Properties

Label 2.2.449.1-7.2-b
Base field \(\Q(\sqrt{449}) \)
Weight $[2, 2]$
Level norm $7$
Level $[7,7,1002w - 11117]$
Dimension $71$
CM no
Base change no

Related objects

Downloads

Learn more

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: $[7,7,1002w - 11117]$
Dimension: $71$
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:

\(x^{71} + 4x^{70} - 95x^{69} - 390x^{68} + 4283x^{67} + 18085x^{66} - 121952x^{65} - 530912x^{64} + 2462184x^{63} + 11080045x^{62} - 37517585x^{61} - 175009458x^{60} + 448397192x^{59} + 2174742002x^{58} - 4312990107x^{57} - 21819431489x^{56} + 33994965485x^{55} + 180001755564x^{54} - 222450485621x^{53} - 1237131581986x^{52} + 1220141126712x^{51} + 7152035165463x^{50} - 5650314871315x^{49} - 35022649730258x^{48} + 22213380410533x^{47} + 145989641447585x^{46} - 74464416889837x^{45} - 519731680520454x^{44} + 213669606641823x^{43} + 1583216791317194x^{42} - 526818868099300x^{41} - 4129350937133095x^{40} + 1121020627191742x^{39} + 9216626732351667x^{38} - 2069922738589043x^{37} - 17574497197849769x^{36} + 3338129782480356x^{35} + 28548089218128703x^{34} - 4733364572004703x^{33} - 39343236672809826x^{32} + 5929429174344717x^{31} + 45747171301673018x^{30} - 6560130275644463x^{29} - 44559866956557033x^{28} + 6360708432231398x^{27} + 36026168700598163x^{26} - 5321669655533502x^{25} - 23893703773030528x^{24} + 3759832637975262x^{23} + 12804409212364772x^{22} - 2186635899113307x^{21} - 5435077169941773x^{20} + 1017163164802570x^{19} + 1778842640797499x^{18} - 366068088425305x^{17} - 432152069037463x^{16} + 97771749190918x^{15} + 73575741085145x^{14} - 18293813934286x^{13} - 7970552044334x^{12} + 2191542022052x^{11} + 451879378553x^{10} - 142721070515x^{9} - 7272857024x^{8} + 3513423108x^{7} - 25171185x^{6} - 32090487x^{5} + 965581x^{4} + 80202x^{3} - 1987x^{2} - 58x + 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w + 10]$ $\phantom{-}e$
2 $[2, 2, w - 11]$ $...$
5 $[5, 5, -116w - 1171]$ $...$
5 $[5, 5, 116w - 1287]$ $...$
7 $[7, 7, -1002w - 10115]$ $...$
7 $[7, 7, 1002w - 11117]$ $\phantom{-}1$
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 $[67, 67, 158w + 1595]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$7$ $[7,7,1002w - 11117]$ $-1$