Properties

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

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Defining parameters

Level: \( N \) = \( 19 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 3 \)
Newforms: \( 4 \)
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

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

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