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 |
$a_{2}$ |
$a_{3}$ |
$a_{5}$ |
$a_{7}$ |
145.1.h.a |
$145$ |
$1$ |
145.h |
145.h |
$4$ |
$2$ |
$1$ |
$0.072$ |
\(\Q(\sqrt{-1}) \) |
$D_{4}$ |
None |
\(\Q(\sqrt{29}) \) |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(-2\) |
$1$ |
|
\(q-iq^{4}-iq^{5}+(-1+i)q^{7}+iq^{9}+\cdots\) |
203.1.c.a |
$203$ |
$1$ |
203.c |
203.c |
$2$ |
$1$ |
$1$ |
$0.101$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-203}) \) |
\(\Q(\sqrt{29}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(-1\) |
$1$ |
|
\(q+q^{4}-q^{7}-q^{9}+q^{16}-2q^{23}+q^{25}+\cdots\) |
464.1.h.a |
$464$ |
$1$ |
464.h |
116.d |
$2$ |
$1$ |
$1$ |
$0.232$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-29}) \) |
\(\Q(\sqrt{29}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(2\) |
\(0\) |
$1$ |
|
\(q+2q^{5}-q^{9}-2q^{13}+3q^{25}-q^{29}+\cdots\) |
667.1.b.a |
$667$ |
$1$ |
667.b |
667.b |
$2$ |
$1$ |
$1$ |
$0.333$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-23}) \), \(\Q(\sqrt{-667}) \) |
\(\Q(\sqrt{29}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+q^{4}+q^{9}-2q^{13}+q^{16}-q^{23}+\cdots\) |
725.1.h.a |
$725$ |
$1$ |
725.h |
145.h |
$4$ |
$2$ |
$1$ |
$0.362$ |
\(\Q(\sqrt{-1}) \) |
$D_{4}$ |
None |
\(\Q(\sqrt{29}) \) |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(2\) |
$1$ |
|
\(q-iq^{4}+(1-i)q^{7}+iq^{9}+(-1-i+\cdots)q^{13}+\cdots\) |
812.1.o.a |
$812$ |
$1$ |
812.o |
203.i |
$6$ |
$2$ |
$1$ |
$0.405$ |
\(\Q(\sqrt{-3}) \) |
$D_{6}$ |
None |
\(\Q(\sqrt{29}) \) |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(-3\) |
\(1\) |
$1$ |
|
\(q+(-1-\zeta_{6})q^{5}+\zeta_{6}q^{7}-\zeta_{6}^{2}q^{9}+\cdots\) |
1015.1.f.a |
$1015$ |
$1$ |
1015.f |
1015.f |
$2$ |
$1$ |
$1$ |
$0.507$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-35}) \), \(\Q(\sqrt{-1015}) \) |
\(\Q(\sqrt{29}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(-1\) |
\(-1\) |
$1$ |
|
\(q-q^{4}-q^{5}-q^{7}+q^{9}+2q^{13}+q^{16}+\cdots\) |
1015.1.f.b |
$1015$ |
$1$ |
1015.f |
1015.f |
$2$ |
$1$ |
$1$ |
$0.507$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-35}) \), \(\Q(\sqrt{-1015}) \) |
\(\Q(\sqrt{29}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(1\) |
\(1\) |
$1$ |
|
\(q-q^{4}+q^{5}+q^{7}+q^{9}-2q^{13}+q^{16}+\cdots\) |
1305.1.o.a |
$1305$ |
$1$ |
1305.o |
145.h |
$4$ |
$2$ |
$1$ |
$0.651$ |
\(\Q(\sqrt{-1}) \) |
$D_{4}$ |
None |
\(\Q(\sqrt{29}) \) |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(-2\) |
$1$ |
|
\(q-iq^{4}+iq^{5}+(-1+i)q^{7}+(1+i+\cdots)q^{13}+\cdots\) |
1421.1.i.a |
$1421$ |
$1$ |
1421.i |
203.i |
$6$ |
$2$ |
$1$ |
$0.709$ |
\(\Q(\sqrt{-3}) \) |
$D_{2}$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-203}) \) |
