Properties

Base field 4.4.4205.1
Weight [2, 2, 2, 2]
Level norm 49
Level $[49, 7, w^{3} - w^{2} - 6w - 1]$
Label 4.4.4205.1-49.1-c
Dimension 4
CM no
Base change no

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Base field 4.4.4205.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} - x + 1\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[49, 7, w^{3} - w^{2} - 6w - 1]$
Label 4.4.4205.1-49.1-c
Dimension 4
Is CM no
Is base change no
Parent newspace dimension 13

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} \) \(\mathstrut +\mathstrut 6x^{3} \) \(\mathstrut -\mathstrut 6x^{2} \) \(\mathstrut -\mathstrut 80x \) \(\mathstrut -\mathstrut 100\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -w^{3} + w^{2} + 5w]$ $\phantom{-}\frac{1}{5}e^{3} + \frac{1}{5}e^{2} - \frac{16}{5}e - 5$
7 $[7, 7, -w^{3} + 2w^{2} + 3w - 3]$ $\phantom{-}e$
7 $[7, 7, w^{3} - 2w^{2} - 3w]$ $-\frac{1}{5}e^{3} - \frac{1}{5}e^{2} + \frac{11}{5}e$
13 $[13, 13, -w^{2} + w + 3]$ $\phantom{-}\frac{2}{5}e^{3} + \frac{7}{5}e^{2} - \frac{27}{5}e - 15$
13 $[13, 13, -w^{2} + w + 2]$ $-\frac{3}{5}e^{3} - \frac{8}{5}e^{2} + \frac{43}{5}e + 21$
16 $[16, 2, 2]$ $\phantom{-}\frac{1}{5}e^{3} + \frac{1}{5}e^{2} - \frac{16}{5}e - 3$
23 $[23, 23, -w^{2} + 3w + 1]$ $-\frac{3}{5}e^{3} - \frac{8}{5}e^{2} + \frac{38}{5}e + 14$
23 $[23, 23, -2w^{3} + 3w^{2} + 9w - 2]$ $\phantom{-}\frac{3}{5}e^{3} + \frac{8}{5}e^{2} - \frac{38}{5}e - 22$
25 $[25, 5, w^{3} - 2w^{2} - 2w + 2]$ $\phantom{-}\frac{2}{5}e^{3} + \frac{2}{5}e^{2} - \frac{32}{5}e - 9$
49 $[49, 7, w^{3} - w^{2} - 6w - 1]$ $\phantom{-}1$
53 $[53, 53, 2w^{3} - 2w^{2} - 8w - 3]$ $-e^{3} - 3e^{2} + 12e + 35$
53 $[53, 53, 2w^{3} - 2w^{2} - 8w - 1]$ $\phantom{-}\frac{7}{5}e^{3} + \frac{17}{5}e^{2} - \frac{92}{5}e - 37$
67 $[67, 67, 2w^{3} - 4w^{2} - 7w + 2]$ $-\frac{3}{5}e^{3} - \frac{8}{5}e^{2} + \frac{53}{5}e + 22$
67 $[67, 67, -2w^{3} + 4w^{2} + 6w - 1]$ $\phantom{-}e^{2} - e - 14$
81 $[81, 3, -3]$ $-\frac{4}{5}e^{3} - \frac{4}{5}e^{2} + \frac{64}{5}e + 15$
83 $[83, 83, 2w^{3} - 3w^{2} - 6w - 1]$ $\phantom{-}e^{3} + 2e^{2} - 14e - 26$
83 $[83, 83, 3w^{3} - 4w^{2} - 12w + 1]$ $-\frac{1}{5}e^{3} - \frac{6}{5}e^{2} + \frac{6}{5}e + 10$
103 $[103, 103, 3w^{3} - 4w^{2} - 12w - 1]$ $\phantom{-}\frac{1}{5}e^{3} + \frac{6}{5}e^{2} - \frac{31}{5}e - 22$
103 $[103, 103, 2w^{3} - 3w^{2} - 6w + 1]$ $-e^{2} + 3e + 14$
107 $[107, 107, w^{3} - w^{2} - 3w - 3]$ $\phantom{-}\frac{2}{5}e^{3} + \frac{7}{5}e^{2} - \frac{27}{5}e - 12$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
49 $[49, 7, w^{3} - w^{2} - 6w - 1]$ $-1$