Label |
Level |
Weight |
Char |
Prim |
Char order |
Dim |
Rel. Dim |
$A$ |
Field |
Image |
CM |
RM |
Self-dual |
Inner twists |
Rank* |
Traces |
Coefficient ring index |
Sato-Tate |
$q$-expansion |
$a_{2}$ |
$a_{3}$ |
$a_{5}$ |
$a_{7}$ |
592.1.b.a |
$592$ |
$1$ |
592.b |
148.b |
$2$ |
$1$ |
$1$ |
$0.295$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-37}) \) |
\(\Q(\sqrt{37}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+q^{9}+q^{25}-q^{37}-2q^{41}+q^{49}+\cdots\) |
1332.1.b.a |
$1332$ |
$1$ |
1332.b |
148.b |
$2$ |
$1$ |
$1$ |
$0.665$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-111}) \), \(\Q(\sqrt{-37}) \) |
\(\Q(\sqrt{3}) \) |
✓ |
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{2}+q^{4}-q^{8}+q^{16}+2q^{23}+q^{25}+\cdots\) |
1332.1.b.b |
$1332$ |
$1$ |
1332.b |
148.b |
$2$ |
$1$ |
$1$ |
$0.665$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-111}) \), \(\Q(\sqrt{-37}) \) |
\(\Q(\sqrt{3}) \) |
✓ |
$4$ |
$0$ |
\(1\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+q^{2}+q^{4}+q^{8}+q^{16}-2q^{23}+q^{25}+\cdots\) |
2368.1.b.a |
$2368$ |
$1$ |
2368.b |
148.b |
$2$ |
$1$ |
$1$ |
$1.182$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-37}) \) |
\(\Q(\sqrt{37}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+q^{9}+q^{25}+q^{37}-2q^{41}+q^{49}+\cdots\) |
2812.1.bj.a |
$2812$ |
$1$ |
2812.bj |
2812.aj |
$6$ |
$2$ |
$1$ |
$1.403$ |
\(\Q(\sqrt{-3}) \) |
$D_{3}$ |
\(\Q(\sqrt{-37}) \) |
None |
|
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+q^{8}-\zeta_{6}q^{9}+\zeta_{6}^{2}q^{16}+\cdots\) |
2812.1.bj.b |
$2812$ |
$1$ |
2812.bj |
2812.aj |
$6$ |
$2$ |
$1$ |
$1.403$ |
\(\Q(\sqrt{-3}) \) |
$D_{3}$ |
\(\Q(\sqrt{-37}) \) |
None |
|
$4$ |
$0$ |
\(1\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-q^{8}-\zeta_{6}q^{9}+\zeta_{6}^{2}q^{16}+\cdots\) |
2812.1.fj.a |
$2812$ |
$1$ |
2812.fj |
2812.ej |
$18$ |
$6$ |
$1$ |
$1.403$ |
\(\Q(\zeta_{18})\) |
$D_{9}$ |
\(\Q(\sqrt{-37}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{18}^{7}q^{2}-\zeta_{18}^{5}q^{4}-\zeta_{18}^{3}q^{8}+\cdots\) |
2812.1.fj.b |
$2812$ |
$1$ |
2812.fj |
2812.ej |
$18$ |
$6$ |
$1$ |
$1.403$ |
\(\Q(\zeta_{18})\) |
$D_{9}$ |
\(\Q(\sqrt{-37}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+\zeta_{18}^{7}q^{2}-\zeta_{18}^{5}q^{4}+\zeta_{18}^{3}q^{8}+\cdots\) |
3404.1.bn.a |
$3404$ |
$1$ |
3404.bn |
3404.an |
$22$ |
$10$ |
$1$ |
$1.699$ |
\(\Q(\zeta_{22})\) |
$D_{11}$ |
\(\Q(\sqrt{-37}) \) |
None |
|
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+\zeta_{22}^{8}q^{2}-\zeta_{22}^{5}q^{4}+\zeta_{22}^{2}q^{8}+\cdots\) |
