Properties

Label 19.5.f
Level $19$
Weight $5$
Character orbit 19.f
Rep. character $\chi_{19}(2,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $36$
Newform subspaces $1$
Sturm bound $8$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 19.f (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(19, [\chi])\).

Total New Old
Modular forms 48 48 0
Cusp forms 36 36 0
Eisenstein series 12 12 0

Trace form

\( 36q - 6q^{2} - 18q^{3} - 48q^{4} - 6q^{5} - 48q^{7} - 9q^{8} + 246q^{9} + O(q^{10}) \) \( 36q - 6q^{2} - 18q^{3} - 48q^{4} - 6q^{5} - 48q^{7} - 9q^{8} + 246q^{9} - 153q^{10} - 48q^{11} + 855q^{12} + 555q^{13} - 399q^{14} - 1647q^{15} - 2112q^{16} + 39q^{17} - 12q^{19} + 2886q^{20} + 912q^{21} + 1386q^{22} + 1074q^{23} + 168q^{24} + 2448q^{25} - 3675q^{26} + 1215q^{27} + 2316q^{28} - 1743q^{29} + 2580q^{30} - 2817q^{31} - 6039q^{32} - 7368q^{33} - 8460q^{34} - 1326q^{35} - 4581q^{36} + 2892q^{38} + 7164q^{39} + 4482q^{40} + 6150q^{41} + 22299q^{42} + 2091q^{43} + 34053q^{44} + 3165q^{45} + 7326q^{46} + 4539q^{47} - 44943q^{48} + 102q^{49} - 51876q^{50} - 25836q^{51} - 3279q^{52} - 11607q^{53} + 6069q^{54} - 7044q^{55} + 2532q^{57} + 13644q^{58} - 681q^{59} + 63654q^{60} + 44346q^{61} + 14796q^{62} + 53388q^{63} + 939q^{64} + 3636q^{65} + 11148q^{66} - 52089q^{67} + 5262q^{68} - 54954q^{69} - 69999q^{70} - 24504q^{71} - 101118q^{72} - 6666q^{73} - 9675q^{74} - 6462q^{76} + 48918q^{77} + 56871q^{78} + 41043q^{79} + 65649q^{80} + 2919q^{81} + 114711q^{82} - 17598q^{83} + 11115q^{84} + 52344q^{85} - 55716q^{86} + 2121q^{87} - 69057q^{88} - 11706q^{89} - 41394q^{90} - 84249q^{91} - 88668q^{92} - 60321q^{93} + 93405q^{95} + 167166q^{96} + 4401q^{97} + 69381q^{98} + 58386q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(19, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
19.5.f.a \(36\) \(1.964\) None \(-6\) \(-18\) \(-6\) \(-48\)