Properties

Base field 6.6.300125.1
Weight [2, 2, 2, 2, 2, 2]
Level norm 49
Level $[49, 7, -5w^{5} + w^{4} + 36w^{3} + 19w^{2} - 22w - 6]$
Label 6.6.300125.1-49.1-b
Dimension 3
CM no
Base change yes

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Base field 6.6.300125.1

Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 7x^{4} + 2x^{3} + 7x^{2} - 2x - 1\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2, 2, 2, 2, 2]
Level $[49, 7, -5w^{5} + w^{4} + 36w^{3} + 19w^{2} - 22w - 6]$
Label 6.6.300125.1-49.1-b
Dimension 3
Is CM no
Is base change yes
Parent newspace dimension 4

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} \) \(\mathstrut -\mathstrut 21x \) \(\mathstrut +\mathstrut 7\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
29 $[29, 29, -9w^{5} + 3w^{4} + 64w^{3} + 26w^{2} - 40w - 10]$ $\phantom{-}\frac{1}{3}e^{2} - \frac{1}{3}e - \frac{14}{3}$
29 $[29, 29, w^{5} - 7w^{3} - 5w^{2} + 2w + 2]$ $\phantom{-}e$
29 $[29, 29, w^{4} - w^{3} - 6w^{2} + 2]$ $\phantom{-}e$
29 $[29, 29, 5w^{5} - w^{4} - 36w^{3} - 19w^{2} + 21w + 9]$ $-\frac{1}{3}e^{2} - \frac{2}{3}e + \frac{14}{3}$
29 $[29, 29, -w^{5} + w^{4} + 7w^{3} - 2w^{2} - 6w + 1]$ $\phantom{-}\frac{1}{3}e^{2} - \frac{1}{3}e - \frac{14}{3}$
29 $[29, 29, 2w^{5} - 15w^{3} - 10w^{2} + 11w + 5]$ $-\frac{1}{3}e^{2} - \frac{2}{3}e + \frac{14}{3}$
41 $[41, 41, 5w^{5} - w^{4} - 36w^{3} - 18w^{2} + 21w + 5]$ $-\frac{2}{3}e^{2} - \frac{4}{3}e + \frac{22}{3}$
41 $[41, 41, -5w^{5} + 2w^{4} + 36w^{3} + 11w^{2} - 25w - 2]$ $\phantom{-}2e - 2$
41 $[41, 41, 6w^{5} - w^{4} - 44w^{3} - 23w^{2} + 30w + 8]$ $\phantom{-}\frac{2}{3}e^{2} - \frac{2}{3}e - \frac{34}{3}$
41 $[41, 41, 13w^{5} - 4w^{4} - 93w^{3} - 39w^{2} + 59w + 16]$ $\phantom{-}2e - 2$
41 $[41, 41, -4w^{5} + 30w^{3} + 19w^{2} - 19w - 8]$ $-\frac{2}{3}e^{2} - \frac{4}{3}e + \frac{22}{3}$
41 $[41, 41, w^{5} - 7w^{3} - 6w^{2} + 2w + 3]$ $\phantom{-}\frac{2}{3}e^{2} - \frac{2}{3}e - \frac{34}{3}$
49 $[49, 7, -5w^{5} + w^{4} + 36w^{3} + 19w^{2} - 22w - 6]$ $-1$
64 $[64, 2, -2]$ $\phantom{-}12$
71 $[71, 71, -8w^{5} + w^{4} + 58w^{3} + 34w^{2} - 34w - 16]$ $-2e + 5$
71 $[71, 71, -6w^{5} + 2w^{4} + 42w^{3} + 18w^{2} - 23w - 6]$ $\phantom{-}\frac{2}{3}e^{2} + \frac{4}{3}e - \frac{13}{3}$
71 $[71, 71, -8w^{5} + 2w^{4} + 58w^{3} + 27w^{2} - 38w - 10]$ $-\frac{2}{3}e^{2} + \frac{2}{3}e + \frac{43}{3}$
71 $[71, 71, 4w^{5} - 30w^{3} - 19w^{2} + 20w + 8]$ $-\frac{2}{3}e^{2} + \frac{2}{3}e + \frac{43}{3}$
71 $[71, 71, -10w^{5} + 3w^{4} + 72w^{3} + 30w^{2} - 48w - 10]$ $-2e + 5$
71 $[71, 71, -8w^{5} + 2w^{4} + 58w^{3} + 26w^{2} - 37w - 8]$ $\phantom{-}\frac{2}{3}e^{2} + \frac{4}{3}e - \frac{13}{3}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
49 $[49, 7, -5w^{5} + w^{4} + 36w^{3} + 19w^{2} - 22w - 6]$ $1$