Properties

Label 19.4.c
Level 19
Weight 4
Character orbit c
Rep. character \(\chi_{19}(7,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 8
Newforms 2
Sturm bound 6
Trace bound 2

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Defining parameters

Level: \( N \) = \( 19 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 19.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 19 \)
Character field: \(\Q(\zeta_{3})\)
Newforms: \( 2 \)
Sturm bound: \(6\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 12 12 0
Cusp forms 8 8 0
Eisenstein series 4 4 0

Trace form

\(8q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 7q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut q^{6} \) \(\mathstrut +\mathstrut 12q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut -\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 7q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut q^{6} \) \(\mathstrut +\mathstrut 12q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut -\mathstrut 4q^{9} \) \(\mathstrut -\mathstrut 32q^{10} \) \(\mathstrut -\mathstrut 10q^{11} \) \(\mathstrut +\mathstrut 42q^{12} \) \(\mathstrut -\mathstrut 73q^{13} \) \(\mathstrut -\mathstrut 142q^{14} \) \(\mathstrut +\mathstrut 91q^{15} \) \(\mathstrut -\mathstrut 43q^{16} \) \(\mathstrut +\mathstrut 187q^{17} \) \(\mathstrut +\mathstrut 60q^{18} \) \(\mathstrut -\mathstrut 139q^{19} \) \(\mathstrut +\mathstrut 668q^{20} \) \(\mathstrut -\mathstrut 130q^{21} \) \(\mathstrut -\mathstrut 121q^{22} \) \(\mathstrut -\mathstrut 115q^{23} \) \(\mathstrut -\mathstrut 39q^{24} \) \(\mathstrut +\mathstrut 75q^{25} \) \(\mathstrut -\mathstrut 320q^{26} \) \(\mathstrut -\mathstrut 212q^{27} \) \(\mathstrut -\mathstrut 454q^{28} \) \(\mathstrut -\mathstrut 137q^{29} \) \(\mathstrut -\mathstrut 128q^{30} \) \(\mathstrut +\mathstrut 576q^{31} \) \(\mathstrut -\mathstrut 465q^{32} \) \(\mathstrut -\mathstrut 737q^{33} \) \(\mathstrut +\mathstrut 916q^{34} \) \(\mathstrut -\mathstrut 324q^{35} \) \(\mathstrut +\mathstrut 938q^{36} \) \(\mathstrut +\mathstrut 1260q^{37} \) \(\mathstrut -\mathstrut 498q^{38} \) \(\mathstrut +\mathstrut 1962q^{39} \) \(\mathstrut -\mathstrut 690q^{40} \) \(\mathstrut -\mathstrut 278q^{41} \) \(\mathstrut -\mathstrut 266q^{42} \) \(\mathstrut +\mathstrut 43q^{43} \) \(\mathstrut +\mathstrut 433q^{44} \) \(\mathstrut -\mathstrut 1772q^{45} \) \(\mathstrut -\mathstrut 1012q^{46} \) \(\mathstrut -\mathstrut 537q^{47} \) \(\mathstrut +\mathstrut 39q^{48} \) \(\mathstrut -\mathstrut 760q^{49} \) \(\mathstrut +\mathstrut 1270q^{50} \) \(\mathstrut -\mathstrut 805q^{51} \) \(\mathstrut -\mathstrut 1074q^{52} \) \(\mathstrut +\mathstrut 623q^{53} \) \(\mathstrut +\mathstrut 53q^{54} \) \(\mathstrut +\mathstrut 1170q^{55} \) \(\mathstrut +\mathstrut 2076q^{56} \) \(\mathstrut -\mathstrut 717q^{57} \) \(\mathstrut +\mathstrut 3352q^{58} \) \(\mathstrut -\mathstrut 316q^{59} \) \(\mathstrut -\mathstrut 1006q^{60} \) \(\mathstrut -\mathstrut 1077q^{61} \) \(\mathstrut -\mathstrut 496q^{62} \) \(\mathstrut +\mathstrut 912q^{63} \) \(\mathstrut -\mathstrut 2602q^{64} \) \(\mathstrut +\mathstrut 186q^{65} \) \(\mathstrut -\mathstrut 863q^{66} \) \(\mathstrut +\mathstrut 184q^{67} \) \(\mathstrut -\mathstrut 1540q^{68} \) \(\mathstrut +\mathstrut 1542q^{69} \) \(\mathstrut -\mathstrut 1908q^{70} \) \(\mathstrut -\mathstrut 1995q^{71} \) \(\mathstrut +\mathstrut 1854q^{72} \) \(\mathstrut -\mathstrut 116q^{73} \) \(\mathstrut +\mathstrut 908q^{74} \) \(\mathstrut +\mathstrut 3014q^{75} \) \(\mathstrut +\mathstrut 1583q^{76} \) \(\mathstrut +\mathstrut 1364q^{77} \) \(\mathstrut -\mathstrut 748q^{78} \) \(\mathstrut +\mathstrut 483q^{79} \) \(\mathstrut +\mathstrut 470q^{80} \) \(\mathstrut +\mathstrut 104q^{81} \) \(\mathstrut -\mathstrut 143q^{82} \) \(\mathstrut -\mathstrut 890q^{83} \) \(\mathstrut -\mathstrut 828q^{84} \) \(\mathstrut +\mathstrut 1575q^{85} \) \(\mathstrut +\mathstrut 654q^{86} \) \(\mathstrut -\mathstrut 1710q^{87} \) \(\mathstrut -\mathstrut 1470q^{88} \) \(\mathstrut -\mathstrut 713q^{89} \) \(\mathstrut +\mathstrut 1588q^{90} \) \(\mathstrut -\mathstrut 1356q^{91} \) \(\mathstrut +\mathstrut 1408q^{92} \) \(\mathstrut -\mathstrut 792q^{93} \) \(\mathstrut -\mathstrut 2184q^{94} \) \(\mathstrut -\mathstrut 2143q^{95} \) \(\mathstrut +\mathstrut 286q^{96} \) \(\mathstrut +\mathstrut 870q^{97} \) \(\mathstrut -\mathstrut 2491q^{98} \) \(\mathstrut -\mathstrut 1642q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.c.a \(4\) \(1.121\) \(\Q(\sqrt{-3}, \sqrt{55})\) None \(-2\) \(0\) \(14\) \(-28\) \(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(7+7\beta _{2})q^{4}+\cdots\)
19.4.c.b \(4\) \(1.121\) \(\Q(\sqrt{-3}, \sqrt{73})\) None \(-1\) \(-2\) \(-19\) \(40\) \(q-\beta _{1}q^{2}-\beta _{2}q^{3}+(-11+\beta _{1}+10\beta _{2}+\cdots)q^{4}+\cdots\)