Properties

Label 19.5
Level 19
Weight 5
Dimension 51
Nonzero newspaces 3
Newform subspaces 4
Sturm bound 150
Trace bound 1

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Defining parameters

Level: \( N \) = \( 19 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 4 \)
Sturm bound: \(150\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(19))\).

Total New Old
Modular forms 69 69 0
Cusp forms 51 51 0
Eisenstein series 18 18 0

Trace form

\( 51 q - 9 q^{2} - 9 q^{3} - 9 q^{4} - 9 q^{5} - 9 q^{6} - 9 q^{7} - 9 q^{8} - 9 q^{9} + O(q^{10}) \) \( 51 q - 9 q^{2} - 9 q^{3} - 9 q^{4} - 9 q^{5} - 9 q^{6} - 9 q^{7} - 9 q^{8} - 9 q^{9} - 9 q^{10} - 9 q^{11} + 855 q^{12} - 69 q^{13} - 873 q^{14} - 1143 q^{15} - 2025 q^{16} - 306 q^{17} + 768 q^{19} + 2574 q^{20} + 2070 q^{21} + 3015 q^{22} + 936 q^{23} + 2583 q^{24} + 117 q^{25} - 1737 q^{26} + 1215 q^{27} + 786 q^{28} + 855 q^{29} - 4860 q^{30} - 2817 q^{31} - 8784 q^{32} - 10809 q^{33} - 7974 q^{34} - 4761 q^{35} - 6255 q^{36} + 4716 q^{38} + 7974 q^{39} + 13266 q^{40} + 4743 q^{41} + 26541 q^{42} + 14028 q^{43} + 30420 q^{44} + 20430 q^{45} + 7326 q^{46} - 4248 q^{47} - 33462 q^{48} - 17148 q^{49} - 51876 q^{50} - 29178 q^{51} - 23241 q^{52} - 10485 q^{53} - 10512 q^{54} - 3933 q^{55} + 5076 q^{57} + 8046 q^{58} + 14706 q^{59} + 72540 q^{60} + 48531 q^{61} + 54828 q^{62} + 29763 q^{63} + 28239 q^{64} + 3636 q^{65} - 10017 q^{66} - 37326 q^{67} - 44424 q^{68} - 54954 q^{69} - 90333 q^{70} - 51768 q^{71} - 100764 q^{72} - 30306 q^{73} - 10449 q^{74} + 13581 q^{76} + 47637 q^{77} + 97137 q^{78} + 65793 q^{79} + 73503 q^{80} + 64503 q^{81} + 100026 q^{82} + 16002 q^{83} + 11115 q^{84} + 21555 q^{85} + 4230 q^{86} - 37089 q^{87} - 69057 q^{88} - 34272 q^{89} - 102024 q^{90} - 75525 q^{91} - 106254 q^{92} - 87849 q^{93} + 91926 q^{95} + 172854 q^{96} + 50688 q^{97} + 94896 q^{98} + 60507 q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(19))\)

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
19.5.b \(\chi_{19}(18, \cdot)\) 19.5.b.a 1 1
19.5.b.b 4
19.5.d \(\chi_{19}(8, \cdot)\) 19.5.d.a 10 2
19.5.f \(\chi_{19}(2, \cdot)\) 19.5.f.a 36 6