Base field 4.4.14013.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} + 6x + 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[13, 13, -w^{3} + 5w + 1]$ |
| Dimension: | $11$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $24$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{11} - 2x^{10} - 19x^{9} + 32x^{8} + 128x^{7} - 180x^{6} - 344x^{5} + 432x^{4} + 244x^{3} - 404x^{2} + 144x - 16\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}\frac{1}{8}e^{10} - \frac{1}{4}e^{9} - \frac{19}{8}e^{8} + 4e^{7} + 16e^{6} - \frac{45}{2}e^{5} - 43e^{4} + 54e^{3} + \frac{63}{2}e^{2} - \frac{103}{2}e + 13$ |
| 3 | $[3, 3, w - 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w + 1]$ | $-\frac{9}{2}e^{10} + \frac{31}{4}e^{9} + \frac{175}{2}e^{8} - \frac{477}{4}e^{7} - 607e^{6} + 635e^{5} + \frac{3433}{2}e^{4} - 1438e^{3} - 1498e^{2} + 1361e - 244$ |
| 7 | $[7, 7, -w^{3} + 5w - 2]$ | $-\frac{85}{8}e^{10} + \frac{73}{4}e^{9} + \frac{1655}{8}e^{8} - 281e^{7} - \frac{2875}{2}e^{6} + \frac{2997}{2}e^{5} + \frac{8145}{2}e^{4} - 3405e^{3} - \frac{7115}{2}e^{2} + \frac{6485}{2}e - 587$ |
| 13 | $[13, 13, -w^{3} + 5w + 1]$ | $-1$ |
| 16 | $[16, 2, 2]$ | $-\frac{159}{8}e^{10} + 34e^{9} + \frac{3101}{8}e^{8} - \frac{2097}{4}e^{7} - 2698e^{6} + 2802e^{5} + \frac{15315}{2}e^{4} - 6391e^{3} - \frac{13413}{2}e^{2} + \frac{12231}{2}e - 1108$ |
| 29 | $[29, 29, w^{3} + w^{2} - 5w - 1]$ | $-\frac{87}{8}e^{10} + \frac{37}{2}e^{9} + \frac{1697}{8}e^{8} - \frac{1139}{4}e^{7} - 1476e^{6} + 1518e^{5} + 4185e^{4} - 3452e^{3} - \frac{7317}{2}e^{2} + \frac{6603}{2}e - 593$ |
| 31 | $[31, 31, -w^{3} + 4w - 1]$ | $\phantom{-}\frac{163}{8}e^{10} - 35e^{9} - \frac{3177}{8}e^{8} + \frac{2161}{4}e^{7} + \frac{5525}{2}e^{6} - 2893e^{5} - 7836e^{4} + 6616e^{3} + \frac{13707}{2}e^{2} - \frac{12671}{2}e + 1159$ |
| 41 | $[41, 41, w^{3} - 6w + 1]$ | $\phantom{-}\frac{27}{8}e^{10} - 6e^{9} - \frac{521}{8}e^{8} + \frac{369}{4}e^{7} + \frac{897}{2}e^{6} - 490e^{5} - 1259e^{4} + 1100e^{3} + \frac{2175}{2}e^{2} - \frac{2039}{2}e + 183$ |
| 43 | $[43, 43, w^{3} + w^{2} - 6w - 1]$ | $-\frac{239}{8}e^{10} + \frac{205}{4}e^{9} + \frac{4657}{8}e^{8} - 790e^{7} - 4048e^{6} + 4221e^{5} + \frac{22955}{2}e^{4} - 9624e^{3} - \frac{20071}{2}e^{2} + \frac{18409}{2}e - 1671$ |
