Base field \(\Q(\sqrt{181}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 45\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[15, 15, -2w + 15]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $41$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} - 14x^{5} - 3x^{4} + 51x^{3} + 27x^{2} - 43x - 28\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w - 6]$ | $\phantom{-}1$ |
| 3 | $[3, 3, -w + 7]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $\phantom{-}\frac{6}{37}e^{6} - \frac{4}{37}e^{5} - \frac{69}{37}e^{4} + \frac{28}{37}e^{3} + \frac{164}{37}e^{2} + \frac{28}{37}e - \frac{67}{37}$ |
| 5 | $[5, 5, 4w + 25]$ | $-1$ |
| 5 | $[5, 5, -4w + 29]$ | $\phantom{-}\frac{19}{37}e^{6} - \frac{25}{37}e^{5} - \frac{237}{37}e^{4} + \frac{249}{37}e^{3} + \frac{692}{37}e^{2} - \frac{343}{37}e - \frac{502}{37}$ |
| 11 | $[11, 11, w - 8]$ | $\phantom{-}\frac{13}{37}e^{6} - \frac{21}{37}e^{5} - \frac{168}{37}e^{4} + \frac{221}{37}e^{3} + \frac{528}{37}e^{2} - \frac{371}{37}e - \frac{472}{37}$ |
| 11 | $[11, 11, -w - 7]$ | $\phantom{-}\frac{9}{37}e^{6} - \frac{6}{37}e^{5} - \frac{122}{37}e^{4} + \frac{42}{37}e^{3} + \frac{394}{37}e^{2} + \frac{42}{37}e - \frac{230}{37}$ |
| 13 | $[13, 13, 3w + 19]$ | $-\frac{18}{37}e^{6} + \frac{12}{37}e^{5} + \frac{244}{37}e^{4} - \frac{121}{37}e^{3} - \frac{862}{37}e^{2} + \frac{212}{37}e + \frac{682}{37}$ |
| 13 | $[13, 13, 3w - 22]$ | $-\frac{3}{37}e^{6} + \frac{2}{37}e^{5} + \frac{53}{37}e^{4} - \frac{14}{37}e^{3} - \frac{267}{37}e^{2} - \frac{14}{37}e + \frac{200}{37}$ |
| 29 | $[29, 29, 6w + 37]$ | $\phantom{-}\frac{51}{37}e^{6} - \frac{71}{37}e^{5} - \frac{642}{37}e^{4} + \frac{719}{37}e^{3} + \frac{1912}{37}e^{2} - \frac{1020}{37}e - \frac{1402}{37}$ |
| 29 | $[29, 29, 6w - 43]$ | $-\frac{27}{37}e^{6} + \frac{18}{37}e^{5} + \frac{366}{37}e^{4} - \frac{200}{37}e^{3} - \frac{1256}{37}e^{2} + \frac{392}{37}e + \frac{986}{37}$ |
| 37 | $[37, 37, 2w - 13]$ | $-\frac{22}{37}e^{6} + \frac{27}{37}e^{5} + \frac{253}{37}e^{4} - \frac{263}{37}e^{3} - \frac{552}{37}e^{2} + \frac{218}{37}e + \frac{110}{37}$ |
| 37 | $[37, 37, 2w + 11]$ | $\phantom{-}\frac{6}{37}e^{6} - \frac{4}{37}e^{5} - \frac{69}{37}e^{4} + \frac{65}{37}e^{3} + \frac{164}{37}e^{2} - \frac{194}{37}e - \frac{104}{37}$ |
| 43 | $[43, 43, -w - 1]$ | $-\frac{2}{37}e^{6} - \frac{11}{37}e^{5} + \frac{23}{37}e^{4} + \frac{114}{37}e^{3} - \frac{30}{37}e^{2} - \frac{219}{37}e - \frac{212}{37}$ |
| 43 | $[43, 43, w - 2]$ | $-\frac{30}{37}e^{6} + \frac{20}{37}e^{5} + \frac{419}{37}e^{4} - \frac{177}{37}e^{3} - \frac{1486}{37}e^{2} + \frac{45}{37}e + \frac{1112}{37}$ |
| 49 | $[49, 7, -7]$ | $-\frac{25}{37}e^{6} + \frac{29}{37}e^{5} + \frac{306}{37}e^{4} - \frac{314}{37}e^{3} - \frac{856}{37}e^{2} + \frac{500}{37}e + \frac{680}{37}$ |
| 59 | $[59, 59, 5w - 37]$ | $-\frac{18}{37}e^{6} + \frac{12}{37}e^{5} + \frac{207}{37}e^{4} - \frac{84}{37}e^{3} - \frac{455}{37}e^{2} - \frac{158}{37}e + \frac{16}{37}$ |
| 59 | $[59, 59, 5w + 32]$ | $-\frac{60}{37}e^{6} + \frac{77}{37}e^{5} + \frac{764}{37}e^{4} - \frac{761}{37}e^{3} - \frac{2343}{37}e^{2} + \frac{978}{37}e + \frac{1780}{37}$ |
| 67 | $[67, 67, 21w + 131]$ | $\phantom{-}\frac{34}{37}e^{6} - \frac{35}{37}e^{5} - \frac{465}{37}e^{4} + \frac{356}{37}e^{3} + \frac{1583}{37}e^{2} - \frac{495}{37}e - \frac{1354}{37}$ |
| 67 | $[67, 67, 21w - 152]$ | $-\frac{26}{37}e^{6} + \frac{42}{37}e^{5} + \frac{299}{37}e^{4} - \frac{368}{37}e^{3} - \frac{649}{37}e^{2} + \frac{261}{37}e + \frac{56}{37}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -w - 6]$ | $-1$ |
| $5$ | $[5, 5, 4w + 25]$ | $1$ |