Properties

Base field 4.4.4205.1
Weight [2, 2, 2, 2]
Level norm 49
Level $[49, 49, -2w^{3} + 3w^{2} + 7w - 1]$
Label 4.4.4205.1-49.3-e
Dimension 6
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 $[49, 49, -2w^{3} + 3w^{2} + 7w - 1]$
Label 4.4.4205.1-49.3-e
Dimension 6
Is CM no
Is base change no
Parent newspace dimension 10

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} \) \(\mathstrut -\mathstrut 34x^{4} \) \(\mathstrut +\mathstrut 240x^{2} \) \(\mathstrut -\mathstrut 32\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -w^{3} + w^{2} + 5w]$ $-\frac{1}{40}e^{4} + \frac{9}{20}e^{2} + \frac{6}{5}$
7 $[7, 7, -w^{3} + 2w^{2} + 3w - 3]$ $\phantom{-}e$
7 $[7, 7, w^{3} - 2w^{2} - 3w]$ $\phantom{-}0$
13 $[13, 13, -w^{2} + w + 3]$ $\phantom{-}\frac{1}{40}e^{5} - \frac{7}{10}e^{3} + \frac{33}{10}e$
13 $[13, 13, -w^{2} + w + 2]$ $\phantom{-}\frac{1}{20}e^{4} - \frac{7}{5}e^{2} + \frac{33}{5}$
16 $[16, 2, 2]$ $\phantom{-}\frac{1}{40}e^{4} - \frac{19}{20}e^{2} + \frac{24}{5}$
23 $[23, 23, -w^{2} + 3w + 1]$ $-\frac{1}{10}e^{5} + \frac{33}{10}e^{3} - \frac{106}{5}e$
23 $[23, 23, -2w^{3} + 3w^{2} + 9w - 2]$ $-\frac{1}{20}e^{4} + \frac{9}{10}e^{2} + \frac{2}{5}$
25 $[25, 5, w^{3} - 2w^{2} - 2w + 2]$ $-\frac{1}{16}e^{5} + \frac{17}{8}e^{3} - 15e$
49 $[49, 7, w^{3} - w^{2} - 6w - 1]$ $\phantom{-}\frac{13}{80}e^{5} - \frac{207}{40}e^{3} + \frac{327}{10}e$
53 $[53, 53, 2w^{3} - 2w^{2} - 8w - 3]$ $\phantom{-}\frac{1}{80}e^{5} - \frac{9}{40}e^{3} + \frac{2}{5}e$
53 $[53, 53, 2w^{3} - 2w^{2} - 8w - 1]$ $\phantom{-}\frac{1}{10}e^{5} - \frac{71}{20}e^{3} + \frac{277}{10}e$
67 $[67, 67, 2w^{3} - 4w^{2} - 7w + 2]$ $\phantom{-}\frac{1}{20}e^{5} - \frac{7}{5}e^{3} + \frac{23}{5}e$
67 $[67, 67, -2w^{3} + 4w^{2} + 6w - 1]$ $-\frac{1}{20}e^{4} + \frac{9}{10}e^{2} + \frac{12}{5}$
81 $[81, 3, -3]$ $-\frac{1}{40}e^{5} + \frac{7}{10}e^{3} - \frac{53}{10}e$
83 $[83, 83, 2w^{3} - 3w^{2} - 6w - 1]$ $\phantom{-}\frac{1}{8}e^{5} - \frac{17}{4}e^{3} + 33e$
83 $[83, 83, 3w^{3} - 4w^{2} - 12w + 1]$ $-\frac{3}{20}e^{4} + \frac{47}{10}e^{2} - \frac{84}{5}$
103 $[103, 103, 3w^{3} - 4w^{2} - 12w - 1]$ $-\frac{3}{20}e^{5} + \frac{26}{5}e^{3} - \frac{179}{5}e$
103 $[103, 103, 2w^{3} - 3w^{2} - 6w + 1]$ $\phantom{-}\frac{1}{20}e^{4} - \frac{9}{10}e^{2} + \frac{8}{5}$
107 $[107, 107, w^{3} - w^{2} - 3w - 3]$ $\phantom{-}\frac{3}{20}e^{5} - \frac{47}{10}e^{3} + \frac{134}{5}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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