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Properties

Label 19.8
Level 19
Weight 8
Dimension 96
Nonzero newspaces 3
Newform subspaces 4
Sturm bound 240
Trace bound 1

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Defining parameters

Level: \( N \) = \( 19 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 4 \)
Sturm bound: \(240\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(19))\).

Total New Old
Modular forms 114 112 2
Cusp forms 96 96 0
Eisenstein series 18 16 2

Trace form

\( 96 q - 9 q^{2} - 9 q^{3} - 9 q^{4} - 9 q^{5} - 9 q^{6} - 9 q^{7} - 9 q^{8} - 9 q^{9} + O(q^{10}) \) \( 96 q - 9 q^{2} - 9 q^{3} - 9 q^{4} - 9 q^{5} - 9 q^{6} - 9 q^{7} - 9 q^{8} - 9 q^{9} - 9 q^{10} - 9 q^{11} + 20727 q^{12} + 22155 q^{13} - 40473 q^{14} - 61731 q^{15} - 29961 q^{16} + 29358 q^{17} + 157446 q^{18} + 100518 q^{19} - 2322 q^{20} - 142326 q^{21} - 317313 q^{22} - 98406 q^{23} - 62217 q^{24} + 258309 q^{25} + 509895 q^{26} - 373266 q^{27} + 175344 q^{28} + 597969 q^{29} + 308754 q^{30} - 424107 q^{31} - 1640574 q^{32} - 1645011 q^{33} - 453564 q^{34} + 583587 q^{35} + 3514149 q^{36} + 911736 q^{37} + 2923002 q^{38} + 1397016 q^{39} - 437688 q^{40} - 793287 q^{41} - 6739839 q^{42} - 4608876 q^{43} - 3617082 q^{44} + 2419218 q^{45} + 6693192 q^{46} + 3408966 q^{47} + 7995888 q^{48} + 4740 q^{49} - 12518334 q^{50} - 11054943 q^{51} - 3729801 q^{52} + 645363 q^{53} + 4934052 q^{54} + 5345955 q^{55} + 18966510 q^{56} + 7469226 q^{57} + 4282254 q^{58} + 1825686 q^{59} - 21412710 q^{60} - 4469223 q^{61} + 3751488 q^{62} + 7586739 q^{63} - 2757009 q^{64} - 8563104 q^{65} - 15979329 q^{66} - 18862410 q^{67} + 2344788 q^{68} - 7312068 q^{69} - 2518605 q^{70} + 2200212 q^{71} - 4600224 q^{72} + 14107029 q^{73} + 26835903 q^{74} + 35437482 q^{75} + 36422901 q^{76} + 12572919 q^{77} + 12726441 q^{78} + 11368761 q^{79} + 28884591 q^{80} - 10725012 q^{81} - 66154266 q^{82} - 26271828 q^{83} - 113748741 q^{84} - 56951685 q^{85} - 38565774 q^{86} - 35059257 q^{87} - 1114065 q^{88} + 45636282 q^{89} + 90215226 q^{90} + 63960531 q^{91} + 59254182 q^{92} + 17980245 q^{93} - 87913278 q^{94} - 8390700 q^{95} + 158330790 q^{96} + 64819800 q^{97} + 147870018 q^{98} + 43795260 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(19))\)

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
19.8.a \(\chi_{19}(1, \cdot)\) 19.8.a.a 4 1
19.8.a.b 6
19.8.c \(\chi_{19}(7, \cdot)\) 19.8.c.a 20 2
19.8.e \(\chi_{19}(4, \cdot)\) 19.8.e.a 66 6