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 |
$a_{2}$ |
$a_{3}$ |
$a_{5}$ |
$a_{7}$ |
260.1.g.a |
$260$ |
$1$ |
260.g |
260.g |
$2$ |
$1$ |
$1$ |
$0.130$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-65}) \) |
\(\Q(\sqrt{65}) \) |
✓ |
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(1\) |
\(0\) |
$1$ |
|
\(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{9}-q^{10}+\cdots\) |
260.1.g.b |
$260$ |
$1$ |
260.g |
260.g |
$2$ |
$1$ |
$1$ |
$0.130$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-65}) \) |
\(\Q(\sqrt{65}) \) |
✓ |
$4$ |
$0$ |
\(1\) |
\(0\) |
\(-1\) |
\(0\) |
$1$ |
|
\(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{9}-q^{10}+\cdots\) |
455.1.h.c |
$455$ |
$1$ |
455.h |
455.h |
$2$ |
$2$ |
$2$ |
$0.227$ |
\(\Q(\sqrt{-1}) \) |
$D_{2}$ |
\(\Q(\sqrt{-35}) \), \(\Q(\sqrt{-91}) \) |
\(\Q(\sqrt{65}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{4}-iq^{5}-iq^{7}-q^{9}-iq^{13}+\cdots\) |
520.1.b.a |
$520$ |
$1$ |
520.b |
520.b |
$2$ |
$2$ |
$2$ |
$0.260$ |
\(\Q(\sqrt{-1}) \) |
$D_{2}$ |
\(\Q(\sqrt{-10}) \), \(\Q(\sqrt{-26}) \) |
\(\Q(\sqrt{65}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-iq^{2}-q^{4}+iq^{5}-iq^{7}+iq^{8}+\cdots\) |
1040.1.cb.a |
$1040$ |
$1$ |
1040.cb |
1040.bb |
$4$ |
$4$ |
$2$ |
$0.519$ |
\(\Q(\zeta_{8})\) |
$D_{4}$ |
None |
\(\Q(\sqrt{65}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+\zeta_{8}q^{5}+(-\zeta_{8}+\cdots)q^{7}+\cdots\) |
1300.1.e.e |
$1300$ |
$1$ |
1300.e |
52.b |
$2$ |
$2$ |
$2$ |
$0.649$ |
\(\Q(\sqrt{-1}) \) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-65}) \) |
\(\Q(\sqrt{65}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-iq^{2}-q^{4}+iq^{8}+q^{9}-iq^{13}+\cdots\) |
2080.1.b.a |
$2080$ |
$1$ |
2080.b |
520.b |
$2$ |
$2$ |
$2$ |
$1.038$ |
\(\Q(\sqrt{-1}) \) |
$D_{2}$ |
\(\Q(\sqrt{-10}) \), \(\Q(\sqrt{-26}) \) |
\(\Q(\sqrt{65}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-iq^{5}-iq^{7}+q^{9}+iq^{13}-q^{25}+\cdots\) |
2275.1.b.a |
$2275$ |
$1$ |
2275.b |
91.b |
$2$ |
$1$ |
$1$ |
$1.135$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-35}) \), \(\Q(\sqrt{-91}) \) |
\(\Q(\sqrt{65}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(-1\) |
$1$ |
|
\(q+q^{4}-q^{7}+q^{9}+q^{13}+q^{16}-q^{28}+\cdots\) |
2275.1.b.b |
$2275$ |
$1$ |
2275.b |
91.b |
$2$ |
$1$ |
$1$ |
$1.135$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-35}) \), \(\Q(\sqrt{-91}) \) |
\(\Q(\sqrt{65}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(1\) |
$1$ |
|
\(q+q^{4}+q^{7}+q^{9}-q^{13}+q^{16}+q^{28}+\cdots\) |
2340.1.i.a |
$2340$ |
$1$ |
2340.i |
260.g |
$2$ |
$1$ |
$1$ |
$1.168$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-65}) \) |
\(\Q(\sqrt{65}) \) |
✓ |
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(1\) |
\(0\) |
$1$ |
|
\(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-q^{13}+\cdots\) |
2340.1.i.b |
$2340$ |
$1$ |
2340.i |
260.g |
$2$ |
$1$ |
$1$ |
$1.168$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-65}) \) |
\(\Q(\sqrt{65}) \) |
✓ |
$4$ |
$0$ |
\(1\) |
\(0\) |
\(-1\) |
\(0\) |
$1$ |
|
\(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+q^{13}+\cdots\) |
2405.1.bh.a |
$2405$ |
$1$ |
2405.bh |
2405.ah |
$4$ |
$4$ |
$2$ |
$1.200$ |
\(\Q(\zeta_{8})\) |
$D_{4}$ |
None |
\(\Q(\sqrt{65}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{8}q^{2}+3\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}+(-\zeta_{8}+\cdots)q^{7}+\cdots\) |
2405.1.ea.a |
$2405$ |
$1$ |
2405.ea |
2405.da |
$12$ |
$8$ |
$2$ |
$1.200$ |
\(\Q(\zeta_{24})\) |
$D_{12}$ |
None |
\(\Q(\sqrt{65}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{24}q^{2}+\zeta_{24}^{11}q^{5}+(\zeta_{24}^{7}+\zeta_{24}^{9}+\cdots)q^{7}+\cdots\) |
2600.1.o.a |
$2600$ |
$1$ |
2600.o |
104.h |
$2$ |
$1$ |
$1$ |
