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

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

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 the 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