Base field \(\Q(\sqrt{449}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 112\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[5, 5, -116w - 1171]$ |
| Dimension: | $56$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $101$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{56} - 5x^{55} - 73x^{54} + 392x^{53} + 2469x^{52} - 14430x^{51} - 51253x^{50} + 331707x^{49} + 728300x^{48} - 5342071x^{47} - 7463309x^{46} + 64099189x^{45} + 56332722x^{44} - 594940640x^{43} - 310640982x^{42} + 4377420739x^{41} + 1172040192x^{40} - 25958415321x^{39} - 2151077621x^{38} + 125466544877x^{37} - 6536019894x^{36} - 497924220724x^{35} + 74460844749x^{34} + 1629577666590x^{33} - 354817407034x^{32} - 4406258941319x^{31} + 1156305214816x^{30} + 9839927691483x^{29} - 2832041204585x^{28} - 18103875213078x^{27} + 5379790348335x^{26} + 27315964184229x^{25} - 8008963372647x^{24} - 33569223961403x^{23} + 9344852647404x^{22} + 33283376331468x^{21} - 8490746687334x^{20} - 26290046167069x^{19} + 5938715291336x^{18} + 16271231475248x^{17} - 3147784898694x^{16} - 7719839135308x^{15} + 1241435900472x^{14} + 2726979113167x^{13} - 358121216834x^{12} - 689372456580x^{11} + 74984992182x^{10} + 118088300993x^{9} - 11468573233x^{8} - 12704598621x^{7} + 1255637463x^{6} + 772161300x^{5} - 83692008x^{4} - 22055671x^{3} + 2539425x^{2} + 195962x - 20893\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 10]$ | $...$ |
| 2 | $[2, 2, w - 11]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -116w - 1171]$ | $-1$ |
| 5 | $[5, 5, 116w - 1287]$ | $...$ |
| 7 | $[7, 7, -1002w - 10115]$ | $...$ |
| 7 | $[7, 7, 1002w - 11117]$ | $...$ |
| 9 | $[9, 3, 3]$ | $...$ |
| 11 | $[11, 11, 10w - 111]$ | $...$ |
| 11 | $[11, 11, -10w - 101]$ | $...$ |
| 23 | $[23, 23, -32w + 355]$ | $...$ |
| 23 | $[23, 23, 32w + 323]$ | $...$ |
| 41 | $[41, 41, -8w - 81]$ | $...$ |
| 41 | $[41, 41, -8w + 89]$ | $...$ |
| 53 | $[53, 53, 4w - 45]$ | $...$ |
| 53 | $[53, 53, 4w + 41]$ | $...$ |
| 59 | $[59, 59, -3892w + 43181]$ | $...$ |
| 59 | $[59, 59, 3892w + 39289]$ | $...$ |
| 61 | $[61, 61, 770w - 8543]$ | $...$ |
| 61 | $[61, 61, -770w - 7773]$ | $...$ |
| 67 | $[67, 67, 158w + 1595]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, -116w - 1171]$ | $1$ |