Properties

Label 19.4.e
Level 19
Weight 4
Character orbit e
Rep. character \(\chi_{19}(4,\cdot)\)
Character field \(\Q(\zeta_{9})\)
Dimension 24
Newforms 1
Sturm bound 6
Trace bound 0

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Defining parameters

Level: \( N \) = \( 19 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 19.e (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 19 \)
Character field: \(\Q(\zeta_{9})\)
Newforms: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(19, [\chi])\).

Total New Old
Modular forms 36 36 0
Cusp forms 24 24 0
Eisenstein series 12 12 0

Trace form

\(24q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 42q^{6} \) \(\mathstrut +\mathstrut 3q^{7} \) \(\mathstrut -\mathstrut 75q^{8} \) \(\mathstrut -\mathstrut 51q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(24q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 42q^{6} \) \(\mathstrut +\mathstrut 3q^{7} \) \(\mathstrut -\mathstrut 75q^{8} \) \(\mathstrut -\mathstrut 51q^{9} \) \(\mathstrut +\mathstrut 75q^{10} \) \(\mathstrut +\mathstrut 39q^{11} \) \(\mathstrut -\mathstrut 219q^{12} \) \(\mathstrut -\mathstrut 156q^{13} \) \(\mathstrut +\mathstrut 93q^{14} \) \(\mathstrut -\mathstrut 192q^{15} \) \(\mathstrut +\mathstrut 504q^{16} \) \(\mathstrut +\mathstrut 12q^{17} \) \(\mathstrut +\mathstrut 264q^{18} \) \(\mathstrut +\mathstrut 546q^{19} \) \(\mathstrut -\mathstrut 198q^{20} \) \(\mathstrut +\mathstrut 453q^{21} \) \(\mathstrut -\mathstrut 6q^{22} \) \(\mathstrut +\mathstrut 6q^{23} \) \(\mathstrut +\mathstrut 192q^{24} \) \(\mathstrut -\mathstrut 498q^{25} \) \(\mathstrut -\mathstrut 639q^{26} \) \(\mathstrut -\mathstrut 870q^{27} \) \(\mathstrut -\mathstrut 1368q^{28} \) \(\mathstrut -\mathstrut 630q^{29} \) \(\mathstrut -\mathstrut 522q^{30} \) \(\mathstrut -\mathstrut 591q^{31} \) \(\mathstrut +\mathstrut 147q^{32} \) \(\mathstrut +\mathstrut 1506q^{33} \) \(\mathstrut -\mathstrut 408q^{34} \) \(\mathstrut +\mathstrut 2001q^{35} \) \(\mathstrut +\mathstrut 1059q^{36} \) \(\mathstrut -\mathstrut 72q^{37} \) \(\mathstrut +\mathstrut 2934q^{38} \) \(\mathstrut +\mathstrut 336q^{39} \) \(\mathstrut +\mathstrut 2886q^{40} \) \(\mathstrut -\mathstrut 477q^{41} \) \(\mathstrut +\mathstrut 237q^{42} \) \(\mathstrut +\mathstrut 588q^{43} \) \(\mathstrut -\mathstrut 3423q^{44} \) \(\mathstrut -\mathstrut 1569q^{45} \) \(\mathstrut -\mathstrut 1728q^{46} \) \(\mathstrut -\mathstrut 1242q^{47} \) \(\mathstrut -\mathstrut 4599q^{48} \) \(\mathstrut -\mathstrut 639q^{49} \) \(\mathstrut -\mathstrut 1788q^{50} \) \(\mathstrut +\mathstrut 9q^{51} \) \(\mathstrut +\mathstrut 2733q^{52} \) \(\mathstrut -\mathstrut 300q^{53} \) \(\mathstrut +\mathstrut 3777q^{54} \) \(\mathstrut +\mathstrut 315q^{55} \) \(\mathstrut +\mathstrut 4638q^{56} \) \(\mathstrut +\mathstrut 3342q^{57} \) \(\mathstrut -\mathstrut 2820q^{58} \) \(\mathstrut +\mathstrut 2097q^{59} \) \(\mathstrut +\mathstrut 1116q^{60} \) \(\mathstrut -\mathstrut 2316q^{61} \) \(\mathstrut -\mathstrut 1320q^{62} \) \(\mathstrut -\mathstrut 2979q^{63} \) \(\mathstrut -\mathstrut 1785q^{64} \) \(\mathstrut -\mathstrut 2433q^{65} \) \(\mathstrut -\mathstrut 1590q^{66} \) \(\mathstrut +\mathstrut 57q^{67} \) \(\mathstrut -\mathstrut 438q^{68} \) \(\mathstrut -\mathstrut 1767q^{69} \) \(\mathstrut -\mathstrut 213q^{70} \) \(\mathstrut -\mathstrut 792q^{71} \) \(\mathstrut -\mathstrut 1686q^{72} \) \(\mathstrut +\mathstrut 4068q^{73} \) \(\mathstrut +\mathstrut 4287q^{74} \) \(\mathstrut +\mathstrut 1332q^{75} \) \(\mathstrut +\mathstrut 5538q^{76} \) \(\mathstrut +\mathstrut 3786q^{77} \) \(\mathstrut +\mathstrut 2121q^{78} \) \(\mathstrut +\mathstrut 1824q^{79} \) \(\mathstrut -\mathstrut 2739q^{80} \) \(\mathstrut +\mathstrut 1536q^{81} \) \(\mathstrut +\mathstrut 2205q^{82} \) \(\mathstrut +\mathstrut 1071q^{83} \) \(\mathstrut -\mathstrut 1437q^{84} \) \(\mathstrut -\mathstrut 2394q^{85} \) \(\mathstrut -\mathstrut 5256q^{86} \) \(\mathstrut +\mathstrut 759q^{87} \) \(\mathstrut +\mathstrut 1101q^{88} \) \(\mathstrut -\mathstrut 3006q^{89} \) \(\mathstrut -\mathstrut 3822q^{90} \) \(\mathstrut -\mathstrut 3285q^{91} \) \(\mathstrut -\mathstrut 1452q^{92} \) \(\mathstrut -\mathstrut 135q^{93} \) \(\mathstrut -\mathstrut 1086q^{94} \) \(\mathstrut -\mathstrut 3078q^{95} \) \(\mathstrut -\mathstrut 1590q^{96} \) \(\mathstrut -\mathstrut 2535q^{97} \) \(\mathstrut -\mathstrut 2403q^{98} \) \(\mathstrut +\mathstrut 492q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(19, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
19.4.e.a \(24\) \(1.121\) None \(-6\) \(-3\) \(-6\) \(3\)