| 47 | $[47, 47, -w^{3} + 2w^{2} + 5w - 11]$ | $\phantom{-}\frac{3}{2}e^{10} - 3e^{9} - \frac{57}{2}e^{8} + \frac{95}{2}e^{7} + 193e^{6} - \frac{523}{2}e^{5} - 531e^{4} + 604e^{3} + 436e^{2} - 545e + 116$ |
| 49 | $[49, 7, w^{2} + w - 1]$ | $-\frac{39}{4}e^{10} + \frac{67}{4}e^{9} + \frac{759}{4}e^{8} - \frac{1031}{4}e^{7} - \frac{2635}{2}e^{6} + 1373e^{5} + \frac{7455}{2}e^{4} - 3115e^{3} - 3245e^{2} + 2966e - 540$ |
| 59 | $[59, 59, w^{3} - w^{2} - 6w + 4]$ | $\phantom{-}\frac{283}{8}e^{10} - \frac{121}{2}e^{9} - \frac{5521}{8}e^{8} + \frac{3733}{4}e^{7} + \frac{9611}{2}e^{6} - \frac{9985}{2}e^{5} - 13647e^{4} + 11405e^{3} + \frac{23923}{2}e^{2} - \frac{21855}{2}e + 1983$ |
| 59 | $[59, 59, w^{2} - w - 4]$ | $\phantom{-}\frac{3}{4}e^{10} - e^{9} - \frac{61}{4}e^{8} + 15e^{7} + 110e^{6} - \frac{153}{2}e^{5} - 323e^{4} + 167e^{3} + 305e^{2} - 170e + 10$ |
| 67 | $[67, 67, 2w^{3} + w^{2} - 9w - 2]$ | $\phantom{-}6e^{10} - \frac{41}{4}e^{9} - 117e^{8} + \frac{631}{4}e^{7} + \frac{1629}{2}e^{6} - 841e^{5} - 2313e^{4} + 1914e^{3} + 2027e^{2} - 1836e + 336$ |
| 71 | $[71, 71, -3w^{3} - w^{2} + 16w + 5]$ | $\phantom{-}\frac{117}{8}e^{10} - \frac{99}{4}e^{9} - \frac{2287}{8}e^{8} + \frac{763}{2}e^{7} + 1994e^{6} - \frac{4079}{2}e^{5} - 5670e^{4} + 4664e^{3} + \frac{9947}{2}e^{2} - \frac{9001}{2}e + 815$ |
| 71 | $[71, 71, 2w - 1]$ | $\phantom{-}\frac{41}{2}e^{10} - 35e^{9} - \frac{799}{2}e^{8} + \frac{1077}{2}e^{7} + 2778e^{6} - \frac{5739}{2}e^{5} - 7875e^{4} + 6522e^{3} + 6886e^{2} - 6235e + 1132$ |
| 73 | $[73, 73, w^{3} - 6w + 4]$ | $-\frac{237}{8}e^{10} + \frac{203}{4}e^{9} + \frac{4623}{8}e^{8} - \frac{1567}{2}e^{7} - 4023e^{6} + \frac{8391}{2}e^{5} + 11422e^{4} - 9591e^{3} - \frac{20019}{2}e^{2} + \frac{18363}{2}e - 1663$ |
| 83 | $[83, 83, w^{3} - w^{2} - 3w + 4]$ | $\phantom{-}\frac{69}{4}e^{10} - \frac{59}{2}e^{9} - \frac{1347}{4}e^{8} + 456e^{7} + 2346e^{6} - 2448e^{5} - 6663e^{4} + 5623e^{3} + 5831e^{2} - 5416e + 996$ |
| 103 | $[103, 103, w^{3} + w^{2} - 4w - 5]$ | $\phantom{-}\frac{151}{4}e^{10} - \frac{259}{4}e^{9} - \frac{2943}{4}e^{8} + \frac{3995}{4}e^{7} + 5117e^{6} - 5341e^{5} - 14508e^{4} + 12186e^{3} + 12681e^{2} - 11641e + 2118$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, -w^{3} + 5w + 1]$ | $1$ |