3404.1.bn.b |
$3404$ |
$1$ |
3404.bn |
3404.an |
$22$ |
$10$ |
$1$ |
$1.699$ |
\(\Q(\zeta_{22})\) |
$D_{11}$ |
\(\Q(\sqrt{-37}) \) |
None |
|
$4$ |
$0$ |
\(1\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{22}^{8}q^{2}-\zeta_{22}^{5}q^{4}-\zeta_{22}^{2}q^{8}+\cdots\) |
3700.1.b.a |
$3700$ |
$1$ |
3700.b |
148.b |
$2$ |
$1$ |
$1$ |
$1.847$ |
\(\Q\) |
$D_{3}$ |
\(\Q(\sqrt{-37}) \) |
None |
✓ |
$2$ |
$0$ |
\(-1\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{2}+q^{4}-q^{8}+q^{9}+q^{16}-q^{18}+\cdots\) |
3700.1.b.b |
$3700$ |
$1$ |
3700.b |
148.b |
$2$ |
$1$ |
$1$ |
$1.847$ |
\(\Q\) |
$D_{3}$ |
\(\Q(\sqrt{-37}) \) |
None |
✓ |
$2$ |
$0$ |
\(-1\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{2}+q^{4}-q^{8}+q^{9}+q^{16}-q^{18}+\cdots\) |
3700.1.b.c |
$3700$ |
$1$ |
3700.b |
148.b |
$2$ |
$1$ |
$1$ |
$1.847$ |
\(\Q\) |
$D_{3}$ |
\(\Q(\sqrt{-37}) \) |
None |
✓ |
$2$ |
$0$ |
\(1\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+q^{2}+q^{4}+q^{8}+q^{9}+q^{16}+q^{18}+\cdots\) |
3700.1.b.d |
$3700$ |
$1$ |
3700.b |
148.b |
$2$ |
$1$ |
$1$ |
$1.847$ |
\(\Q\) |
$D_{3}$ |
\(\Q(\sqrt{-37}) \) |
None |
✓ |
$2$ |
$0$ |
\(1\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+q^{2}+q^{4}+q^{8}+q^{9}+q^{16}+q^{18}+\cdots\) |
3700.1.g.a |
$3700$ |
$1$ |
3700.g |
740.g |
$2$ |
$2$ |
$2$ |
$1.847$ |
\(\Q(\sqrt{-1}) \) |
$D_{3}$ |
\(\Q(\sqrt{-37}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-iq^{2}-q^{4}+iq^{8}-q^{9}+q^{16}+iq^{18}+\cdots\) |
3700.1.g.b |
$3700$ |
$1$ |
3700.g |
740.g |
$2$ |
$2$ |
$2$ |
$1.847$ |
\(\Q(\sqrt{-1}) \) |
$D_{3}$ |
\(\Q(\sqrt{-37}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-iq^{2}-q^{4}+iq^{8}-q^{9}+q^{16}+iq^{18}+\cdots\) |
148.3.b.a |
$148$ |
$3$ |
148.b |
148.b |
$2$ |
$1$ |
$1$ |
$4.033$ |
\(\Q\) |
$_{}$ |
\(\Q(\sqrt{-37}) \) |
None |
✓ |
$2$ |
$0$ |
\(-2\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-2q^{2}+4q^{4}-8q^{8}+9q^{9}+2^{4}q^{16}+\cdots\) |
148.3.b.b |
$148$ |
$3$ |
148.b |
148.b |
$2$ |
$1$ |
$1$ |
$4.033$ |
\(\Q\) |
$_{}$ |
\(\Q(\sqrt{-37}) \) |
None |
✓ |
$2$ |
$0$ |
\(2\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+2q^{2}+4q^{4}+8q^{8}+9q^{9}+2^{4}q^{16}+\cdots\) |
1184.2.g.d |
$1184$ |
$2$ |
1184.g |
37.b |
$2$ |
$4$ |
$4$ |
$9.454$ |
\(\Q(i, \sqrt{37})\) |
$_{}$ |
\(\Q(\sqrt{-37}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{4}$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-3q^{9}+\beta _{1}q^{19}+(\beta _{1}+\beta _{2})q^{23}+5q^{25}+\cdots\) |
1332.2.g.a |
$1332$ |
$2$ |
1332.g |
444.g |
$2$ |
$4$ |
$4$ |
