Properties

Base field \(\Q(\sqrt{197}) \)
Weight [2, 2]
Level norm 23
Level $[23,23,-w + 9]$
Label 2.2.197.1-23.2-d
Dimension 43
CM no
Base change no

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Base field \(\Q(\sqrt{197}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 49\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2]
Level $[23,23,-w + 9]$
Label 2.2.197.1-23.2-d
Dimension 43
Is CM no
Is base change no
Parent newspace dimension 81

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{43} \) \(\mathstrut +\mathstrut x^{42} \) \(\mathstrut -\mathstrut 107x^{41} \) \(\mathstrut -\mathstrut 99x^{40} \) \(\mathstrut +\mathstrut 5241x^{39} \) \(\mathstrut +\mathstrut 4485x^{38} \) \(\mathstrut -\mathstrut 155769x^{37} \) \(\mathstrut -\mathstrut 123524x^{36} \) \(\mathstrut +\mathstrut 3139252x^{35} \) \(\mathstrut +\mathstrut 2317834x^{34} \) \(\mathstrut -\mathstrut 45408975x^{33} \) \(\mathstrut -\mathstrut 31472838x^{32} \) \(\mathstrut +\mathstrut 486755778x^{31} \) \(\mathstrut +\mathstrut 320524340x^{30} \) \(\mathstrut -\mathstrut 3936468390x^{29} \) \(\mathstrut -\mathstrut 2502154113x^{28} \) \(\mathstrut +\mathstrut 24224789798x^{27} \) \(\mathstrut +\mathstrut 15152766533x^{26} \) \(\mathstrut -\mathstrut 113612777248x^{25} \) \(\mathstrut -\mathstrut 71456797540x^{24} \) \(\mathstrut +\mathstrut 404182681269x^{23} \) \(\mathstrut +\mathstrut 261401784490x^{22} \) \(\mathstrut -\mathstrut 1078900632199x^{21} \) \(\mathstrut -\mathstrut 733521886572x^{20} \) \(\mathstrut +\mathstrut 2122148793234x^{19} \) \(\mathstrut +\mathstrut 1550076768340x^{18} \) \(\mathstrut -\mathstrut 2991079606593x^{17} \) \(\mathstrut -\mathstrut 2404324635504x^{16} \) \(\mathstrut +\mathstrut 2889688891017x^{15} \) \(\mathstrut +\mathstrut 2646278115486x^{14} \) \(\mathstrut -\mathstrut 1764399735113x^{13} \) \(\mathstrut -\mathstrut 1973838845927x^{12} \) \(\mathstrut +\mathstrut 551685723463x^{11} \) \(\mathstrut +\mathstrut 930522569120x^{10} \) \(\mathstrut +\mathstrut 1896113944x^{9} \) \(\mathstrut -\mathstrut 243160998066x^{8} \) \(\mathstrut -\mathstrut 53416477930x^{7} \) \(\mathstrut +\mathstrut 24121560188x^{6} \) \(\mathstrut +\mathstrut 11263533068x^{5} \) \(\mathstrut +\mathstrut 1002782647x^{4} \) \(\mathstrut -\mathstrut 177217223x^{3} \) \(\mathstrut -\mathstrut 30288781x^{2} \) \(\mathstrut +\mathstrut 195578x \) \(\mathstrut +\mathstrut 151276\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, 2]$ $\phantom{-}e$
7 $[7, 7, w - 7]$ $...$
7 $[7, 7, w + 6]$ $...$
9 $[9, 3, 3]$ $...$
19 $[19, 19, w + 5]$ $...$
19 $[19, 19, w - 6]$ $...$
23 $[23, 23, w + 8]$ $...$
23 $[23, 23, -w + 9]$ $-1$
25 $[25, 5, 5]$ $...$
29 $[29, 29, -w - 4]$ $...$
29 $[29, 29, w - 5]$ $...$
37 $[37, 37, -w - 3]$ $...$
37 $[37, 37, w - 4]$ $...$
41 $[41, 41, -w - 9]$ $...$
41 $[41, 41, w - 10]$ $...$
43 $[43, 43, -w - 2]$ $...$
43 $[43, 43, w - 3]$ $...$
47 $[47, 47, -w - 1]$ $...$
47 $[47, 47, w - 2]$ $...$
53 $[53, 53, 2w - 13]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
23 $[23,23,-w + 9]$ $1$