# Properties

 Base field $$\Q(\sqrt{157})$$ Weight [2, 2] Level norm 12 Level $[12, 6, 2w + 12]$ Label 2.2.157.1-12.1-g Dimension 6 CM no Base change no

# Related objects

• L-function not available

## Base field $$\Q(\sqrt{157})$$

Generator $$w$$, with minimal polynomial $$x^{2} - x - 39$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2] Level $[12, 6, 2w + 12]$ Label 2.2.157.1-12.1-g Dimension 6 Is CM no Is base change no Parent newspace dimension 22

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{6}$$ $$\mathstrut -\mathstrut 3x^{5}$$ $$\mathstrut -\mathstrut 10x^{4}$$ $$\mathstrut +\mathstrut 33x^{3}$$ $$\mathstrut -\mathstrut 8x^{2}$$ $$\mathstrut -\mathstrut 8x$$ $$\mathstrut -\mathstrut 1$$
Norm Prime Eigenvalue
3 $[3, 3, w + 6]$ $-1$
3 $[3, 3, -w + 7]$ $\phantom{-}e$
4 $[4, 2, 2]$ $-1$
11 $[11, 11, -3w - 17]$ $\phantom{-}12e^{5} - 39e^{4} - 111e^{3} + 425e^{2} - 194e - 58$
11 $[11, 11, 3w - 20]$ $-3e^{5} + 10e^{4} + 27e^{3} - 109e^{2} + 57e + 14$
13 $[13, 13, 2w - 13]$ $\phantom{-}4e^{5} - 13e^{4} - 37e^{3} + 141e^{2} - 65e - 15$
13 $[13, 13, 2w + 11]$ $\phantom{-}4e^{5} - 13e^{4} - 37e^{3} + 142e^{2} - 63e - 23$
17 $[17, 17, w + 7]$ $\phantom{-}e^{3} - 11e + 4$
17 $[17, 17, -w + 8]$ $\phantom{-}19e^{5} - 61e^{4} - 178e^{3} + 664e^{2} - 284e - 91$
19 $[19, 19, -w - 4]$ $\phantom{-}2e^{5} - 6e^{4} - 19e^{3} + 66e^{2} - 27e - 11$
19 $[19, 19, -w + 5]$ $\phantom{-}17e^{5} - 55e^{4} - 158e^{3} + 599e^{2} - 266e - 83$
25 $[25, 5, 5]$ $\phantom{-}6e^{5} - 19e^{4} - 56e^{3} + 207e^{2} - 89e - 30$
31 $[31, 31, -6w - 35]$ $\phantom{-}26e^{5} - 83e^{4} - 243e^{3} + 904e^{2} - 393e - 123$
31 $[31, 31, -6w + 41]$ $\phantom{-}7e^{5} - 22e^{4} - 65e^{3} + 239e^{2} - 108e - 28$
37 $[37, 37, -w - 1]$ $\phantom{-}17e^{5} - 55e^{4} - 158e^{3} + 600e^{2} - 268e - 86$
37 $[37, 37, w - 2]$ $\phantom{-}17e^{5} - 55e^{4} - 159e^{3} + 599e^{2} - 256e - 86$
47 $[47, 47, 3w + 16]$ $-21e^{5} + 68e^{4} + 195e^{3} - 741e^{2} + 330e + 104$
47 $[47, 47, -3w + 19]$ $\phantom{-}13e^{5} - 42e^{4} - 122e^{3} + 457e^{2} - 193e - 59$
49 $[49, 7, -7]$ $-5e^{5} + 16e^{4} + 46e^{3} - 175e^{2} + 83e + 21$
67 $[67, 67, 3w - 22]$ $-31e^{5} + 99e^{4} + 289e^{3} - 1078e^{2} + 475e + 150$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 6]$ $1$
4 $[4, 2, 2]$ $1$