$10.636$ |
\(\Q(\sqrt{-2}, \sqrt{37})\) |
$_{}$ |
\(\Q(\sqrt{-37}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{2}$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+\beta _{1}q^{2}-2q^{4}-2\beta _{1}q^{8}+4q^{16}+\cdots\) |
1332.2.g.b |
$1332$ |
$2$ |
1332.g |
444.g |
$2$ |
$4$ |
$4$ |
$10.636$ |
\(\Q(\sqrt{-2}, \sqrt{37})\) |
$_{}$ |
\(\Q(\sqrt{-37}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{2}$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+\beta _{1}q^{2}-2q^{4}-2\beta _{1}q^{8}+4q^{16}+\cdots\) |
148.5.b.a |
$148$ |
$5$ |
148.b |
148.b |
$2$ |
$1$ |
$1$ |
$15.299$ |
\(\Q\) |
$_{}$ |
\(\Q(\sqrt{-37}) \) |
None |
✓ |
$2$ |
$0$ |
\(-4\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-4q^{2}+2^{4}q^{4}-2^{6}q^{8}+3^{4}q^{9}+2^{8}q^{16}+\cdots\) |
148.5.b.b |
$148$ |
$5$ |
148.b |
148.b |
$2$ |
$1$ |
$1$ |
$15.299$ |
\(\Q\) |
$_{}$ |
\(\Q(\sqrt{-37}) \) |
None |
✓ |
$2$ |
$0$ |
\(4\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+4q^{2}+2^{4}q^{4}+2^{6}q^{8}+3^{4}q^{9}+2^{8}q^{16}+\cdots\) |
592.3.b.a |
$592$ |
$3$ |
592.b |
148.b |
$2$ |
$2$ |
$2$ |
$16.131$ |
\(\Q(\sqrt{37}) \) |
$_{}$ |
\(\Q(\sqrt{-37}) \) |
None |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{2}$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+9q^{9}+\beta q^{19}-3\beta q^{23}+5^{2}q^{25}+\cdots\) |
2368.2.g.i |
$2368$ |
$2$ |
2368.g |
37.b |
$2$ |
$4$ |
$4$ |
$18.909$ |
\(\Q(i, \sqrt{37})\) |
$_{}$ |
\(\Q(\sqrt{-37}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{4}$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-3q^{9}+\beta _{1}q^{19}+(-\beta _{1}-\beta _{2})q^{23}+\cdots\) |
5328.2.l.a |
$5328$ |
$2$ |
5328.l |
444.g |
$2$ |
$4$ |
$4$ |
$42.544$ |
\(\Q(\sqrt{-2}, \sqrt{37})\) |
$_{}$ |
\(\Q(\sqrt{-37}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{2}\cdot 3$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+(-1-\beta _{1})q^{19}-\beta _{2}q^{23}-5q^{25}+\cdots\) |
5328.2.l.c |
$5328$ |
$2$ |
5328.l |
444.g |
$2$ |
$4$ |
$4$ |
$42.544$ |
\(\Q(\sqrt{-2}, \sqrt{37})\) |
$_{}$ |
\(\Q(\sqrt{-37}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{2}\cdot 3$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+(1+\beta _{1})q^{19}-\beta _{2}q^{23}-5q^{25}+(5+\cdots)q^{31}+\cdots\) |
592.5.b.b |
$592$ |
$5$ |
592.b |
148.b |
$2$ |
$2$ |
$2$ |
$61.195$ |
\(\Q(\sqrt{37}) \) |
$_{}$ |
\(\Q(\sqrt{-37}) \) |
None |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{4}\cdot 3$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+3^{4}q^{9}-3\beta q^{19}+7\beta q^{23}+5^{4}q^{25}+\cdots\) |