Properties

Label 4.4.14197.1-9.1-a
Base field 4.4.14197.1
Weight $[2, 2, 2, 2]$
Level norm $9$
Level $[9, 3, w^{3} - 5w - 2]$
Dimension $5$
CM no
Base change no

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Base field 4.4.14197.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[9, 3, w^{3} - 5w - 2]$
Dimension: $5$
CM: no
Base change: no
Newspace dimension: $10$

Hecke eigenvalues ($q$-expansion)

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

\(x^{5} - 7x^{4} + 5x^{3} + 50x^{2} - 113x + 68\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
7 $[7, 7, w - 1]$ $\phantom{-}e$
9 $[9, 3, w^{3} - 5w - 2]$ $-1$
9 $[9, 3, w^{3} - w^{2} - 4w]$ $\phantom{-}6e^{4} - 33e^{3} - 19e^{2} + 270e - 274$
13 $[13, 13, -w + 2]$ $-6e^{4} + 33e^{3} + 19e^{2} - 270e + 278$
16 $[16, 2, 2]$ $\phantom{-}e^{4} - 5e^{3} - 5e^{2} + 39e - 31$
17 $[17, 17, w^{3} - w^{2} - 5w]$ $-e^{4} + 5e^{3} + 5e^{2} - 40e + 34$
19 $[19, 19, -w^{3} + w^{2} + 6w]$ $-7e^{4} + 39e^{3} + 20e^{2} - 319e + 336$
23 $[23, 23, -w^{2} + w + 3]$ $-7e^{4} + 39e^{3} + 21e^{2} - 321e + 332$
29 $[29, 29, w^{3} - 5w]$ $\phantom{-}16e^{4} - 89e^{3} - 48e^{2} + 731e - 754$
31 $[31, 31, w^{3} - 6w - 1]$ $-7e^{4} + 39e^{3} + 21e^{2} - 320e + 332$
31 $[31, 31, w^{2} - 2]$ $-12e^{4} + 67e^{3} + 35e^{2} - 552e + 576$
37 $[37, 37, -w - 3]$ $\phantom{-}e^{4} - 5e^{3} - 4e^{2} + 40e - 42$
37 $[37, 37, w^{3} - 4w - 1]$ $\phantom{-}11e^{4} - 61e^{3} - 34e^{2} + 500e - 510$
37 $[37, 37, w^{3} - 7w - 4]$ $\phantom{-}13e^{4} - 73e^{3} - 37e^{2} + 603e - 630$
37 $[37, 37, w^{2} - 3]$ $\phantom{-}8e^{4} - 45e^{3} - 23e^{2} + 370e - 378$
43 $[43, 43, w^{2} + w - 3]$ $-8e^{4} + 45e^{3} + 22e^{2} - 371e + 392$
43 $[43, 43, w^{3} - w^{2} - 5w - 1]$ $-13e^{4} + 73e^{3} + 37e^{2} - 600e + 628$
47 $[47, 47, -w^{3} + w^{2} + 5w - 4]$ $-10e^{4} + 54e^{3} + 35e^{2} - 443e + 444$
53 $[53, 53, w^{3} - 6w]$ $-15e^{4} + 83e^{3} + 47e^{2} - 681e + 698$
61 $[61, 61, w^{3} - w^{2} - 7w - 2]$ $\phantom{-}2e^{4} - 11e^{3} - 7e^{2} + 93e - 94$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$9$ $[9, 3, w^{3} - 5w - 2]$ $1$