Base field 3.3.1300.1
Generator \(w\), with minimal polynomial \(x^{3} - 10x - 10\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[17, 17, -w^{2} + 2w + 7]$ |
| Dimension: | $15$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $37$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{15} + 3x^{14} - 17x^{13} - 54x^{12} + 102x^{11} + 360x^{10} - 250x^{9} - 1111x^{8} + 166x^{7} + 1595x^{6} + 149x^{5} - 937x^{4} - 66x^{3} + 226x^{2} - 8x - 12\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w^{2} + 2w + 5]$ | $\phantom{-}e^{14} + 4e^{13} - 14e^{12} - \frac{141}{2}e^{11} + \frac{99}{2}e^{10} + 453e^{9} + 84e^{8} - \frac{2603}{2}e^{7} - 782e^{6} + \frac{3169}{2}e^{5} + 1291e^{4} - \frac{1139}{2}e^{3} - 469e^{2} + 81e + 33$ |
| 7 | $[7, 7, w + 3]$ | $\phantom{-}e^{14} + 2e^{13} - \frac{37}{2}e^{12} - \frac{69}{2}e^{11} + \frac{255}{2}e^{10} + \frac{431}{2}e^{9} - \frac{811}{2}e^{8} - 601e^{7} + 583e^{6} + 724e^{5} - 320e^{4} - 268e^{3} + \frac{135}{2}e^{2} + 16e + 2$ |
| 11 | $[11, 11, -2w^{2} + 5w + 9]$ | $-e^{14} - \frac{9}{2}e^{13} + 13e^{12} + \frac{159}{2}e^{11} - 32e^{10} - \frac{1025}{2}e^{9} - \frac{391}{2}e^{8} + \frac{2957}{2}e^{7} + \frac{2201}{2}e^{6} - \frac{3617}{2}e^{5} - \frac{3363}{2}e^{4} + 656e^{3} + 613e^{2} - 98e - 45$ |
| 13 | $[13, 13, -w^{2} + w + 7]$ | $-e^{14} - 2e^{13} + \frac{37}{2}e^{12} + \frac{69}{2}e^{11} - \frac{255}{2}e^{10} - \frac{431}{2}e^{9} + \frac{811}{2}e^{8} + 601e^{7} - 583e^{6} - 724e^{5} + 320e^{4} + 267e^{3} - \frac{137}{2}e^{2} - 11e - 1$ |
| 13 | $[13, 13, w - 3]$ | $-e^{14} - \frac{3}{2}e^{13} + \frac{39}{2}e^{12} + 25e^{11} - 145e^{10} - \frac{295}{2}e^{9} + 517e^{8} + \frac{745}{2}e^{7} - 903e^{6} - \frac{731}{2}e^{5} + 726e^{4} + 40e^{3} - 243e^{2} + 32e + 14$ |
| 17 | $[17, 17, -w^{2} + 2w + 7]$ | $-1$ |
| 17 | $[17, 17, -2w^{2} + 5w + 7]$ | $\phantom{-}3e^{14} + \frac{17}{2}e^{13} - 50e^{12} - \frac{297}{2}e^{11} + 287e^{10} + \frac{1885}{2}e^{9} - \frac{1233}{2}e^{8} - \frac{5333}{2}e^{7} + \frac{159}{2}e^{6} + \frac{6389}{2}e^{5} + \frac{1959}{2}e^{4} - 1100e^{3} - 382e^{2} + 108e + 27$ |
| 17 | $[17, 17, -w^{2} + 3w + 3]$ | $\phantom{-}2e^{14} + \frac{7}{2}e^{13} - 38e^{12} - \frac{119}{2}e^{11} + \frac{545}{2}e^{10} + 363e^{9} - \frac{1845}{2}e^{8} - \frac{1947}{2}e^{7} + 1486e^{6} + \frac{2181}{2}e^{5} - 1047e^{4} - 316e^{3} + \frac{635}{2}e^{2} - 6e - 18$ |
| 19 | $[19, 19, -w + 1]$ | $-\frac{1}{2}e^{14} + e^{13} + \frac{27}{2}e^{12} - 19e^{11} - 137e^{10} + 134e^{9} + \frac{1319}{2}e^{8} - \frac{851}{2}e^{7} - 1560e^{6} + \frac{1127}{2}e^{5} + \frac{3341}{2}e^{4} - 231e^{3} - \frac{1145}{2}e^{2} + 59e + 38$ |
