Properties

Base field 5.5.160801.1
Weight [2, 2, 2, 2, 2]
Level norm 17
Level $[17, 17, w^{4} - w^{3} - 5w^{2} + 3w + 1]$
Label 5.5.160801.1-17.1-b
Dimension 12
CM no
Base change no

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Base field 5.5.160801.1

Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 5x^{3} + 4x^{2} + 3x - 1\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2, 2, 2, 2]
Level $[17, 17, w^{4} - w^{3} - 5w^{2} + 3w + 1]$
Label 5.5.160801.1-17.1-b
Dimension 12
Is CM no
Is base change no
Parent newspace dimension 27

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{12} \) \(\mathstrut +\mathstrut 5x^{11} \) \(\mathstrut -\mathstrut 11x^{10} \) \(\mathstrut -\mathstrut 76x^{9} \) \(\mathstrut +\mathstrut 22x^{8} \) \(\mathstrut +\mathstrut 363x^{7} \) \(\mathstrut -\mathstrut 22x^{6} \) \(\mathstrut -\mathstrut 754x^{5} \) \(\mathstrut +\mathstrut 108x^{4} \) \(\mathstrut +\mathstrut 648x^{3} \) \(\mathstrut -\mathstrut 158x^{2} \) \(\mathstrut -\mathstrut 162x \) \(\mathstrut +\mathstrut 39\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ $\phantom{-}e$
9 $[9, 3, -w^{4} + 5w^{2} - 3]$ $\phantom{-}\frac{217}{927}e^{11} + \frac{1387}{927}e^{10} - \frac{269}{309}e^{9} - \frac{18619}{927}e^{8} - \frac{16375}{927}e^{7} + \frac{68554}{927}e^{6} + \frac{72298}{927}e^{5} - \frac{100811}{927}e^{4} - \frac{86725}{927}e^{3} + \frac{54292}{927}e^{2} + \frac{8345}{309}e - \frac{1850}{309}$
9 $[9, 3, -w^{4} + w^{3} + 5w^{2} - 3w - 2]$ $...$
13 $[13, 13, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ $...$
17 $[17, 17, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ $-1$
19 $[19, 19, -w^{3} + w^{2} + 4w - 2]$ $-\frac{1016}{309}e^{11} - \frac{6353}{309}e^{10} + \frac{1109}{103}e^{9} + \frac{81644}{309}e^{8} + \frac{78320}{309}e^{7} - \frac{273830}{309}e^{6} - \frac{313589}{309}e^{5} + \frac{381826}{309}e^{4} + \frac{355679}{309}e^{3} - \frac{218861}{309}e^{2} - \frac{35392}{103}e + \frac{10586}{103}$
23 $[23, 23, -w^{2} + 3]$ $-\frac{222}{103}e^{11} - \frac{1362}{103}e^{10} + \frac{818}{103}e^{9} + \frac{17550}{103}e^{8} + \frac{16037}{103}e^{7} - \frac{59161}{103}e^{6} - \frac{65693}{103}e^{5} + \frac{82306}{103}e^{4} + \frac{75020}{103}e^{3} - \frac{46881}{103}e^{2} - \frac{22135}{103}e + \frac{6921}{103}$
31 $[31, 31, w^{3} - 4w + 2]$ $\phantom{-}\frac{740}{927}e^{11} + \frac{4952}{927}e^{10} - \frac{268}{309}e^{9} - \frac{61178}{927}e^{8} - \frac{74915}{927}e^{7} + \frac{185942}{927}e^{6} + \frac{264125}{927}e^{5} - \frac{238990}{927}e^{4} - \frac{273791}{927}e^{3} + \frac{133919}{927}e^{2} + \frac{24274}{309}e - \frac{6454}{309}$
32 $[32, 2, 2]$ $...$
37 $[37, 37, w^{3} - 3w - 1]$ $-\frac{1879}{927}e^{11} - \frac{11617}{927}e^{10} + \frac{2147}{309}e^{9} + \frac{148846}{927}e^{8} + \frac{141274}{927}e^{7} - \frac{494197}{927}e^{6} - \frac{569113}{927}e^{5} + \frac{671117}{927}e^{4} + \frac{645892}{927}e^{3} - \frac{364645}{927}e^{2} - \frac{65447}{309}e + \frac{16190}{309}$
