Properties

 Label 4.4.4400.1-49.1-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

Related objects

• L-function not available

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:

 $$x^{6} - 6x^{5} + 3x^{4} + 34x^{3} - 41x^{2} - 30x + 25$$
Norm Prime Eigenvalue
4 $[4, 2, -w^{2} + w + 3]$ $\phantom{-}e$
5 $[5, 5, w + 1]$ $\phantom{-}\frac{2}{5}e^{5} - \frac{7}{5}e^{4} - \frac{14}{5}e^{3} + \frac{43}{5}e^{2} + \frac{28}{5}e - 5$
5 $[5, 5, -w^{3} + w^{2} + 4w - 4]$ $-\frac{4}{5}e^{5} + \frac{14}{5}e^{4} + \frac{23}{5}e^{3} - \frac{76}{5}e^{2} - \frac{36}{5}e + 8$
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 $[29, 29, w^{3} - 2w^{2} - 3w + 7]$ $-\frac{1}{5}e^{5} + \frac{6}{5}e^{4} - \frac{3}{5}e^{3} - \frac{34}{5}e^{2} + \frac{26}{5}e + 8$
29 $[29, 29, -w^{3} - 2w^{2} + 3w + 7]$ $-\frac{7}{5}e^{5} + \frac{22}{5}e^{4} + \frac{44}{5}e^{3} - \frac{128}{5}e^{2} - \frac{53}{5}e + 16$
31 $[31, 31, -w^{3} + w^{2} + 4w - 2]$ $-\frac{6}{5}e^{5} + \frac{21}{5}e^{4} + \frac{32}{5}e^{3} - \frac{114}{5}e^{2} - \frac{44}{5}e + 15$
31 $[31, 31, -w^{3} - w^{2} + 4w + 2]$ $\phantom{-}\frac{7}{5}e^{5} - \frac{22}{5}e^{4} - \frac{44}{5}e^{3} + \frac{118}{5}e^{2} + \frac{68}{5}e - 4$
41 $[41, 41, w^{3} + 2w^{2} - 4w - 6]$ $-\frac{4}{5}e^{5} + \frac{14}{5}e^{4} + \frac{23}{5}e^{3} - \frac{86}{5}e^{2} - \frac{16}{5}e + 14$
41 $[41, 41, w^{3} - 5w + 2]$ $\phantom{-}\frac{2}{5}e^{5} - \frac{7}{5}e^{4} - \frac{14}{5}e^{3} + \frac{48}{5}e^{2} + \frac{18}{5}e - 4$
49 $[49, 7, -w^{3} + w^{2} + 4w - 1]$ $-1$
49 $[49, 7, w^{3} + w^{2} - 4w - 1]$ $\phantom{-}\frac{6}{5}e^{5} - \frac{21}{5}e^{4} - \frac{32}{5}e^{3} + \frac{104}{5}e^{2} + \frac{44}{5}e - 3$
59 $[59, 59, -3w^{2} - w + 10]$ $-\frac{2}{5}e^{5} + \frac{2}{5}e^{4} + \frac{24}{5}e^{3} - \frac{3}{5}e^{2} - \frac{88}{5}e + 1$
59 $[59, 59, -3w^{2} + w + 10]$ $-\frac{2}{5}e^{5} + \frac{12}{5}e^{4} - \frac{1}{5}e^{3} - \frac{68}{5}e^{2} + \frac{47}{5}e + 6$
61 $[61, 61, -2w^{3} + 2w^{2} + 7w - 5]$ $-\frac{2}{5}e^{5} + \frac{7}{5}e^{4} + \frac{4}{5}e^{3} - \frac{33}{5}e^{2} + \frac{22}{5}e + 8$
61 $[61, 61, 2w^{3} + w^{2} - 8w - 6]$ $-\frac{9}{5}e^{5} + \frac{24}{5}e^{4} + \frac{68}{5}e^{3} - \frac{136}{5}e^{2} - \frac{131}{5}e + 14$
71 $[71, 71, 2w^{2} + w - 9]$ $\phantom{-}\frac{11}{5}e^{5} - \frac{36}{5}e^{4} - \frac{77}{5}e^{3} + \frac{214}{5}e^{2} + \frac{154}{5}e - 26$
71 $[71, 71, 2w^{2} - w - 9]$ $\phantom{-}\frac{11}{5}e^{5} - \frac{36}{5}e^{4} - \frac{57}{5}e^{3} + \frac{184}{5}e^{2} + \frac{54}{5}e - 16$
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 $[101, 101, 2w^{2} - w - 10]$ $-\frac{6}{5}e^{5} + \frac{21}{5}e^{4} + \frac{32}{5}e^{3} - \frac{99}{5}e^{2} - \frac{54}{5}e$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

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