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: | $[7, 7, -1002w - 10115]$ |
| Dimension: | $77$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $149$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{77} + 2x^{76} - 116x^{75} - 224x^{74} + 6449x^{73} + 11987x^{72} - 228805x^{71} - 408025x^{70} + 5819866x^{69} + 9922344x^{68} - 113032130x^{67} - 183550676x^{66} + 1743211969x^{65} + 2685457851x^{64} - 21919324940x^{63} - 31897012432x^{62} + 228961632009x^{61} + 313291366435x^{60} - 2014212192035x^{59} - 2578779585359x^{58} + 15075985089431x^{57} + 17964303990298x^{56} - 96743989866651x^{55} - 106674823525719x^{54} + 535290182059099x^{53} + 542759218950952x^{52} - 2564321967169195x^{51} - 2374422062158366x^{50} + 10666034356796728x^{49} + 8949479499666709x^{48} - 38585697676969407x^{47} - 29082768648094416x^{46} + 121494521353244680x^{45} + 81436754813733092x^{44} - 332895083396744916x^{43} - 196116861457704881x^{42} + 792877033015535577x^{41} + 404782693806106734x^{40} - 1638300718138096406x^{39} - 712255216604352633x^{38} + 2928280328550440159x^{37} + 1060145543303042542x^{36} - 4510005878625776795x^{35} - 1319490755027742730x^{34} + 5955655854993978943x^{33} + 1349052407693309898x^{32} - 6701609514400639106x^{31} - 1099239930720031178x^{30} + 6377018259949174789x^{29} + 671175947514305160x^{28} - 5084067895505384463x^{27} - 256010801568079580x^{26} + 3357858750812123771x^{25} - 1453390478486256x^{24} - 1812343725206765952x^{23} + 84819025893384239x^{22} + 786301525518728850x^{21} - 69417114263627724x^{20} - 268862513661096817x^{19} + 33390144569814709x^{18} + 70783349090354425x^{17} - 10866708037845197x^{16} - 13968724117291539x^{15} + 2442722786345220x^{14} + 2006739606263881x^{13} - 373997639542968x^{12} - 203699783018620x^{11} + 37818908798051x^{10} + 14198969485184x^{9} - 2415247372495x^{8} - 659419889657x^{7} + 90892222344x^{6} + 19458064945x^{5} - 1762414409x^{4} - 326556702x^{3} + 11737072x^{2} + 2280520x + 33069\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 10]$ | $...$ |
| 2 | $[2, 2, w - 11]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -116w - 1171]$ | $...$ |
| 5 | $[5, 5, 116w - 1287]$ | $...$ |
| 7 | $[7, 7, -1002w - 10115]$ | $-1$ |
| 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 |
|---|---|---|
| $7$ | $[7, 7, -1002w - 10115]$ | $1$ |