Properties

Label 3.3.1396.1-10.3-c
Base field 3.3.1396.1
Weight $[2, 2, 2]$
Level norm $10$
Level $[10, 10, w^{2} - 3w]$
Dimension $4$
CM no
Base change no

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Base field 3.3.1396.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 7x + 5\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[10, 10, w^{2} - 3w]$
Dimension: $4$
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:

\(x^{4} - 12x^{2} - 4x + 16\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w + 1]$ $-1$
5 $[5, 5, w]$ $-1$
5 $[5, 5, -w^{2} + 6]$ $\phantom{-}e$
5 $[5, 5, -w + 2]$ $-\frac{1}{4}e^{3} + 2e + 2$
7 $[7, 7, w + 2]$ $\phantom{-}\frac{1}{4}e^{3} - \frac{1}{2}e^{2} - 2e + 2$
11 $[11, 11, 2w - 1]$ $\phantom{-}\frac{1}{4}e^{3} + \frac{1}{2}e^{2} - 3e - 4$
13 $[13, 13, w^{2} + w - 3]$ $\phantom{-}\frac{1}{4}e^{3} - \frac{1}{2}e^{2} - 3e$
27 $[27, 3, 3]$ $-\frac{1}{4}e^{3} + 2e^{2} + 2e - 12$
41 $[41, 41, w^{2} - w - 1]$ $-\frac{1}{4}e^{3} + \frac{1}{2}e^{2} + e - 6$
41 $[41, 41, 3w^{2} - w - 23]$ $-e^{2} + 3e + 6$
41 $[41, 41, w^{2} - 2]$ $-\frac{1}{2}e^{3} - e^{2} + 5e + 4$
43 $[43, 43, w^{2} - w - 3]$ $\phantom{-}\frac{1}{2}e^{3} - e^{2} - 5e$
47 $[47, 47, -w - 4]$ $\phantom{-}\frac{1}{2}e^{3} - e^{2} - 4e + 8$
49 $[49, 7, 3w^{2} - 2w - 24]$ $-\frac{1}{2}e^{3} + 5e + 4$
53 $[53, 53, 2w^{2} - w - 12]$ $-e^{3} + e^{2} + 9e - 2$
59 $[59, 59, w^{2} - 2w - 4]$ $-\frac{1}{2}e^{3} + 2e^{2} + e - 14$
61 $[61, 61, -w^{2} + 3w - 3]$ $\phantom{-}\frac{3}{4}e^{3} - e^{2} - 8e - 2$
71 $[71, 71, w^{2} + w - 7]$ $\phantom{-}\frac{3}{4}e^{3} - 11e$
79 $[79, 79, 2w + 3]$ $\phantom{-}e^{3} - 7e - 8$
89 $[89, 89, 2w - 7]$ $-\frac{5}{4}e^{3} + e^{2} + 12e - 2$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, -w + 1]$ $1$
$5$ $[5, 5, w]$ $1$