Properties

Label 3.3.985.1-7.1-b
Base field 3.3.985.1
Weight $[2, 2, 2]$
Level norm $7$
Level $[7, 7, -w + 2]$
Dimension $5$
CM no
Base change no

Related objects

Downloads

Learn more

Base field 3.3.985.1

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

Form

Weight: $[2, 2, 2]$
Level: $[7, 7, -w + 2]$
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:

\(x^{5} + 4x^{4} - 11x^{3} - 38x^{2} + 28x + 24\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, w + 1]$ $\phantom{-}e$
5 $[5, 5, w - 1]$ $-\frac{1}{8}e^{4} - \frac{1}{4}e^{3} + \frac{11}{8}e^{2} + \frac{3}{2}e - \frac{5}{2}$
7 $[7, 7, -w + 2]$ $-1$
8 $[8, 2, 2]$ $\phantom{-}\frac{1}{8}e^{4} + \frac{1}{4}e^{3} - \frac{15}{8}e^{2} - 3e + \frac{9}{2}$
11 $[11, 11, -w^{2} + 2w + 2]$ $\phantom{-}\frac{1}{2}e^{3} + e^{2} - \frac{9}{2}e - 3$
17 $[17, 17, -w - 3]$ $\phantom{-}e - 2$
17 $[17, 17, -w^{2} + 2w + 1]$ $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e - 5$
17 $[17, 17, -w^{2} + w + 4]$ $-4$
23 $[23, 23, -w^{2} + 3]$ $-\frac{1}{2}e^{3} + \frac{11}{2}e - 5$
27 $[27, 3, -3]$ $\phantom{-}\frac{1}{8}e^{4} - \frac{1}{4}e^{3} - \frac{15}{8}e^{2} + \frac{9}{2}e + \frac{5}{2}$
29 $[29, 29, w^{2} - w - 8]$ $-\frac{1}{4}e^{4} - \frac{3}{2}e^{3} + \frac{7}{4}e^{2} + 12e - 3$
29 $[29, 29, w^{2} - w - 3]$ $\phantom{-}\frac{1}{4}e^{4} + \frac{1}{2}e^{3} - \frac{13}{4}e^{2} - \frac{5}{2}e + 6$
29 $[29, 29, w^{2} - w - 1]$ $-\frac{1}{8}e^{4} - \frac{3}{4}e^{3} - \frac{1}{8}e^{2} + \frac{9}{2}e + \frac{11}{2}$
31 $[31, 31, w^{2} - 2]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{11}{2}e + 5$
37 $[37, 37, 2w - 5]$ $\phantom{-}\frac{1}{4}e^{4} + e^{3} - \frac{13}{4}e^{2} - 10e + 5$
43 $[43, 43, w^{2} - 2w - 5]$ $-\frac{1}{8}e^{4} + \frac{1}{4}e^{3} + \frac{15}{8}e^{2} - \frac{5}{2}e + \frac{3}{2}$
47 $[47, 47, w^{2} - 3w - 2]$ $-\frac{1}{2}e^{4} - e^{3} + \frac{11}{2}e^{2} + 4e - 10$
49 $[49, 7, w^{2} + w - 4]$ $-\frac{1}{8}e^{4} - \frac{3}{4}e^{3} + \frac{3}{8}e^{2} + 4e - \frac{3}{2}$
53 $[53, 53, w^{2} - 2w - 6]$ $\phantom{-}\frac{1}{4}e^{4} + \frac{1}{2}e^{3} - \frac{7}{4}e^{2} - 2e - 9$
71 $[71, 71, w - 5]$ $\phantom{-}\frac{1}{8}e^{4} + \frac{3}{4}e^{3} + \frac{1}{8}e^{2} - \frac{9}{2}e - \frac{11}{2}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$7$ $[7, 7, -w + 2]$ $1$