\(\Q(\sqrt{29}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{9}+\zeta_{6}^{2}q^{16}-\zeta_{6}^{2}q^{23}+\cdots\) |
1711.1.d.a |
$1711$ |
$1$ |
1711.d |
1711.d |
$2$ |
$1$ |
$1$ |
$0.854$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-59}) \), \(\Q(\sqrt{-1711}) \) |
\(\Q(\sqrt{29}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(-2\) |
\(-2\) |
$1$ |
|
\(q-q^{4}-2q^{5}-2q^{7}+q^{9}+q^{16}+2q^{20}+\cdots\) |
1827.1.b.a |
$1827$ |
$1$ |
1827.b |
203.c |
$2$ |
$1$ |
$1$ |
$0.912$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-203}) \) |
\(\Q(\sqrt{29}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(-1\) |
$1$ |
|
\(q+q^{4}-q^{7}+q^{16}+2q^{23}+q^{25}+\cdots\) |
1856.1.h.b |
$1856$ |
$1$ |
1856.h |
116.d |
$2$ |
$1$ |
$1$ |
$0.926$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-29}) \) |
\(\Q(\sqrt{29}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(-2\) |
\(0\) |
$1$ |
|
\(q-2q^{5}-q^{9}+2q^{13}+3q^{25}+q^{29}+\cdots\) |
1885.1.v.a |
$1885$ |
$1$ |
1885.v |
1885.v |
$4$ |
$2$ |
$1$ |
$0.941$ |
\(\Q(\sqrt{-1}) \) |
$D_{4}$ |
None |
\(\Q(\sqrt{29}) \) |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(-2\) |
$1$ |
|
\(q-iq^{4}-iq^{5}+(-1+i)q^{7}-iq^{9}+\cdots\) |
1885.1.v.b |
$1885$ |
$1$ |
1885.v |
1885.v |
$4$ |
$2$ |
$1$ |
$0.941$ |
\(\Q(\sqrt{-1}) \) |
$D_{4}$ |
None |
\(\Q(\sqrt{29}) \) |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(2\) |
$1$ |
|
\(q-iq^{4}+iq^{5}+(1-i)q^{7}-iq^{9}+q^{13}+\cdots\) |
1943.1.d.a |
$1943$ |
$1$ |
1943.d |
1943.d |
$2$ |
$1$ |
$1$ |
$0.970$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-67}) \), \(\Q(\sqrt{-1943}) \) |
\(\Q(\sqrt{29}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{4}-q^{9}+q^{16}+2q^{23}+q^{25}+\cdots\) |
2059.1.b.a |
$2059$ |
$1$ |
2059.b |
2059.b |
$2$ |
$1$ |
$1$ |
$1.028$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-71}) \), \(\Q(\sqrt{-2059}) \) |
\(\Q(\sqrt{29}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(-2\) |
\(0\) |
$1$ |
|
\(q+q^{4}-2q^{5}+q^{9}+q^{16}-2q^{20}+\cdots\) |
2320.1.h.a |
$2320$ |
$1$ |
2320.h |
580.e |
$2$ |
$1$ |
$1$ |
$1.158$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-145}) \) |
\(\Q(\sqrt{29}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(-1\) |
\(-2\) |
$1$ |
|
\(q-q^{5}-2q^{7}+q^{9}+2q^{23}+q^{25}+\cdots\) |
2320.1.h.b |
$2320$ |
$1$ |
2320.h |
580.e |
$2$ |
$1$ |
$1$ |
$1.158$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-145}) \) |
\(\Q(\sqrt{29}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(-1\) |
\(2\) |
$1$ |
|
\(q-q^{5}+2q^{7}+q^{9}-2q^{23}+q^{25}+\cdots\) |
2320.1.bm.a |
$2320$ |
$1$ |
2320.bm |
145.h |
$4$ |
$2$ |
$1$ |
$1.158$ |
\(\Q(\sqrt{-1}) \) |
$D_{4}$ |
None |
\(\Q(\sqrt{29}) \) |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(2\) |
