Properties

Base field 6.6.434581.1
Weight [2, 2, 2, 2, 2, 2]
Level norm 49
Level $[49, 7, w^{5} - 4w^{4} + 11w^{2} - 3w - 4]$
Label 6.6.434581.1-49.1-c
Dimension 6
CM no
Base change yes

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Base field 6.6.434581.1

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

Form

Weight [2, 2, 2, 2, 2, 2]
Level $[49, 7, w^{5} - 4w^{4} + 11w^{2} - 3w - 4]$
Label 6.6.434581.1-49.1-c
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:
\(x^{6} \) \(\mathstrut -\mathstrut 33x^{4} \) \(\mathstrut +\mathstrut 16x^{3} \) \(\mathstrut +\mathstrut 292x^{2} \) \(\mathstrut -\mathstrut 248x \) \(\mathstrut -\mathstrut 272\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
13 $[13, 13, -w^{5} + 3w^{4} + 2w^{3} - 9w^{2} + w + 4]$ $\phantom{-}e$
13 $[13, 13, -w^{2} + w + 2]$ $\phantom{-}e$
27 $[27, 3, 2w^{5} - 4w^{4} - 7w^{3} + 9w^{2} + 4w - 2]$ $\phantom{-}\frac{1}{10}e^{5} + \frac{3}{10}e^{4} - \frac{19}{10}e^{3} - \frac{51}{10}e^{2} + \frac{32}{5}e + \frac{72}{5}$
27 $[27, 3, -2w^{5} + 5w^{4} + 5w^{3} - 12w^{2} - w + 5]$ $\phantom{-}\frac{1}{10}e^{5} + \frac{3}{10}e^{4} - \frac{19}{10}e^{3} - \frac{51}{10}e^{2} + \frac{32}{5}e + \frac{72}{5}$
29 $[29, 29, w^{3} - 2w^{2} - 2w + 3]$ $\phantom{-}\frac{1}{40}e^{5} + \frac{1}{5}e^{4} - \frac{29}{40}e^{3} - \frac{17}{5}e^{2} + \frac{38}{5}e + \frac{28}{5}$
29 $[29, 29, 2w^{5} - 4w^{4} - 7w^{3} + 8w^{2} + 4w - 2]$ $\phantom{-}\frac{1}{40}e^{5} + \frac{1}{5}e^{4} - \frac{29}{40}e^{3} - \frac{17}{5}e^{2} + \frac{38}{5}e + \frac{28}{5}$
43 $[43, 43, -w^{5} + 3w^{4} + w^{3} - 6w^{2} + 3w + 1]$ $-\frac{3}{8}e^{5} - \frac{3}{2}e^{4} + \frac{59}{8}e^{3} + \frac{47}{2}e^{2} - \frac{69}{2}e - 33$
43 $[43, 43, -w^{4} + w^{3} + 5w^{2} - 4]$ $-\frac{3}{8}e^{5} - \frac{3}{2}e^{4} + \frac{59}{8}e^{3} + \frac{47}{2}e^{2} - \frac{69}{2}e - 33$
49 $[49, 7, w^{5} - 4w^{4} + 11w^{2} - 3w - 4]$ $-1$
64 $[64, 2, -2]$ $-\frac{1}{5}e^{5} - \frac{3}{5}e^{4} + \frac{19}{5}e^{3} + \frac{46}{5}e^{2} - \frac{74}{5}e - \frac{44}{5}$
71 $[71, 71, 2w^{5} - 6w^{4} - 4w^{3} + 17w^{2} - w - 6]$ $\phantom{-}\frac{3}{8}e^{5} + \frac{5}{4}e^{4} - \frac{55}{8}e^{3} - \frac{73}{4}e^{2} + 24e + 24$
71 $[71, 71, 2w^{4} - 4w^{3} - 6w^{2} + 7w + 2]$ $-\frac{7}{40}e^{5} - \frac{3}{20}e^{4} + \frac{143}{40}e^{3} + \frac{31}{20}e^{2} - \frac{137}{10}e - \frac{16}{5}$
71 $[71, 71, -w^{5} + 3w^{4} + 2w^{3} - 7w^{2} - w]$ $\phantom{-}\frac{3}{8}e^{5} + \frac{5}{4}e^{4} - \frac{55}{8}e^{3} - \frac{73}{4}e^{2} + 24e + 24$
71 $[71, 71, -2w^{5} + 5w^{4} + 6w^{3} - 14w^{2} - 3w + 5]$ $-\frac{7}{40}e^{5} - \frac{3}{20}e^{4} + \frac{143}{40}e^{3} + \frac{31}{20}e^{2} - \frac{137}{10}e - \frac{16}{5}$
83 $[83, 83, -3w^{5} + 7w^{4} + 9w^{3} - 17w^{2} - 5w + 5]$ $-\frac{2}{5}e^{5} - \frac{6}{5}e^{4} + \frac{43}{5}e^{3} + \frac{92}{5}e^{2} - \frac{213}{5}e - \frac{128}{5}$
83 $[83, 83, 3w^{5} - 6w^{4} - 10w^{3} + 12w^{2} + 5w - 2]$ $\phantom{-}\frac{1}{10}e^{5} + \frac{3}{10}e^{4} - \frac{29}{10}e^{3} - \frac{51}{10}e^{2} + \frac{107}{5}e + \frac{22}{5}$
83 $[83, 83, -2w^{5} + 5w^{4} + 5w^{3} - 11w^{2} - 3w + 3]$ $-\frac{2}{5}e^{5} - \frac{6}{5}e^{4} + \frac{43}{5}e^{3} + \frac{92}{5}e^{2} - \frac{213}{5}e - \frac{128}{5}$
83 $[83, 83, 3w^{5} - 7w^{4} - 8w^{3} + 15w^{2} + 2w - 4]$ $\phantom{-}\frac{1}{10}e^{5} + \frac{3}{10}e^{4} - \frac{29}{10}e^{3} - \frac{51}{10}e^{2} + \frac{107}{5}e + \frac{22}{5}$
97 $[97, 97, -3w^{5} + 6w^{4} + 10w^{3} - 12w^{2} - 5w + 3]$ $\phantom{-}\frac{1}{10}e^{5} + \frac{4}{5}e^{4} - \frac{19}{10}e^{3} - \frac{68}{5}e^{2} + \frac{57}{5}e + \frac{112}{5}$
97 $[97, 97, w^{5} - 2w^{4} - 4w^{3} + 5w^{2} + 5w - 3]$ $-\frac{3}{20}e^{5} - \frac{7}{10}e^{4} + \frac{67}{20}e^{3} + \frac{99}{10}e^{2} - \frac{108}{5}e + \frac{12}{5}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
49 $[49, 7, w^{5} - 4w^{4} + 11w^{2} - 3w - 4]$ $1$