Base field 3.3.361.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x + 7\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[37,37,-w^{2} - 2w + 6]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 4x^{5} - 9x^{4} + 36x^{3} - 7x^{2} - 46x + 28\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, w]$ | $\phantom{-}\frac{5}{4}e^{5} - 3e^{4} - 16e^{3} + \frac{75}{4}e^{2} + \frac{45}{2}e - 18$ |
| 7 | $[7, 7, w^{2} - 4]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w^{2} + w - 5]$ | $-\frac{1}{2}e^{5} + e^{4} + 7e^{3} - \frac{11}{2}e^{2} - 12e + 7$ |
| 8 | $[8, 2, 2]$ | $-\frac{7}{4}e^{5} + \frac{19}{4}e^{4} + \frac{87}{4}e^{3} - 35e^{2} - \frac{61}{2}e + 40$ |
| 11 | $[11, 11, w + 1]$ | $-\frac{3}{2}e^{5} + 4e^{4} + 19e^{3} - \frac{59}{2}e^{2} - 29e + 35$ |
| 11 | $[11, 11, -w^{2} - w + 6]$ | $\phantom{-}\frac{1}{2}e^{5} - e^{4} - 7e^{3} + \frac{11}{2}e^{2} + 12e - 5$ |
| 11 | $[11, 11, -w^{2} + 3]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{3}{2}e^{4} - 6e^{3} + \frac{23}{2}e^{2} + \frac{19}{2}e - 12$ |
| 19 | $[19, 19, -w^{2} + w + 4]$ | $\phantom{-}\frac{5}{2}e^{5} - 7e^{4} - 31e^{3} + \frac{107}{2}e^{2} + 46e - 63$ |
| 27 | $[27, 3, -3]$ | $\phantom{-}4e^{5} - \frac{21}{2}e^{4} - 50e^{3} + 74e^{2} + \frac{141}{2}e - 83$ |
| 31 | $[31, 31, w^{2} - 8]$ | $\phantom{-}2e^{5} - \frac{21}{4}e^{4} - \frac{101}{4}e^{3} + \frac{149}{4}e^{2} + 36e - 39$ |
| 31 | $[31, 31, 2w^{2} - 9]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - \frac{15}{2}e + 3$ |
| 31 | $[31, 31, 2w^{2} + 2w - 9]$ | $-\frac{1}{2}e^{4} + \frac{1}{2}e^{3} + \frac{15}{2}e^{2} + 3e - 12$ |
| 37 | $[37, 37, 2w^{2} + w - 8]$ | $-\frac{9}{2}e^{5} + \frac{23}{2}e^{4} + 57e^{3} - \frac{159}{2}e^{2} - \frac{169}{2}e + 92$ |
| 37 | $[37, 37, w^{2} + 2w - 6]$ | $\phantom{-}1$ |
| 37 | $[37, 37, w^{2} - w - 5]$ | $-2e^{5} + \frac{21}{4}e^{4} + \frac{99}{4}e^{3} - \frac{143}{4}e^{2} - \frac{63}{2}e + 35$ |
| 83 | $[83, 83, -2w - 3]$ | $-\frac{9}{4}e^{5} + 5e^{4} + \frac{59}{2}e^{3} - \frac{113}{4}e^{2} - 44e + 32$ |
| 83 | $[83, 83, 2w^{2} - 5]$ | $-\frac{5}{4}e^{5} + \frac{7}{2}e^{4} + \frac{31}{2}e^{3} - \frac{109}{4}e^{2} - \frac{45}{2}e + 41$ |
| 83 | $[83, 83, 2w^{2} + 2w - 13]$ | $\phantom{-}\frac{5}{2}e^{5} - 6e^{4} - 32e^{3} + \frac{77}{2}e^{2} + 42e - 35$ |
| 103 | $[103, 103, 3w^{2} + 2w - 17]$ | $-\frac{5}{2}e^{5} + 6e^{4} + 33e^{3} - \frac{81}{2}e^{2} - 53e + 44$ |
| 103 | $[103, 103, 2w^{2} - w - 5]$ | $\phantom{-}\frac{7}{2}e^{5} - \frac{19}{2}e^{4} - 43e^{3} + \frac{139}{2}e^{2} + \frac{111}{2}e - 75$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $37$ | $[37,37,-w^{2} - 2w + 6]$ | $-1$ |