Base field 4.4.17725.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 12x^{2} + 13x + 41\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[1, 1, 1]$ |
Dimension: | $6$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} + 2x^{5} - 35x^{4} - 46x^{3} + 310x^{2} + 116x - 375\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
9 | $[9, 3, -w^{3} + 3w^{2} + 5w - 15]$ | $\phantom{-}e$ |
9 | $[9, 3, -w^{3} + 8w + 8]$ | $\phantom{-}e$ |
16 | $[16, 2, 2]$ | $-\frac{1}{42}e^{5} + \frac{7}{12}e^{3} - \frac{9}{28}e^{2} - \frac{73}{42}e + \frac{167}{28}$ |
19 | $[19, 19, w + 1]$ | $\phantom{-}\frac{1}{84}e^{5} + \frac{1}{12}e^{4} - \frac{1}{4}e^{3} - \frac{43}{21}e^{2} + \frac{19}{42}e + \frac{165}{28}$ |
19 | $[19, 19, -w^{2} + 6]$ | $-\frac{1}{12}e^{4} + \frac{1}{12}e^{3} + \frac{11}{6}e^{2} - \frac{31}{12}e - \frac{5}{2}$ |
19 | $[19, 19, -w^{2} + 2w + 5]$ | $-\frac{1}{12}e^{4} + \frac{1}{12}e^{3} + \frac{11}{6}e^{2} - \frac{31}{12}e - \frac{5}{2}$ |
19 | $[19, 19, -w + 2]$ | $\phantom{-}\frac{1}{84}e^{5} + \frac{1}{12}e^{4} - \frac{1}{4}e^{3} - \frac{43}{21}e^{2} + \frac{19}{42}e + \frac{165}{28}$ |
25 | $[25, 5, 2w^{2} - 2w - 13]$ | $\phantom{-}\frac{1}{84}e^{5} + \frac{1}{12}e^{4} - \frac{1}{4}e^{3} - \frac{43}{21}e^{2} + \frac{19}{42}e + \frac{333}{28}$ |
29 | $[29, 29, -w^{2} + 9]$ | $\phantom{-}\frac{1}{42}e^{5} - \frac{5}{6}e^{3} + \frac{1}{14}e^{2} + \frac{241}{42}e - \frac{5}{7}$ |
29 | $[29, 29, -w^{2} + 2w + 6]$ | $-\frac{1}{84}e^{5} + \frac{5}{12}e^{3} + \frac{13}{28}e^{2} - \frac{241}{84}e - \frac{65}{14}$ |
29 | $[29, 29, w^{2} - 7]$ | $-\frac{1}{84}e^{5} + \frac{5}{12}e^{3} + \frac{13}{28}e^{2} - \frac{241}{84}e - \frac{65}{14}$ |
29 | $[29, 29, -w^{2} + 2w + 8]$ | $\phantom{-}\frac{1}{42}e^{5} - \frac{5}{6}e^{3} + \frac{1}{14}e^{2} + \frac{241}{42}e - \frac{5}{7}$ |
31 | $[31, 31, -2w^{2} + w + 12]$ | $-\frac{1}{42}e^{5} - \frac{1}{12}e^{4} + \frac{2}{3}e^{3} + \frac{127}{84}e^{2} - \frac{121}{28}e - \frac{43}{28}$ |
31 | $[31, 31, 2w^{2} - 3w - 11]$ | $-\frac{1}{42}e^{5} - \frac{1}{12}e^{4} + \frac{2}{3}e^{3} + \frac{127}{84}e^{2} - \frac{121}{28}e - \frac{43}{28}$ |
41 | $[41, 41, -w]$ | $-\frac{1}{4}e^{3} - \frac{1}{4}e^{2} + 4e + \frac{1}{4}$ |
41 | $[41, 41, -w + 1]$ | $-\frac{1}{4}e^{3} - \frac{1}{4}e^{2} + 4e + \frac{1}{4}$ |
49 | $[49, 7, w^{3} + 2w^{2} - 10w - 20]$ | $-\frac{1}{84}e^{5} - \frac{1}{12}e^{4} + \frac{1}{2}e^{3} + \frac{193}{84}e^{2} - \frac{229}{42}e - \frac{50}{7}$ |
49 | $[49, 7, w^{3} - 5w^{2} - 3w + 27]$ | $-\frac{1}{84}e^{5} - \frac{1}{12}e^{4} + \frac{1}{2}e^{3} + \frac{193}{84}e^{2} - \frac{229}{42}e - \frac{50}{7}$ |
61 | $[61, 61, 2w^{2} - 3w - 14]$ | $-\frac{1}{42}e^{5} + \frac{1}{12}e^{4} + \frac{3}{4}e^{3} - \frac{40}{21}e^{2} - \frac{349}{84}e + \frac{31}{14}$ |
61 | $[61, 61, 2w^{2} - w - 15]$ | $-\frac{1}{42}e^{5} + \frac{1}{12}e^{4} + \frac{3}{4}e^{3} - \frac{40}{21}e^{2} - \frac{349}{84}e + \frac{31}{14}$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).