Properties

Label 4.4.11197.1-27.2-c
Base field 4.4.11197.1
Weight $[2, 2, 2, 2]$
Level norm $27$
Level $[27, 27, -w^{2} + w + 2]$
Dimension $6$
CM no
Base change no

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Base field 4.4.11197.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[27, 27, -w^{2} + w + 2]$
Dimension: $6$
CM: no
Base change: no
Newspace dimension: $20$

Hecke eigenvalues ($q$-expansion)

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

\(x^{6} - 45x^{4} + 306x^{2} - 567\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $\phantom{-}0$
7 $[7, 7, w^{3} - 2w^{2} - 3w + 1]$ $\phantom{-}\frac{1}{9}e^{4} - \frac{14}{3}e^{2} + 16$
11 $[11, 11, -w - 2]$ $-\frac{7}{9}e^{4} + 32e^{2} - 114$
11 $[11, 11, -w^{3} + 2w^{2} + 3w - 2]$ $\phantom{-}e$
13 $[13, 13, -w^{2} + 2w + 2]$ $\phantom{-}\frac{5}{27}e^{5} - \frac{23}{3}e^{3} + \frac{86}{3}e$
16 $[16, 2, 2]$ $\phantom{-}\frac{4}{27}e^{5} - 6e^{3} + \frac{55}{3}e$
19 $[19, 19, -w^{3} + 2w^{2} + 4w - 1]$ $\phantom{-}\frac{4}{9}e^{4} - \frac{55}{3}e^{2} + 64$
23 $[23, 23, -w^{2} + w + 3]$ $-\frac{2}{3}e^{4} + \frac{82}{3}e^{2} - 99$
23 $[23, 23, -w^{2} + 3]$ $\phantom{-}\frac{4}{9}e^{4} - 18e^{2} + 60$
27 $[27, 3, w^{3} - 3w^{2} - w + 4]$ $-\frac{5}{27}e^{5} + \frac{23}{3}e^{3} - \frac{89}{3}e$
29 $[29, 29, -w^{3} + 3w^{2} + 3w - 5]$ $\phantom{-}e^{4} - 41e^{2} + 141$
29 $[29, 29, w^{3} - 2w^{2} - 4w]$ $-\frac{2}{9}e^{5} + 9e^{3} - 29e$
47 $[47, 47, -w^{3} + 2w^{2} + 3w - 5]$ $-\frac{4}{9}e^{5} + \frac{55}{3}e^{3} - 67e$
47 $[47, 47, w^{2} - 3w - 2]$ $\phantom{-}e$
61 $[61, 61, -w^{3} + 2w^{2} + 5w - 3]$ $-\frac{14}{27}e^{5} + \frac{64}{3}e^{3} - \frac{233}{3}e$
67 $[67, 67, -w^{3} + w^{2} + 5w - 1]$ $-\frac{11}{27}e^{5} + \frac{50}{3}e^{3} - \frac{167}{3}e$
67 $[67, 67, -2w^{3} + 3w^{2} + 11w - 7]$ $\phantom{-}\frac{16}{27}e^{5} - \frac{73}{3}e^{3} + \frac{256}{3}e$
83 $[83, 83, -2w + 3]$ $\phantom{-}\frac{5}{9}e^{4} - 23e^{2} + 84$
89 $[89, 89, 3w^{3} - 7w^{2} - 9w + 9]$ $-\frac{1}{3}e^{4} + \frac{40}{3}e^{2} - 48$
97 $[97, 97, w^{3} - w^{2} - 4w - 3]$ $-\frac{23}{27}e^{5} + 35e^{3} - \frac{368}{3}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w + 1]$ $-1$