$1$ |
|
\(q+iq^{5}+(1+i)q^{7}-iq^{9}+(1-i)q^{13}+\cdots\) |
2407.1.d.a |
$2407$ |
$1$ |
2407.d |
2407.d |
$2$ |
$1$ |
$1$ |
$1.201$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-83}) \), \(\Q(\sqrt{-2407}) \) |
\(\Q(\sqrt{29}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(2\) |
$1$ |
|
\(q-q^{4}+2q^{7}+q^{9}+q^{16}-2q^{23}+\cdots\) |
2639.1.h.a |
$2639$ |
$1$ |
2639.h |
2639.h |
$2$ |
$1$ |
$1$ |
$1.317$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-91}) \), \(\Q(\sqrt{-2639}) \) |
\(\Q(\sqrt{29}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(-2\) |
\(-1\) |
$1$ |
|
\(q-q^{4}-2q^{5}-q^{7}-q^{9}-q^{13}+q^{16}+\cdots\) |
2639.1.h.b |
$2639$ |
$1$ |
2639.h |
2639.h |
$2$ |
$1$ |
$1$ |
$1.317$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-91}) \), \(\Q(\sqrt{-2639}) \) |
\(\Q(\sqrt{29}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(2\) |
\(1\) |
$1$ |
|
\(q-q^{4}+2q^{5}+q^{7}-q^{9}+q^{13}+q^{16}+\cdots\) |
2639.1.y.a |
$2639$ |
$1$ |
2639.y |
2639.y |
$6$ |
$2$ |
$1$ |
$1.317$ |
\(\Q(\sqrt{-3}) \) |
$D_{6}$ |
None |
\(\Q(\sqrt{29}) \) |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(-2\) |
$1$ |
|
\(q+q^{4}-q^{7}+\zeta_{6}q^{9}-\zeta_{6}^{2}q^{13}+q^{16}+\cdots\) |
2639.1.bk.a |
$2639$ |
$1$ |
2639.bk |
2639.ak |
$6$ |
$2$ |
$1$ |
$1.317$ |
\(\Q(\sqrt{-3}) \) |
$D_{6}$ |
None |
\(\Q(\sqrt{29}) \) |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(-2\) |
\(-1\) |
$1$ |
|
\(q-\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{7}-q^{9}+\cdots\) |
2639.1.bw.a |
$2639$ |
$1$ |
2639.bw |
2639.aw |
$6$ |
$2$ |
$1$ |
$1.317$ |
\(\Q(\sqrt{-3}) \) |
$D_{6}$ |
None |
\(\Q(\sqrt{29}) \) |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(1\) |
$1$ |
|
\(q-\zeta_{6}q^{4}+\zeta_{6}q^{7}-q^{9}+\zeta_{6}^{2}q^{13}+\cdots\) |
2639.1.bx.a |
$2639$ |
$1$ |
2639.bx |
2639.ax |
$6$ |
$2$ |
$1$ |
$1.317$ |
\(\Q(\sqrt{-3}) \) |
$D_{6}$ |
None |
\(\Q(\sqrt{29}) \) |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(2\) |
\(-2\) |
$1$ |
|
\(q-q^{4}+\zeta_{6}q^{5}-q^{7}-\zeta_{6}^{2}q^{9}+\zeta_{6}q^{13}+\cdots\) |
2987.1.c.a |
$2987$ |
$1$ |
2987.c |
2987.c |
$2$ |
$1$ |
$1$ |
$1.491$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-103}) \), \(\Q(\sqrt{-2987}) \) |
\(\Q(\sqrt{29}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(-2\) |
$1$ |
|
\(q+q^{4}-2q^{7}-q^{9}+2q^{13}+q^{16}+\cdots\) |
2987.1.j.a |
$2987$ |
$1$ |
2987.j |
2987.j |
$6$ |
$2$ |
$1$ |
$1.491$ |
\(\Q(\sqrt{-3}) \) |
$D_{6}$ |
None |
\(\Q(\sqrt{29}) \) |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(3\) |
\(-1\) |
$1$ |
|
\(q-\zeta_{6}q^{4}+(1-\zeta_{6}^{2})q^{5}-\zeta_{6}q^{7}-q^{9}+\cdots\) |
3103.1.d.a |
$3103$ |
$1$ |
3103.d |
3103.d |