$1.298$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-10}) \), \(\Q(\sqrt{-26}) \) |
\(\Q(\sqrt{65}) \) |
✓ |
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(0\) |
\(-2\) |
$1$ |
|
\(q-q^{2}+q^{4}-2q^{7}-q^{8}-q^{9}+q^{13}+\cdots\) |
2600.1.o.c |
$2600$ |
$1$ |
2600.o |
104.h |
$2$ |
$1$ |
$1$ |
$1.298$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-10}) \), \(\Q(\sqrt{-26}) \) |
\(\Q(\sqrt{65}) \) |
✓ |
$4$ |
$0$ |
\(1\) |
\(0\) |
\(0\) |
\(2\) |
$1$ |
|
\(q+q^{2}+q^{4}+2q^{7}+q^{8}-q^{9}-q^{13}+\cdots\) |
2925.1.o.a |
$2925$ |
$1$ |
2925.o |
65.h |
$4$ |
$4$ |
$2$ |
$1.460$ |
\(\Q(\zeta_{8})\) |
$D_{2}$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-195}) \) |
\(\Q(\sqrt{65}) \) |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{8}^{2}q^{4}-\zeta_{8}q^{7}+\zeta_{8}^{3}q^{13}-q^{16}+\cdots\) |
3055.1.g.e |
$3055$ |
$1$ |
3055.g |
3055.g |
$2$ |
$2$ |
$2$ |
$1.525$ |
\(\Q(\sqrt{-1}) \) |
$D_{2}$ |
\(\Q(\sqrt{-235}) \), \(\Q(\sqrt{-611}) \) |
\(\Q(\sqrt{65}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{4}-iq^{5}+q^{9}-iq^{13}+q^{16}+\cdots\) |
3185.1.bf.c |
$3185$ |
$1$ |
3185.bf |
455.af |
$6$ |
$4$ |
$2$ |
$1.590$ |
\(\Q(\zeta_{12})\) |
$D_{2}$ |
\(\Q(\sqrt{-35}) \), \(\Q(\sqrt{-91}) \) |
\(\Q(\sqrt{65}) \) |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{12}^{4}q^{4}+\zeta_{12}^{5}q^{5}+\zeta_{12}^{2}q^{9}+\cdots\) |
3380.1.h.a |
$3380$ |
$1$ |
3380.h |
20.d |
$2$ |
$2$ |
$2$ |
$1.687$ |
\(\Q(\sqrt{-1}) \) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-65}) \) |
\(\Q(\sqrt{65}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+iq^{2}-q^{4}-iq^{5}-iq^{8}-q^{9}+q^{10}+\cdots\) |
3380.1.v.a |
$3380$ |
$1$ |
3380.v |
260.v |
$6$ |
$4$ |
$2$ |
$1.687$ |
\(\Q(\zeta_{12})\) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-65}) \) |
\(\Q(\sqrt{65}) \) |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{5}-\zeta_{12}^{3}q^{8}+\cdots\) |
3380.1.w.a |
$3380$ |
$1$ |
3380.w |
260.w |
$6$ |
$2$ |
$1$ |
$1.687$ |
\(\Q(\sqrt{-3}) \) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-65}) \) |
\(\Q(\sqrt{65}) \) |
|
$8$ |
$0$ |
\(-1\) |
\(0\) |
\(-2\) |
\(0\) |
$1$ |
|
\(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-q^{5}+q^{8}+\zeta_{6}q^{9}+\cdots\) |
3380.1.w.d |
$3380$ |
$1$ |
3380.w |
260.w |
$6$ |
$2$ |
$1$ |
$1.687$ |
\(\Q(\sqrt{-3}) \) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-65}) \) |
\(\Q(\sqrt{65}) \) |
|
$8$ |
$0$ |
\(1\) |
\(0\) |
\(2\) |
\(0\) |
$1$ |
|
\(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+q^{5}-q^{8}+\zeta_{6}q^{9}+\cdots\) |
3640.1.n.a |
$3640$ |
$1$ |
3640.n |
3640.n |
$2$ |
$1$ |
$1$ |
$1.817$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-14}) \), \(\Q(\sqrt{-910}) \) |
\(\Q(\sqrt{65}) \) |
✓ |
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(-1\) |
\(1\) |
$1$ |
|
\(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{9}+\cdots\) |
3640.1.n.b |
$3640$ |
$1$ |
3640.n |
3640.n |
$2$ |
$1$ |
$1$ |
$1.817$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-14}) \), \(\Q(\sqrt{-910}) \) |
\(\Q(\sqrt{65}) \) |
✓ |
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(1\) |
\(1\) |
$1$ |
|
\(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}+q^{9}+\cdots\) |
3640.1.n.c |
$3640$ |
$1$ |
3640.n |
3640.n |
$2$ |
$1$ |
$1$ |
$1.817$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-14}) \), \(\Q(\sqrt{-910}) \) |
\(\Q(\sqrt{65}) \) |
✓ |
$4$ |
$0$ |
\(1\) |
\(0\) |
\(-1\) |
\(-1\) |
$1$ |
|
\(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}+q^{9}+\cdots\) |
3640.1.n.d |
$3640$ |
$1$ |
3640.n |
3640.n |
$2$ |
$1$ |
$1$ |
$1.817$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-14}) \), \(\Q(\sqrt{-910}) \) |
\(\Q(\sqrt{65}) \) |
✓ |
$4$ |
$0$ |
\(1\) |
\(0\) |
\(1\) |
\(-1\) |
$1$ |
|
\(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{9}+\cdots\) |