q^{47} + 207576 q^{48} + 14970 q^{49} - 38718 q^{50} - 72315 q^{51} - 30633 q^{52} - 52533 q^{53} - 125532 q^{54} - 103005 q^{55} - 338706 q^{56} - 138564 q^{57} - 96642 q^{58} - 88614 q^{59} - 354654 q^{60} - 179835 q^{61} + 40320 q^{62} + 224595 q^{63} + 593967 q^{64} + 510246 q^{65} + 760671 q^{66} + 417090 q^{67} + 440172 q^{68} + 145278 q^{69} - 107325 q^{70} - 277020 q^{71} - 874008 q^{72} - 438675 q^{73} - 378657 q^{74} - 472518 q^{75} - 499419 q^{76} - 656127 q^{77} - 787383 q^{78} - 290967 q^{79} + 37071 q^{80} + 286182 q^{81} + 682110 q^{82} + 410400 q^{83} + 1613403 q^{84} + 843075 q^{85} + 759114 q^{86} + 871047 q^{87} + 640143 q^{88} + 273204 q^{89} - 245574 q^{90} - 401181 q^{91} - 1081026 q^{92} - 1299591 q^{93} - 1980990 q^{94} - 1015812 q^{95} - 1847898 q^{96} - 201690 q^{97} + 214938 q^{98} + 413604 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(19))\)

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
19.6.a \(\chi_{19}(1, \cdot)\) 19.6.a.a 1 1
19.6.a.b 1
19.6.a.c 2
19.6.a.d 4
19.6.c \(\chi_{19}(7, \cdot)\) 19.6.c.a 16 2
19.6.e \(\chi_{19}(4, \cdot)\) 19.6.e.a 42 6