Properties

Label 19.4
Level 19
Weight 4
Dimension 36
Nonzero newspaces 3
Newforms 5
Sturm bound 120
Trace bound 1

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 19 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 3 \)
Newforms: \( 5 \)
Sturm bound: \(120\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(19))\).

Total New Old
Modular forms 54 52 2
Cusp forms 36 36 0
Eisenstein series 18 16 2

Trace form

\(36q \) \(\mathstrut -\mathstrut 9q^{2} \) \(\mathstrut -\mathstrut 9q^{3} \) \(\mathstrut -\mathstrut 9q^{4} \) \(\mathstrut -\mathstrut 9q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 9q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut -\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(36q \) \(\mathstrut -\mathstrut 9q^{2} \) \(\mathstrut -\mathstrut 9q^{3} \) \(\mathstrut -\mathstrut 9q^{4} \) \(\mathstrut -\mathstrut 9q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 9q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut -\mathstrut 9q^{9} \) \(\mathstrut -\mathstrut 9q^{10} \) \(\mathstrut -\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 297q^{12} \) \(\mathstrut -\mathstrut 153q^{13} \) \(\mathstrut -\mathstrut 45q^{14} \) \(\mathstrut +\mathstrut 99q^{15} \) \(\mathstrut +\mathstrut 423q^{16} \) \(\mathstrut +\mathstrut 135q^{17} \) \(\mathstrut +\mathstrut 468q^{18} \) \(\mathstrut +\mathstrut 369q^{19} \) \(\mathstrut +\mathstrut 558q^{20} \) \(\mathstrut +\mathstrut 243q^{21} \) \(\mathstrut +\mathstrut 153q^{22} \) \(\mathstrut -\mathstrut 27q^{23} \) \(\mathstrut -\mathstrut 441q^{24} \) \(\mathstrut -\mathstrut 441q^{25} \) \(\mathstrut -\mathstrut 693q^{26} \) \(\mathstrut -\mathstrut 1314q^{27} \) \(\mathstrut -\mathstrut 2304q^{28} \) \(\mathstrut -\mathstrut 639q^{29} \) \(\mathstrut -\mathstrut 1206q^{30} \) \(\mathstrut -\mathstrut 99q^{31} \) \(\mathstrut +\mathstrut 306q^{32} \) \(\mathstrut +\mathstrut 909q^{33} \) \(\mathstrut +\mathstrut 1116q^{34} \) \(\mathstrut +\mathstrut 1107q^{35} \) \(\mathstrut +\mathstrut 3069q^{36} \) \(\mathstrut +\mathstrut 648q^{37} \) \(\mathstrut +\mathstrut 2322q^{38} \) \(\mathstrut +\mathstrut 1872q^{39} \) \(\mathstrut +\mathstrut 1872q^{40} \) \(\mathstrut +\mathstrut 441q^{41} \) \(\mathstrut +\mathstrut 1521q^{42} \) \(\mathstrut -\mathstrut 135q^{43} \) \(\mathstrut -\mathstrut 2934q^{44} \) \(\mathstrut -\mathstrut 3087q^{45} \) \(\mathstrut -\mathstrut 3528q^{46} \) \(\mathstrut -\mathstrut 1881q^{47} \) \(\mathstrut -\mathstrut 5616q^{48} \) \(\mathstrut -\mathstrut 1719q^{49} \) \(\mathstrut -\mathstrut 2214q^{50} \) \(\mathstrut -\mathstrut 144q^{51} \) \(\mathstrut +\mathstrut 2367q^{52} \) \(\mathstrut +\mathstrut 1575q^{53} \) \(\mathstrut +\mathstrut 2448q^{54} \) \(\mathstrut +\mathstrut 1935q^{55} \) \(\mathstrut +\mathstrut 6030q^{56} \) \(\mathstrut +\mathstrut 2511q^{57} \) \(\mathstrut +\mathstrut 1926q^{58} \) \(\mathstrut +\mathstrut 2241q^{59} \) \(\mathstrut +\mathstrut 1530q^{60} \) \(\mathstrut -\mathstrut 2763q^{61} \) \(\mathstrut -\mathstrut 3420q^{62} \) \(\mathstrut -\mathstrut 3393q^{63} \) \(\mathstrut -\mathstrut 4113q^{64} \) \(\mathstrut -\mathstrut 2619q^{65} \) \(\mathstrut -\mathstrut 3537q^{66} \) \(\mathstrut -\mathstrut 927q^{67} \) \(\mathstrut -\mathstrut 3600q^{68} \) \(\mathstrut -\mathstrut 333q^{69} \) \(\mathstrut +\mathstrut 315q^{70} \) \(\mathstrut -\mathstrut 2187q^{71} \) \(\mathstrut +\mathstrut 2952q^{72} \) \(\mathstrut +\mathstrut 4932q^{73} \) \(\mathstrut +\mathstrut 5175q^{74} \) \(\mathstrut +\mathstrut 6282q^{75} \) \(\mathstrut +\mathstrut 6741q^{76} \) \(\mathstrut +\mathstrut 4644q^{77} \) \(\mathstrut -\mathstrut 279q^{78} \) \(\mathstrut +\mathstrut 2655q^{79} \) \(\mathstrut -\mathstrut 2889q^{80} \) \(\mathstrut +\mathstrut 468q^{81} \) \(\mathstrut +\mathstrut 2214q^{82} \) \(\mathstrut -\mathstrut 351q^{83} \) \(\mathstrut -\mathstrut 1413q^{84} \) \(\mathstrut -\mathstrut 945q^{85} \) \(\mathstrut -\mathstrut 1422q^{86} \) \(\mathstrut -\mathstrut 1377q^{87} \) \(\mathstrut -\mathstrut 1161q^{88} \) \(\mathstrut -\mathstrut 4059q^{89} \) \(\mathstrut -\mathstrut 4194q^{90} \) \(\mathstrut -\mathstrut 4977q^{91} \) \(\mathstrut -\mathstrut 2538q^{92} \) \(\mathstrut -\mathstrut 315q^{93} \) \(\mathstrut -\mathstrut 2862q^{94} \) \(\mathstrut -\mathstrut 5715q^{95} \) \(\mathstrut -\mathstrut 666q^{96} \) \(\mathstrut -\mathstrut 3357q^{97} \) \(\mathstrut -\mathstrut 6678q^{98} \) \(\mathstrut -\mathstrut 792q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(19))\)

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
19.4.a \(\chi_{19}(1, \cdot)\) 19.4.a.a 1 1
19.4.a.b 3
19.4.c \(\chi_{19}(7, \cdot)\) 19.4.c.a 4 2
19.4.c.b 4
19.4.e \(\chi_{19}(4, \cdot)\) 19.4.e.a 24 6