Properties

 Base field 4.4.18625.1 Weight [2, 2, 2, 2] Level norm 1 Level $[1, 1, 1]$ Label 4.4.18625.1-1.1-b Dimension 6 CM no Base change yes

Related objects

• L-function not available

Base field 4.4.18625.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 14x^{2} + 9x + 41$$; narrow class number $$2$$ and class number $$1$$.

Form

 Weight [2, 2, 2, 2] Level $[1, 1, 1]$ Label 4.4.18625.1-1.1-b Dimension 6 Is CM no Is base change yes Parent newspace dimension 8

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{6}$$ $$\mathstrut -\mathstrut 17x^{4}$$ $$\mathstrut +\mathstrut 56x^{2}$$ $$\mathstrut -\mathstrut 4$$
Norm Prime Eigenvalue
4 $[4, 2, \frac{1}{6}w^{3} - \frac{7}{3}w - \frac{17}{6}]$ $\phantom{-}e$
4 $[4, 2, w - 3]$ $\phantom{-}e$
5 $[5, 5, -\frac{1}{6}w^{3} + w^{2} + \frac{1}{3}w - \frac{25}{6}]$ $\phantom{-}\frac{1}{8}e^{5} - \frac{19}{8}e^{3} + \frac{39}{4}e$
9 $[9, 3, \frac{1}{6}w^{3} - \frac{7}{3}w + \frac{13}{6}]$ $\phantom{-}\frac{3}{8}e^{5} - \frac{49}{8}e^{3} + \frac{73}{4}e$
9 $[9, 3, -w - 2]$ $\phantom{-}\frac{3}{8}e^{5} - \frac{49}{8}e^{3} + \frac{73}{4}e$
11 $[11, 11, -\frac{1}{6}w^{3} + \frac{7}{3}w + \frac{11}{6}]$ $-\frac{1}{8}e^{4} + \frac{11}{8}e^{2} - \frac{11}{4}$
11 $[11, 11, -w + 2]$ $-\frac{1}{8}e^{4} + \frac{11}{8}e^{2} - \frac{11}{4}$
41 $[41, 41, -w]$ $\phantom{-}\frac{1}{8}e^{4} - \frac{19}{8}e^{2} + \frac{15}{4}$
41 $[41, 41, \frac{1}{6}w^{3} - \frac{7}{3}w + \frac{1}{6}]$ $\phantom{-}\frac{1}{8}e^{4} - \frac{19}{8}e^{2} + \frac{15}{4}$
59 $[59, 59, -\frac{1}{6}w^{3} + \frac{1}{3}w + \frac{23}{6}]$ $-\frac{3}{4}e^{5} + \frac{53}{4}e^{3} - \frac{91}{2}e$
59 $[59, 59, -\frac{1}{3}w^{3} + \frac{11}{3}w + \frac{11}{3}]$ $-\frac{3}{4}e^{5} + \frac{53}{4}e^{3} - \frac{91}{2}e$
61 $[61, 61, -\frac{5}{3}w^{3} - 3w^{2} + \frac{46}{3}w + \frac{79}{3}]$ $-\frac{3}{8}e^{4} + \frac{41}{8}e^{2} - \frac{29}{4}$
61 $[61, 61, \frac{5}{6}w^{3} + w^{2} - \frac{23}{3}w - \frac{55}{6}]$ $-\frac{3}{8}e^{4} + \frac{41}{8}e^{2} - \frac{29}{4}$
61 $[61, 61, w^{3} + 2w^{2} - 9w - 17]$ $\phantom{-}\frac{1}{8}e^{4} - \frac{11}{8}e^{2} - \frac{5}{4}$
61 $[61, 61, -\frac{1}{6}w^{3} + \frac{10}{3}w + \frac{35}{6}]$ $\phantom{-}\frac{1}{8}e^{4} - \frac{11}{8}e^{2} - \frac{5}{4}$
71 $[71, 71, -\frac{1}{2}w^{3} + 2w^{2} + 4w - \frac{33}{2}]$ $\phantom{-}\frac{3}{8}e^{4} - \frac{49}{8}e^{2} + \frac{41}{4}$
71 $[71, 71, \frac{1}{6}w^{3} - w^{2} - \frac{4}{3}w + \frac{67}{6}]$ $\phantom{-}\frac{3}{8}e^{4} - \frac{49}{8}e^{2} + \frac{41}{4}$
79 $[79, 79, \frac{1}{2}w^{3} - 3w + \frac{1}{2}]$ $\phantom{-}\frac{5}{8}e^{5} - \frac{87}{8}e^{3} + \frac{135}{4}e$
79 $[79, 79, -\frac{2}{3}w^{3} + \frac{19}{3}w - \frac{2}{3}]$ $\phantom{-}\frac{5}{8}e^{5} - \frac{87}{8}e^{3} + \frac{135}{4}e$
89 $[89, 89, \frac{1}{2}w^{3} + w^{2} - 5w - \frac{15}{2}]$ $\phantom{-}\frac{3}{8}e^{5} - \frac{41}{8}e^{3} + \frac{37}{4}e$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

This form has no Atkin-Lehner eigenvalues since the level is $$(1)$$.