Properties

Label 4.4.18097.1-27.1-a
Base field 4.4.18097.1
Weight $[2, 2, 2, 2]$
Level norm $27$
Level $[27, 3, -w^{3} + 7w + 1]$
Dimension $33$
CM no
Base change no

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Base field 4.4.18097.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + 6x + 4\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[27, 3, -w^{3} + 7w + 1]$
Dimension: $33$
CM: no
Base change: no
Newspace dimension: $66$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{33} - 17x^{32} + 77x^{31} + 280x^{30} - 3404x^{29} + 4710x^{28} + 46753x^{27} - 168557x^{26} - 217772x^{25} + 1953163x^{24} - 1049731x^{23} - 11771427x^{22} + 19021382x^{21} + 38124905x^{20} - 111704092x^{19} - 46891180x^{18} + 367180134x^{17} - 105158409x^{16} - 741649235x^{15} + 545295624x^{14} + 934967853x^{13} - 1050081353x^{12} - 717536180x^{11} + 1147658028x^{10} + 312002124x^{9} - 765745003x^{8} - 66456453x^{7} + 313547145x^{6} + 7097051x^{5} - 75708648x^{4} - 2305779x^{3} + 9252663x^{2} + 609703x - 312948\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w + 1]$ $\phantom{-}e$
4 $[4, 2, w]$ $...$
4 $[4, 2, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{7}{2}w - 3]$ $...$
7 $[7, 7, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{5}{2}w - 2]$ $...$
13 $[13, 13, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{7}{2}w - 1]$ $...$
17 $[17, 17, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w]$ $...$
27 $[27, 3, -w^{3} + 7w + 1]$ $-1$
31 $[31, 31, w + 3]$ $...$
31 $[31, 31, -w^{2} + 5]$ $...$
37 $[37, 37, w^{2} - 3]$ $...$
41 $[41, 41, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{3}{2}w - 2]$ $...$
47 $[47, 47, w^{3} - 5w - 3]$ $...$
53 $[53, 53, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w]$ $...$
61 $[61, 61, w^{3} - w^{2} - 5w + 3]$ $...$
83 $[83, 83, w^{3} + w^{2} - 6w - 7]$ $...$
83 $[83, 83, -w^{3} + 5w + 1]$ $...$
83 $[83, 83, 2w - 1]$ $...$
83 $[83, 83, -\frac{3}{2}w^{3} - \frac{1}{2}w^{2} + \frac{19}{2}w + 2]$ $...$
89 $[89, 89, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w - 2]$ $...$
89 $[89, 89, w^{3} - 5w + 5]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$27$ $[27, 3, -w^{3} + 7w + 1]$ $1$