Properties

Label 19.5.d
Level $19$
Weight $5$
Character orbit 19.d
Rep. character $\chi_{19}(8,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $10$
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.d (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{6})\)
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 14 14 0
Cusp forms 10 10 0
Eisenstein series 4 4 0

Trace form

\( 10q - 3q^{2} + 9q^{3} + 29q^{4} + 8q^{5} - 35q^{6} - 24q^{7} - 58q^{9} + O(q^{10}) \) \( 10q - 3q^{2} + 9q^{3} + 29q^{4} + 8q^{5} - 35q^{6} - 24q^{7} - 58q^{9} + 144q^{10} + 50q^{11} - 624q^{13} - 474q^{14} + 504q^{15} + 285q^{16} - 292q^{17} + 305q^{19} - 652q^{20} + 1158q^{21} + 1629q^{22} + 98q^{23} + 505q^{24} - 681q^{25} + 1524q^{26} - 1472q^{28} + 2598q^{29} - 6656q^{30} - 2745q^{32} - 3441q^{33} + 486q^{34} + 694q^{35} + 3402q^{36} - 342q^{38} - 5552q^{39} + 8784q^{40} - 1407q^{41} + 292q^{42} + 5424q^{43} + 4151q^{44} + 9572q^{45} - 2416q^{47} + 11481q^{48} - 17826q^{49} - 3342q^{51} - 19962q^{52} + 1122q^{53} - 1039q^{54} + 11424q^{55} - 7906q^{57} - 20236q^{58} + 15387q^{59} + 8886q^{60} + 860q^{61} + 21636q^{62} + 5318q^{63} + 19710q^{64} - 13921q^{66} + 14763q^{67} - 48844q^{68} - 20334q^{70} - 27264q^{71} + 354q^{72} + 1561q^{73} + 17094q^{74} + 1955q^{76} - 18392q^{77} + 40266q^{78} + 24750q^{79} - 2002q^{80} + 14311q^{81} + 14479q^{82} + 6002q^{83} - 14944q^{85} + 59946q^{86} - 31996q^{87} - 22566q^{89} - 60630q^{90} + 8724q^{91} + 9572q^{92} + 12476q^{93} - 7312q^{95} - 41850q^{96} + 46287q^{97} + 25515q^{98} - 2048q^{99} + O(q^{100}) \)

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.d.a \(10\) \(1.964\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(-3\) \(9\) \(8\) \(-24\) \(q-\beta _{1}q^{2}+(\beta _{3}+\beta _{5})q^{3}+(6\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)