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Properties

Label 19.3.f
Level $19$
Weight $3$
Character orbit 19.f
Rep. character $\chi_{19}(2,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $12$
Newform subspaces $1$
Sturm bound $5$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 19 \)
Weight: \( k \) \(=\) \( 3 \)
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: \(5\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(19, [\chi])\).

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

Trace form

\( 12 q - 6 q^{2} - 6 q^{5} - 36 q^{6} + 6 q^{7} - 9 q^{8} - 24 q^{9} + O(q^{10}) \) \( 12 q - 6 q^{2} - 6 q^{5} - 36 q^{6} + 6 q^{7} - 9 q^{8} - 24 q^{9} + 51 q^{10} - 18 q^{11} + 63 q^{12} + 21 q^{13} + 9 q^{14} + 63 q^{15} - 12 q^{16} - 3 q^{17} - 24 q^{19} - 90 q^{20} + 30 q^{21} - 78 q^{22} - 102 q^{23} - 12 q^{24} - 156 q^{25} + 21 q^{26} - 27 q^{27} + 12 q^{28} + 147 q^{29} + 24 q^{30} + 99 q^{31} + 165 q^{32} + 84 q^{33} + 132 q^{34} + 96 q^{35} + 63 q^{36} + 72 q^{38} - 108 q^{39} - 138 q^{40} - 144 q^{41} - 237 q^{42} - 27 q^{43} - 123 q^{44} - 3 q^{45} - 54 q^{46} - 99 q^{47} - 51 q^{48} - 24 q^{49} + 72 q^{50} - 42 q^{51} + 93 q^{52} + 111 q^{53} + 21 q^{54} + 162 q^{55} - 168 q^{57} - 132 q^{58} + 3 q^{59} - 30 q^{60} + 150 q^{61} + 108 q^{62} + 234 q^{63} + 27 q^{64} + 126 q^{65} + 168 q^{66} + 135 q^{67} - 30 q^{68} + 72 q^{69} + 225 q^{70} - 168 q^{71} - 102 q^{72} - 90 q^{73} - 231 q^{74} + 42 q^{76} + 246 q^{77} - 189 q^{78} - 75 q^{79} + 21 q^{80} - 159 q^{81} - 117 q^{82} - 156 q^{83} + 99 q^{84} - 300 q^{85} - 144 q^{86} + 69 q^{87} - 405 q^{88} - 558 q^{89} - 66 q^{90} - 453 q^{91} + 48 q^{92} - 57 q^{93} - 69 q^{95} + 558 q^{96} + 465 q^{97} + 777 q^{98} + 462 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(19, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
19.3.f.a 19.f 19.f $12$ $0.518$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-6\) \(0\) \(-6\) \(6\) $\mathrm{SU}(2)[C_{18}]$ \(q+\beta _{10}q^{2}+(\beta _{1}-\beta _{4}-\beta _{5}+\beta _{6}-\beta _{7}+\cdots)q^{3}+\cdots\)