Properties

Label 4.4.4400.1-49.2-c
Base field 4.4.4400.1
Weight $[2, 2, 2, 2]$
Level norm $49$
Level $[49,7,w^{3} + w^{2} - 4w - 1]$
Dimension $6$
CM no
Base change no

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Base field 4.4.4400.1

Generator \(w\), with minimal polynomial \(x^{4} - 7x^{2} + 11\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[49,7,w^{3} + w^{2} - 4w - 1]$
Dimension: $6$
CM: no
Base change: no
Newspace dimension: $14$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{6} - 6x^{5} + 3x^{4} + 34x^{3} - 41x^{2} - 30x + 25\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -w^{2} + w + 3]$ $\phantom{-}e$
5 $[5, 5, w + 1]$ $-\frac{4}{5}e^{5} + \frac{14}{5}e^{4} + \frac{23}{5}e^{3} - \frac{76}{5}e^{2} - \frac{36}{5}e + 8$
5 $[5, 5, -w^{3} + w^{2} + 4w - 4]$ $\phantom{-}\frac{2}{5}e^{5} - \frac{7}{5}e^{4} - \frac{14}{5}e^{3} + \frac{43}{5}e^{2} + \frac{28}{5}e - 5$
11 $[11, 11, w]$ $\phantom{-}\frac{4}{5}e^{5} - \frac{14}{5}e^{4} - \frac{18}{5}e^{3} + \frac{71}{5}e^{2} + \frac{6}{5}e - 5$
29 $[29, 29, w^{3} - 2w^{2} - 3w + 7]$ $-\frac{7}{5}e^{5} + \frac{22}{5}e^{4} + \frac{44}{5}e^{3} - \frac{128}{5}e^{2} - \frac{53}{5}e + 16$
29 $[29, 29, -w^{3} - 2w^{2} + 3w + 7]$ $-\frac{1}{5}e^{5} + \frac{6}{5}e^{4} - \frac{3}{5}e^{3} - \frac{34}{5}e^{2} + \frac{26}{5}e + 8$
31 $[31, 31, -w^{3} + w^{2} + 4w - 2]$ $\phantom{-}\frac{7}{5}e^{5} - \frac{22}{5}e^{4} - \frac{44}{5}e^{3} + \frac{118}{5}e^{2} + \frac{68}{5}e - 4$
31 $[31, 31, -w^{3} - w^{2} + 4w + 2]$ $-\frac{6}{5}e^{5} + \frac{21}{5}e^{4} + \frac{32}{5}e^{3} - \frac{114}{5}e^{2} - \frac{44}{5}e + 15$
41 $[41, 41, w^{3} + 2w^{2} - 4w - 6]$ $\phantom{-}\frac{2}{5}e^{5} - \frac{7}{5}e^{4} - \frac{14}{5}e^{3} + \frac{48}{5}e^{2} + \frac{18}{5}e - 4$
41 $[41, 41, w^{3} - 5w + 2]$ $-\frac{4}{5}e^{5} + \frac{14}{5}e^{4} + \frac{23}{5}e^{3} - \frac{86}{5}e^{2} - \frac{16}{5}e + 14$
49 $[49, 7, -w^{3} + w^{2} + 4w - 1]$ $\phantom{-}\frac{6}{5}e^{5} - \frac{21}{5}e^{4} - \frac{32}{5}e^{3} + \frac{104}{5}e^{2} + \frac{44}{5}e - 3$
49 $[49, 7, w^{3} + w^{2} - 4w - 1]$ $-1$
59 $[59, 59, -3w^{2} - w + 10]$ $-\frac{2}{5}e^{5} + \frac{12}{5}e^{4} - \frac{1}{5}e^{3} - \frac{68}{5}e^{2} + \frac{47}{5}e + 6$
59 $[59, 59, -3w^{2} + w + 10]$ $-\frac{2}{5}e^{5} + \frac{2}{5}e^{4} + \frac{24}{5}e^{3} - \frac{3}{5}e^{2} - \frac{88}{5}e + 1$
61 $[61, 61, -2w^{3} + 2w^{2} + 7w - 5]$ $-\frac{9}{5}e^{5} + \frac{24}{5}e^{4} + \frac{68}{5}e^{3} - \frac{136}{5}e^{2} - \frac{131}{5}e + 14$
61 $[61, 61, 2w^{3} + w^{2} - 8w - 6]$ $-\frac{2}{5}e^{5} + \frac{7}{5}e^{4} + \frac{4}{5}e^{3} - \frac{33}{5}e^{2} + \frac{22}{5}e + 8$
71 $[71, 71, 2w^{2} + w - 9]$ $\phantom{-}\frac{11}{5}e^{5} - \frac{36}{5}e^{4} - \frac{57}{5}e^{3} + \frac{184}{5}e^{2} + \frac{54}{5}e - 16$
71 $[71, 71, 2w^{2} - w - 9]$ $\phantom{-}\frac{11}{5}e^{5} - \frac{36}{5}e^{4} - \frac{77}{5}e^{3} + \frac{214}{5}e^{2} + \frac{154}{5}e - 26$
81 $[81, 3, -3]$ $-\frac{6}{5}e^{5} + \frac{26}{5}e^{4} + \frac{22}{5}e^{3} - \frac{139}{5}e^{2} - \frac{14}{5}e + 15$
101 $[101, 101, 2w^{2} - w - 10]$ $-2e^{5} + 6e^{4} + 14e^{3} - 34e^{2} - 27e + 12$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$49$ $[49,7,w^{3} + w^{2} - 4w - 1]$ $1$