Base field \(\Q(\sqrt{377}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 94\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[8,8,-w + 3]$ |
| Dimension: | $56$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $116$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{56} + 91x^{54} + 3901x^{52} + 104765x^{50} + 1977391x^{48} + 27893479x^{46} + 305295364x^{44} + 2656940084x^{42} + 18693007974x^{40} + 107521669772x^{38} + 509382081147x^{36} + 1996327661681x^{34} + 6484570983198x^{32} + 17451501146686x^{30} + 38813016018220x^{28} + 70992934836924x^{26} + 106007871387254x^{24} + 127884507219330x^{22} + 122873649201850x^{20} + 92224195160072x^{18} + 52656689726845x^{16} + 22039146841153x^{14} + 6411123479398x^{12} + 1197343088922x^{10} + 127129868073x^{8} + 6366681441x^{6} + 95339816x^{4} + 457488x^{2} + 256\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}0$ |
| 9 | $[9, 3, 3]$ | $...$ |
| 11 | $[11, 11, w + 2]$ | $...$ |
| 11 | $[11, 11, w + 8]$ | $...$ |
| 13 | $[13, 13, 4w - 41]$ | $...$ |
| 19 | $[19, 19, w + 7]$ | $...$ |
| 19 | $[19, 19, w + 11]$ | $...$ |
| 23 | $[23, 23, -2w + 21]$ | $...$ |
| 23 | $[23, 23, -2w - 19]$ | $...$ |
| 25 | $[25, 5, -5]$ | $...$ |
| 29 | $[29, 29, 6w - 61]$ | $...$ |
| 31 | $[31, 31, w + 12]$ | $...$ |
| 31 | $[31, 31, w + 18]$ | $...$ |
| 37 | $[37, 37, w + 4]$ | $...$ |
| 37 | $[37, 37, w + 32]$ | $...$ |
| 41 | $[41, 41, w + 3]$ | $...$ |
| 41 | $[41, 41, w + 37]$ | $...$ |
| 47 | $[47, 47, w]$ | $...$ |
| 47 | $[47, 47, w + 46]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,-w + 1]$ | $\frac{540020771530963493116602371065345}{11350236774784490351497857741547339776}e^{55} + \frac{12380316537402034437169728307859741}{2837559193696122587874464435386834944}e^{53} + \frac{713526280013740377601052631201451867}{3783412258261496783832619247182446592}e^{51} + \frac{29002299322737459854210270182388908147}{5675118387392245175748928870773669888}e^{49} + \frac{52640292293173139945727645865181284945}{540487465465928111976088463883206656}e^{47} + \frac{3939281601629345527088781608248120650049}{2837559193696122587874464435386834944}e^{45} + \frac{3114506137066319555086594991431704556411}{202682799549723041991033173956202496}e^{43} + \frac{384093989029274964823276480465130036727991}{2837559193696122587874464435386834944}e^{41} + \frac{5475470838413523086929707183417974198044721}{5675118387392245175748928870773669888}e^{39} + \frac{10646115854484745519555128830887505387467141}{1891706129130748391916309623591223296}e^{37} + \frac{102394654935015450677733405745438622462381987}{3783412258261496783832619247182446592}e^{35} + \frac{87380239383587636921874352369514960850383839}{810731198198892167964132695824809984}e^{33} + \frac{2255580842830922215591692864245371098443267}{6333837485928845062219786686131328}e^{31} + \frac{1846074769649180101358890487155153536118964661}{1891706129130748391916309623591223296}e^{29} + \frac{1793494460719187738755642730505666680638522043}{810731198198892167964132695824809984}e^{27} + \frac{23427005978876231608464894378441094868573196083}{5675118387392245175748928870773669888}e^{25} + \frac{850388369568242002042887464005645908513911023}{135121866366482027994022115970801664}e^{23} + \frac{14673072486854711643551854261016716458217353773}{1891706129130748391916309623591223296}e^{21} + \frac{10806400364609988349127206955280245224042836707}{1418779596848061293937232217693417472}e^{19} + \frac{690814674981963645474660062037555391583578633}{118231633070671774494769351474451456}e^{17} + \frac{38685142286806847104492560861329838015306931165}{11350236774784490351497857741547339776}e^{15} + \frac{8262970732934676461239269190578943810597002859}{5675118387392245175748928870773669888}e^{13} + \frac{408190752261280817619431954843738555743516753}{945853064565374195958154811795611648}e^{11} + \frac{154952689959274404205420173143488828629707393}{1891706129130748391916309623591223296}e^{9} + \frac{33341135311701791490854200416339223621720341}{3783412258261496783832619247182446592}e^{7} + \frac{211735563124314287960833636276777314393211}{472926532282687097979077405897805824}e^{5} + \frac{5008185255017581158733478727115844706839}{709389798424030646968616108846708736}e^{3} + \frac{1942945853125655253542493480823289783}{44336862401501915435538506802919296}e$ |