Properties

Label 19.3
Level 19
Weight 3
Dimension 21
Nonzero newspaces 3
Newforms 4
Sturm bound 90
Trace bound 1

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Defining parameters

Level: \( N \) = \( 19 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 3 \)
Newforms: \( 4 \)
Sturm bound: \(90\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(19))\).

Total New Old
Modular forms 39 39 0
Cusp forms 21 21 0
Eisenstein series 18 18 0

Trace form

\(21q \) \(\mathstrut -\mathstrut 9q^{2} \) \(\mathstrut -\mathstrut 9q^{3} \) \(\mathstrut -\mathstrut 9q^{4} \) \(\mathstrut -\mathstrut 9q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 9q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut -\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(21q \) \(\mathstrut -\mathstrut 9q^{2} \) \(\mathstrut -\mathstrut 9q^{3} \) \(\mathstrut -\mathstrut 9q^{4} \) \(\mathstrut -\mathstrut 9q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 9q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut -\mathstrut 9q^{9} \) \(\mathstrut -\mathstrut 9q^{10} \) \(\mathstrut -\mathstrut 9q^{11} \) \(\mathstrut +\mathstrut 63q^{12} \) \(\mathstrut +\mathstrut 51q^{13} \) \(\mathstrut +\mathstrut 63q^{14} \) \(\mathstrut +\mathstrut 45q^{15} \) \(\mathstrut +\mathstrut 63q^{16} \) \(\mathstrut -\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 90q^{20} \) \(\mathstrut -\mathstrut 72q^{21} \) \(\mathstrut -\mathstrut 117q^{22} \) \(\mathstrut -\mathstrut 54q^{23} \) \(\mathstrut -\mathstrut 225q^{24} \) \(\mathstrut -\mathstrut 135q^{25} \) \(\mathstrut -\mathstrut 153q^{26} \) \(\mathstrut -\mathstrut 27q^{27} \) \(\mathstrut +\mathstrut 114q^{28} \) \(\mathstrut +\mathstrut 135q^{29} \) \(\mathstrut +\mathstrut 432q^{30} \) \(\mathstrut +\mathstrut 99q^{31} \) \(\mathstrut +\mathstrut 216q^{32} \) \(\mathstrut +\mathstrut 207q^{33} \) \(\mathstrut +\mathstrut 126q^{34} \) \(\mathstrut +\mathstrut 63q^{35} \) \(\mathstrut +\mathstrut 117q^{36} \) \(\mathstrut -\mathstrut 72q^{38} \) \(\mathstrut -\mathstrut 126q^{39} \) \(\mathstrut -\mathstrut 234q^{40} \) \(\mathstrut -\mathstrut 81q^{41} \) \(\mathstrut -\mathstrut 459q^{42} \) \(\mathstrut -\mathstrut 186q^{43} \) \(\mathstrut -\mathstrut 144q^{45} \) \(\mathstrut -\mathstrut 54q^{46} \) \(\mathstrut +\mathstrut 54q^{47} \) \(\mathstrut -\mathstrut 198q^{48} \) \(\mathstrut -\mathstrut 78q^{49} \) \(\mathstrut +\mathstrut 72q^{50} \) \(\mathstrut +\mathstrut 90q^{51} \) \(\mathstrut +\mathstrut 255q^{52} \) \(\mathstrut +\mathstrut 99q^{53} \) \(\mathstrut +\mathstrut 180q^{54} \) \(\mathstrut +\mathstrut 27q^{55} \) \(\mathstrut -\mathstrut 54q^{57} \) \(\mathstrut -\mathstrut 90q^{58} \) \(\mathstrut -\mathstrut 144q^{59} \) \(\mathstrut -\mathstrut 252q^{60} \) \(\mathstrut +\mathstrut 231q^{61} \) \(\mathstrut +\mathstrut 252q^{62} \) \(\mathstrut +\mathstrut 315q^{63} \) \(\mathstrut +\mathstrut 255q^{64} \) \(\mathstrut +\mathstrut 126q^{65} \) \(\mathstrut -\mathstrut 81q^{66} \) \(\mathstrut +\mathstrut 336q^{67} \) \(\mathstrut -\mathstrut 324q^{68} \) \(\mathstrut +\mathstrut 72q^{69} \) \(\mathstrut +\mathstrut 27q^{70} \) \(\mathstrut -\mathstrut 270q^{71} \) \(\mathstrut +\mathstrut 108q^{72} \) \(\mathstrut +\mathstrut 102q^{73} \) \(\mathstrut +\mathstrut 99q^{74} \) \(\mathstrut -\mathstrut 99q^{76} \) \(\mathstrut -\mathstrut 45q^{77} \) \(\mathstrut +\mathstrut 261q^{78} \) \(\mathstrut -\mathstrut 75q^{79} \) \(\mathstrut +\mathstrut 243q^{80} \) \(\mathstrut -\mathstrut 27q^{81} \) \(\mathstrut -\mathstrut 522q^{82} \) \(\mathstrut +\mathstrut 99q^{84} \) \(\mathstrut -\mathstrut 405q^{85} \) \(\mathstrut -\mathstrut 414q^{86} \) \(\mathstrut -\mathstrut 369q^{87} \) \(\mathstrut -\mathstrut 405q^{88} \) \(\mathstrut -\mathstrut 630q^{89} \) \(\mathstrut -\mathstrut 504q^{90} \) \(\mathstrut -\mathstrut 669q^{91} \) \(\mathstrut -\mathstrut 630q^{92} \) \(\mathstrut -\mathstrut 477q^{93} \) \(\mathstrut +\mathstrut 612q^{95} \) \(\mathstrut +\mathstrut 918q^{96} \) \(\mathstrut +\mathstrut 486q^{97} \) \(\mathstrut +\mathstrut 1188q^{98} \) \(\mathstrut +\mathstrut 513q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(19))\)

We only show spaces with odd 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
19.3.b \(\chi_{19}(18, \cdot)\) 19.3.b.a 1 1
19.3.b.b 2
19.3.d \(\chi_{19}(8, \cdot)\) 19.3.d.a 6 2
19.3.f \(\chi_{19}(2, \cdot)\) 19.3.f.a 12 6