$2$ |
$1$ |
$1$ |
$1.549$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-107}) \), \(\Q(\sqrt{-3103}) \) |
\(\Q(\sqrt{29}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{4}+q^{9}-2q^{13}+q^{16}+2q^{23}+\cdots\) |
3161.1.g.a |
$3161$ |
$1$ |
3161.g |
3161.g |
$4$ |
$2$ |
$1$ |
$1.578$ |
\(\Q(\sqrt{-1}) \) |
$D_{4}$ |
None |
\(\Q(\sqrt{29}) \) |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(4\) |
\(0\) |
$1$ |
|
\(q-iq^{4}+q^{5}+q^{9}+(-1-i)q^{13}+\cdots\) |
3248.1.k.b |
$3248$ |
$1$ |
3248.k |
203.c |
$2$ |
$1$ |
$1$ |
$1.621$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-203}) \) |
\(\Q(\sqrt{29}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(1\) |
$1$ |
|
\(q+q^{7}-q^{9}+2q^{23}+q^{25}-q^{29}+\cdots\) |
3248.1.bp.a |
$3248$ |
$1$ |
3248.bp |
812.n |
$6$ |
$2$ |
$1$ |
$1.621$ |
\(\Q(\sqrt{-3}) \) |
$D_{6}$ |
None |
\(\Q(\sqrt{29}) \) |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(1\) |
\(-1\) |
$1$ |
|
\(q+\zeta_{6}q^{5}+\zeta_{6}^{2}q^{7}+\zeta_{6}q^{9}+q^{13}+\cdots\) |
3248.1.bp.b |
$3248$ |
$1$ |
3248.bp |
812.n |
$6$ |
$2$ |
$1$ |
$1.621$ |
\(\Q(\sqrt{-3}) \) |
$D_{6}$ |
None |
\(\Q(\sqrt{29}) \) |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(1\) |
\(1\) |
$1$ |
|
\(q+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}+\zeta_{6}q^{9}+q^{13}+\cdots\) |
3248.1.bu.a |
$3248$ |
$1$ |
3248.bu |
203.i |
$6$ |
$2$ |
$1$ |
$1.621$ |
\(\Q(\sqrt{-3}) \) |
$D_{6}$ |
None |
\(\Q(\sqrt{29}) \) |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(-3\) |
\(-1\) |
$1$ |
|
\(q+(-1-\zeta_{6})q^{5}-\zeta_{6}q^{7}-\zeta_{6}^{2}q^{9}+\cdots\) |
3335.1.h.a |
$3335$ |
$1$ |
3335.h |
3335.h |
$2$ |
$1$ |
$1$ |
$1.664$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-115}) \), \(\Q(\sqrt{-3335}) \) |
\(\Q(\sqrt{29}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(-1\) |
\(2\) |
$1$ |
|
\(q-q^{4}-q^{5}+2q^{7}-q^{9}+q^{16}+q^{20}+\cdots\) |
3335.1.h.b |
$3335$ |
$1$ |
3335.h |
3335.h |
$2$ |
$1$ |
$1$ |
$1.664$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-115}) \), \(\Q(\sqrt{-3335}) \) |
\(\Q(\sqrt{29}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(1\) |
\(-2\) |
$1$ |
|
\(q-q^{4}+q^{5}-2q^{7}-q^{9}+q^{16}-q^{20}+\cdots\) |
3393.1.s.b |
$3393$ |
$1$ |
3393.s |
377.g |
$4$ |
$2$ |
$1$ |
$1.693$ |
\(\Q(\sqrt{-1}) \) |
$D_{4}$ |
None |
\(\Q(\sqrt{29}) \) |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(-2\) |
\(2\) |
$1$ |
|
\(q+iq^{4}+(-1-i)q^{5}+(1-i)q^{7}-q^{13}+\cdots\) |
3393.1.s.c |
$3393$ |
$1$ |
3393.s |
377.g |
$4$ |
$2$ |
$1$ |
$1.693$ |
\(\Q(\sqrt{-1}) \) |
$D_{4}$ |
None |
\(\Q(\sqrt{29}) \) |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(2\) |
\(2\) |
$1$ |
|
\(q+iq^{4}+(1+i)q^{5}+(1-i)q^{7}-q^{13}+\cdots\) |