Properties

Base field \(\Q(\sqrt{109}) \)
Weight [2, 2]
Level norm 7
Level $[7,7,-w - 4]$
Label 2.2.109.1-7.2-b
Dimension 6
CM no
Base change no

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Base field \(\Q(\sqrt{109}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 27\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2]
Level $[7,7,-w - 4]$
Label 2.2.109.1-7.2-b
Dimension 6
Is CM no
Is base change no
Parent newspace dimension 13

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} \) \(\mathstrut -\mathstrut 2x^{5} \) \(\mathstrut -\mathstrut 17x^{4} \) \(\mathstrut +\mathstrut 30x^{3} \) \(\mathstrut +\mathstrut 81x^{2} \) \(\mathstrut -\mathstrut 87x \) \(\mathstrut -\mathstrut 143\)

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Norm Prime Eigenvalue
3 $[3, 3, -w + 6]$ $\phantom{-}e$
3 $[3, 3, w + 5]$ $-\frac{1}{5}e^{5} + \frac{17}{5}e^{3} + \frac{4}{5}e^{2} - \frac{68}{5}e - \frac{44}{5}$
4 $[4, 2, 2]$ $\phantom{-}\frac{8}{5}e^{5} + e^{4} - \frac{121}{5}e^{3} - \frac{77}{5}e^{2} + \frac{414}{5}e + \frac{402}{5}$
5 $[5, 5, -3w + 17]$ $\phantom{-}\frac{3}{5}e^{5} - \frac{46}{5}e^{3} - \frac{7}{5}e^{2} + \frac{154}{5}e + \frac{112}{5}$
5 $[5, 5, -3w - 14]$ $\phantom{-}\frac{9}{5}e^{5} + e^{4} - \frac{133}{5}e^{3} - \frac{76}{5}e^{2} + \frac{442}{5}e + \frac{406}{5}$
7 $[7, 7, w - 5]$ $\phantom{-}\frac{7}{5}e^{5} + e^{4} - \frac{104}{5}e^{3} - \frac{73}{5}e^{2} + \frac{346}{5}e + \frac{353}{5}$
7 $[7, 7, w + 4]$ $-1$
29 $[29, 29, -w - 7]$ $\phantom{-}\frac{7}{5}e^{5} + 2e^{4} - \frac{104}{5}e^{3} - \frac{138}{5}e^{2} + \frac{361}{5}e + \frac{503}{5}$
29 $[29, 29, -w + 8]$ $\phantom{-}3e^{5} + 2e^{4} - 45e^{3} - 31e^{2} + 152e + 159$
31 $[31, 31, -5w + 28]$ $-\frac{1}{5}e^{5} + \frac{17}{5}e^{3} + \frac{9}{5}e^{2} - \frac{63}{5}e - \frac{84}{5}$
31 $[31, 31, -5w - 23]$ $-3e^{5} - 3e^{4} + 44e^{3} + 41e^{2} - 148e - 166$
43 $[43, 43, 6w + 29]$ $-\frac{9}{5}e^{5} - e^{4} + \frac{143}{5}e^{3} + \frac{101}{5}e^{2} - \frac{527}{5}e - \frac{566}{5}$
43 $[43, 43, -6w + 35]$ $\phantom{-}e^{4} - 2e^{3} - 15e^{2} + 20e + 48$
61 $[61, 61, 3w - 19]$ $-\frac{27}{5}e^{5} - 4e^{4} + \frac{409}{5}e^{3} + \frac{308}{5}e^{2} - \frac{1421}{5}e - \frac{1503}{5}$
61 $[61, 61, -3w - 16]$ $-\frac{17}{5}e^{5} - e^{4} + \frac{254}{5}e^{3} + \frac{93}{5}e^{2} - \frac{836}{5}e - \frac{683}{5}$
71 $[71, 71, -7w - 34]$ $\phantom{-}7e^{5} + 4e^{4} - 104e^{3} - 62e^{2} + 349e + 333$
71 $[71, 71, 7w - 41]$ $-\frac{23}{5}e^{5} - e^{4} + \frac{346}{5}e^{3} + \frac{112}{5}e^{2} - \frac{1149}{5}e - \frac{917}{5}$
73 $[73, 73, 2w - 7]$ $\phantom{-}\frac{7}{5}e^{5} + 2e^{4} - \frac{104}{5}e^{3} - \frac{138}{5}e^{2} + \frac{351}{5}e + \frac{488}{5}$
73 $[73, 73, -2w - 5]$ $\phantom{-}\frac{17}{5}e^{5} + 2e^{4} - \frac{259}{5}e^{3} - \frac{163}{5}e^{2} + \frac{896}{5}e + \frac{868}{5}$
83 $[83, 83, -w - 10]$ $\phantom{-}\frac{4}{5}e^{5} - \frac{53}{5}e^{3} + \frac{4}{5}e^{2} + \frac{132}{5}e + \frac{81}{5}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
7 $[7,7,-w - 4]$ $1$