53 $[53, 53, -2w^{4} + w^{3} + 9w^{2} - 3w - 2]$ $-\frac{568}{309}e^{11} - \frac{3649}{309}e^{10} + \frac{444}{103}e^{9} + \frac{46225}{309}e^{8} + \frac{50554}{309}e^{7} - \frac{149035}{309}e^{6} - \frac{197581}{309}e^{5} + \frac{195659}{309}e^{4} + \frac{226642}{309}e^{3} - \frac{106246}{309}e^{2} - \frac{23297}{103}e + \frac{5112}{103}$
59 $[59, 59, -w^{4} + 5w^{2} + w - 4]$ $-\frac{601}{309}e^{11} - \frac{3793}{309}e^{10} + \frac{633}{103}e^{9} + \frac{49243}{309}e^{8} + \frac{48385}{309}e^{7} - \frac{169297}{309}e^{6} - \frac{201574}{309}e^{5} + \frac{242858}{309}e^{4} + \frac{242398}{309}e^{3} - \frac{146758}{309}e^{2} - \frac{26187}{103}e + \frac{8190}{103}$
61 $[61, 61, -w^{4} + w^{3} + 5w^{2} - 4w]$ $-\frac{1184}{927}e^{11} - \frac{7367}{927}e^{10} + \frac{1294}{309}e^{9} + \frac{94733}{927}e^{8} + \frac{92981}{927}e^{7} - \frac{316418}{927}e^{6} - \frac{385520}{927}e^{5} + \frac{425953}{927}e^{4} + \frac{460499}{927}e^{3} - \frac{227990}{927}e^{2} - \frac{49159}{309}e + \frac{10450}{309}$
67 $[67, 67, -w^{4} + 6w^{2} + 2w - 4]$ $-\frac{2077}{309}e^{11} - \frac{12790}{309}e^{10} + \frac{2663}{103}e^{9} + \frac{166645}{309}e^{8} + \frac{147109}{309}e^{7} - \frac{577453}{309}e^{6} - \frac{615628}{309}e^{5} + \frac{830402}{309}e^{4} + \frac{714472}{309}e^{3} - \frac{484735}{309}e^{2} - \frac{71766}{103}e + \frac{23328}{103}$
71 $[71, 71, 2w^{4} - w^{3} - 9w^{2} + 4w + 5]$ $-\frac{2318}{309}e^{11} - \frac{14366}{309}e^{10} + \frac{2826}{103}e^{9} + \frac{186560}{309}e^{8} + \frac{169154}{309}e^{7} - \frac{641585}{309}e^{6} - \frac{698555}{309}e^{5} + \frac{916858}{309}e^{4} + \frac{807431}{309}e^{3} - \frac{533489}{309}e^{2} - \frac{81960}{103}e + \frac{26115}{103}$
79 $[79, 79, 2w^{4} - w^{3} - 10w^{2} + 2w + 7]$ $\phantom{-}\frac{262}{927}e^{11} + \frac{1162}{927}e^{10} - \frac{1229}{309}e^{9} - \frac{20122}{927}e^{8} + \frac{11696}{927}e^{7} + \frac{111016}{927}e^{6} + \frac{10999}{927}e^{5} - \frac{223490}{927}e^{4} - \frac{50905}{927}e^{3} + \frac{156307}{927}e^{2} + \frac{8915}{309}e - \frac{6890}{309}$
83 $[83, 83, -w^{4} + 2w^{3} + 5w^{2} - 7w - 2]$ $-\frac{1598}{309}e^{11} - \frac{9932}{309}e^{10} + \frac{1886}{103}e^{9} + \frac{128831}{309}e^{8} + \frac{119564}{309}e^{7} - \frac{441143}{309}e^{6} - \frac{495251}{309}e^{5} + \frac{622594}{309}e^{4} + \frac{575297}{309}e^{3} - \frac{356639}{309}e^{2} - \frac{58111}{103}e + \frac{17575}{103}$
83 $[83, 83, -w^{4} + w^{3} + 4w^{2} - 3w + 3]$ $-\frac{107}{103}e^{11} - \frac{701}{103}e^{10} + \frac{256}{103}e^{9} + \frac{9074}{103}e^{8} + \frac{9597}{103}e^{7} - \frac{30987}{103}e^{6} - \frac{38491}{103}e^{5} + \frac{44318}{103}e^{4} + \frac{45123}{103}e^{3} - \frac{27402}{103}e^{2} - \frac{14263}{103}e + \frac{4846}{103}$
83 $[83, 83, w^{4} - w^{3} - 5w^{2} + 4w - 1]$ $...$
83 $[83, 83, -w^{4} + w^{3} + 4w^{2} - 4w - 2]$ $-\frac{876}{103}e^{11} - \frac{5405}{103}e^{10} + \frac{3225}{103}e^{9} + \frac{70067}{103}e^{8} + \frac{63785}{103}e^{7} - \frac{239782}{103}e^{6} - \frac{264513}{103}e^{5} + \frac{339749}{103}e^{4} + \frac{306645}{103}e^{3} - \frac{196164}{103}e^{2} - \frac{93131}{103}e + \frac{28802}{103}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
17 $[17, 17, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ $1$