Properties

Base field 4.4.9909.1
Weight [2, 2, 2, 2]
Level norm 7
Level $[7, 7, w^{3} - w^{2} - 4w + 1]$
Label 4.4.9909.1-7.1-a
Dimension 6
CM no
Base change no

Related objects

Downloads

Learn more about

Base field 4.4.9909.1

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

Form

Weight [2, 2, 2, 2]
Level $[7, 7, w^{3} - w^{2} - 4w + 1]$
Label 4.4.9909.1-7.1-a
Dimension 6
Is CM no
Is base change no
Parent newspace dimension 6

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} \) \(\mathstrut -\mathstrut 28x^{4} \) \(\mathstrut +\mathstrut 213x^{2} \) \(\mathstrut -\mathstrut 236\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}\frac{2}{5}e^{4} - \frac{29}{5}e^{2} + \frac{32}{5}$
5 $[5, 5, w - 1]$ $\phantom{-}e$
7 $[7, 7, w^{3} - w^{2} - 4w + 1]$ $-1$
11 $[11, 11, -w^{2} + w + 2]$ $-\frac{1}{5}e^{5} + \frac{17}{5}e^{3} - \frac{46}{5}e$
13 $[13, 13, -w^{3} + w^{2} + 3w - 1]$ $-\frac{1}{5}e^{4} + \frac{12}{5}e^{2} + \frac{14}{5}$
16 $[16, 2, 2]$ $\phantom{-}\frac{1}{5}e^{4} - \frac{17}{5}e^{2} + \frac{41}{5}$
17 $[17, 17, -w^{3} + 5w + 2]$ $-\frac{1}{5}e^{5} + \frac{12}{5}e^{3} + \frac{19}{5}e$
29 $[29, 29, -w^{2} + w + 1]$ $\phantom{-}\frac{1}{5}e^{5} - \frac{12}{5}e^{3} - \frac{19}{5}e$
37 $[37, 37, -w^{3} + 2w^{2} + 4w - 4]$ $\phantom{-}\frac{6}{5}e^{4} - \frac{92}{5}e^{2} + \frac{166}{5}$
41 $[41, 41, -w^{3} + w^{2} + 5w + 1]$ $-\frac{1}{5}e^{5} + \frac{17}{5}e^{3} - \frac{41}{5}e$
41 $[41, 41, w^{2} - 5]$ $-\frac{1}{5}e^{5} + \frac{17}{5}e^{3} - \frac{41}{5}e$
47 $[47, 47, w^{3} - w^{2} - 5w - 2]$ $-\frac{2}{5}e^{5} + \frac{29}{5}e^{3} - \frac{32}{5}e$
47 $[47, 47, -w^{3} + 2w^{2} + 4w - 1]$ $-\frac{2}{5}e^{5} + \frac{29}{5}e^{3} - \frac{32}{5}e$
53 $[53, 53, w^{3} - 4w - 4]$ $\phantom{-}e$
53 $[53, 53, 2w^{3} - 2w^{2} - 9w + 1]$ $\phantom{-}e$
61 $[61, 61, -w^{3} + w^{2} + 6w - 2]$ $\phantom{-}\frac{6}{5}e^{4} - \frac{92}{5}e^{2} + \frac{126}{5}$
71 $[71, 71, w^{3} - w^{2} - 6w - 2]$ $\phantom{-}\frac{2}{5}e^{5} - \frac{34}{5}e^{3} + \frac{92}{5}e$
103 $[103, 103, 2w^{3} - 2w^{2} - 8w + 1]$ $\phantom{-}\frac{7}{5}e^{4} - \frac{104}{5}e^{2} + \frac{152}{5}$
103 $[103, 103, -3w^{3} + 3w^{2} + 13w - 5]$ $\phantom{-}\frac{6}{5}e^{4} - \frac{87}{5}e^{2} + \frac{76}{5}$
109 $[109, 109, 2w^{3} - w^{2} - 8w - 4]$ $-\frac{4}{5}e^{4} + \frac{63}{5}e^{2} - \frac{94}{5}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
7 $[7, 7, w^{3} - w^{2} - 4w + 1]$ $1$