| 27 | $[27, 3, -3]$ | $-\frac{1}{2}e^{14} - \frac{5}{2}e^{13} + 6e^{12} + \frac{89}{2}e^{11} - \frac{15}{2}e^{10} - \frac{579}{2}e^{9} - \frac{299}{2}e^{8} + \frac{1685}{2}e^{7} + 689e^{6} - \frac{2065}{2}e^{5} - \frac{2003}{2}e^{4} + \frac{731}{2}e^{3} + \frac{727}{2}e^{2} - 53e - 29$ |
| 31 | $[31, 31, w^{2} - 2w - 9]$ | $\phantom{-}\frac{5}{2}e^{14} + \frac{13}{2}e^{13} - 43e^{12} - \frac{225}{2}e^{11} + 262e^{10} + 703e^{9} - \frac{1309}{2}e^{8} - \frac{3871}{2}e^{7} + \frac{901}{2}e^{6} + \frac{4381}{2}e^{5} + 362e^{4} - \frac{1189}{2}e^{3} - 144e^{2} + 21e + 11$ |
| 37 | $[37, 37, w^{2} - 7]$ | $-2e^{14} - 5e^{13} + \frac{69}{2}e^{12} + \frac{173}{2}e^{11} - \frac{423}{2}e^{10} - \frac{1083}{2}e^{9} + \frac{1073}{2}e^{8} + 1504e^{7} - 396e^{6} - 1757e^{5} - 267e^{4} + 568e^{3} + \frac{297}{2}e^{2} - 47e - 10$ |
| 41 | $[41, 41, w^{2} - w - 11]$ | $-\frac{7}{2}e^{14} - 10e^{13} + \frac{117}{2}e^{12} + \frac{351}{2}e^{11} - \frac{677}{2}e^{10} - 1122e^{9} + \frac{1497}{2}e^{8} + 3214e^{7} - 192e^{6} - 3951e^{5} - \frac{2043}{2}e^{4} + \frac{2995}{2}e^{3} + \frac{851}{2}e^{2} - 179e - 33$ |
| 47 | $[47, 47, w^{2} - 3]$ | $-\frac{3}{2}e^{14} - \frac{19}{2}e^{13} + \frac{27}{2}e^{12} + \frac{337}{2}e^{11} + 55e^{10} - \frac{2181}{2}e^{9} - 931e^{8} + 3147e^{7} + \frac{6795}{2}e^{6} - 3791e^{5} - 4534e^{4} + 1270e^{3} + \frac{3101}{2}e^{2} - 190e - 102$ |
| 49 | $[49, 7, w^{2} - 3w - 1]$ | $-\frac{5}{2}e^{14} - \frac{19}{2}e^{13} + \frac{73}{2}e^{12} + \frac{335}{2}e^{11} - \frac{301}{2}e^{10} - 1077e^{9} - 35e^{8} + 3099e^{7} + 1436e^{6} - 3789e^{5} - \frac{5095}{2}e^{4} + 1380e^{3} + 869e^{2} - 188e - 55$ |
| 59 | $[59, 59, w^{2} - 4w + 1]$ | $\phantom{-}\frac{1}{2}e^{14} + 5e^{13} - \frac{1}{2}e^{12} - 89e^{11} - 88e^{10} + 578e^{9} + \frac{1501}{2}e^{8} - \frac{3337}{2}e^{7} - 2371e^{6} + \frac{3963}{2}e^{5} + \frac{5975}{2}e^{4} - 603e^{3} - \frac{2029}{2}e^{2} + 87e + 69$ |
| 67 | $[67, 67, w^{2} - 3w - 7]$ | $-6e^{14} - 15e^{13} + 104e^{12} + 260e^{11} - 643e^{10} - 1631e^{9} + 1663e^{8} + 4537e^{7} - 1347e^{6} - 5296e^{5} - 573e^{4} + 1683e^{3} + 321e^{2} - 116e - 37$ |
| 71 | $[71, 71, 4w + 9]$ | $\phantom{-}2e^{14} + \frac{15}{2}e^{13} - \frac{59}{2}e^{12} - 132e^{11} + \frac{251}{2}e^{10} + 846e^{9} - 3e^{8} - \frac{4839}{2}e^{7} - \frac{2135}{2}e^{6} + \frac{5839}{2}e^{5} + \frac{3911}{2}e^{4} - 1014e^{3} - \frac{1365}{2}e^{2} + 121e + 42$ |
| 73 | $[73, 73, -4w^{2} + 8w + 23]$ | $-\frac{3}{2}e^{14} + \frac{5}{2}e^{13} + 40e^{12} - 47e^{11} - \frac{805}{2}e^{10} + 327e^{9} + \frac{3851}{2}e^{8} - 1017e^{7} - \frac{9045}{2}e^{6} + 1283e^{5} + 4766e^{4} - 438e^{3} - 1553e^{2} + 132e + 101$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17, 17, -w^{2} + 2w + 7]$ | $1$ |