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✓ label
level
weight
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Pari/GP
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Label
Level
Weight
Char
Prim
Char order
Dim
Rel. Dim
$A$
Field
Image
CM
RM
Self-dual
Twist minimal
Largest
Maximal
Minimal twist
Inner twists
Rank*
Traces
Fricke sign
Coefficient ring index
Sato-Tate
$q$-expansion
$a_{2}$
$a_{3}$
$a_{5}$
$a_{7}$
1472.1.f.a
$1472$
$1$
1472.f
23.b
$2$
$1$
$1$
$0.735$
\(\Q\)
$D_{3}$
\(\Q(\sqrt{-23}) \)
None
✓
23.1.b.a
$2$
$0$
\(0\)
\(-1\)
\(0\)
\(0\)
$1$
\(q-q^{3}+q^{13}-q^{23}+q^{25}+q^{27}+\cdots\)
1472.1.f.b
$1472$
$1$
1472.f
23.b
$2$
$1$
$1$
$0.735$
\(\Q\)
$D_{3}$
\(\Q(\sqrt{-23}) \)
None
✓
23.1.b.a
$2$
$0$
\(0\)
\(1\)
\(0\)
\(0\)
$1$
\(q+q^{3}+q^{13}+q^{23}+q^{25}-q^{27}+\cdots\)
1472.1.k.a
$1472$
$1$
1472.k
368.k
$4$
$2$
$1$
$0.735$
\(\Q(\sqrt{-1}) \)
$D_{4}$
\(\Q(\sqrt{-23}) \)
None
368.1.k.a
$4$
$0$
\(0\)
\(-2\)
\(0\)
\(0\)
$1$
\(q+(-1-i)q^{3}+iq^{9}+(-1-i)q^{13}+\cdots\)
1472.1.k.b
$1472$
$1$
1472.k
368.k
$4$
$4$
$2$
$0.735$
\(\Q(\zeta_{12})\)
$D_{12}$
\(\Q(\sqrt{-23}) \)
None
✓
368.1.k.b
$4$
$0$
\(0\)
\(2\)
\(0\)
\(0\)
$2$
\(q+(-\zeta_{12}+\zeta_{12}^{2})q^{3}+(\zeta_{12}^{2}-\zeta_{12}^{3}+\cdots)q^{9}+\cdots\)
1472.1.s.a
$1472$
$1$
1472.s
1472.s
$16$
$8$
$1$
$0.735$
\(\Q(\zeta_{16})\)
$D_{16}$
\(\Q(\sqrt{-23}) \)
None
✓
1472.1.s.a
$4$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$1$
\(q+\zeta_{16}q^{2}+(\zeta_{16}-\zeta_{16}^{4})q^{3}+\zeta_{16}^{2}q^{4}+\cdots\)
1472.1.s.b
$1472$
$1$
1472.s
1472.s
$16$
$16$
$2$
$0.735$
\(\Q(\zeta_{48})\)
$D_{48}$
\(\Q(\sqrt{-23}) \)
None
✓
✓
1472.1.s.b
$4$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$1$
\(q+\zeta_{48}q^{2}+(-\zeta_{48}^{4}+\zeta_{48}^{17})q^{3}+\cdots\)
1472.2.a.a
$1472$
$2$
1472.a
1.a
$1$
$1$
$1$
$11.754$
\(\Q\)
$_{}$
None
None
✓
184.2.a.d
$1$
$0$
\(0\)
\(-3\)
\(0\)
\(-2\)
$-$
$1$
$\mathrm{SU}(2)$
\(q-3q^{3}-2q^{7}+6q^{9}+5q^{13}-6q^{17}+\cdots\)
1472.2.a.b
$1472$
$2$
1472.a
1.a
$1$
$1$
$1$
$11.754$
\(\Q\)
$_{}$
None
None
✓
92.2.a.a
$1$
$0$
\(0\)
\(-3\)
\(2\)
\(4\)
$-$
$1$
$\mathrm{SU}(2)$
\(q-3q^{3}+2q^{5}+4q^{7}+6q^{9}+2q^{11}+\cdots\)
1472.2.a.c
$1472$
$2$
1472.a
1.a
$1$
$1$
$1$
$11.754$
\(\Q\)
$_{}$
None
None
✓
92.2.a.b
$1$
$1$
\(0\)
\(-1\)
\(0\)
\(2\)
$+$
$1$
$\mathrm{SU}(2)$
\(q-q^{3}+2q^{7}-2q^{9}+q^{13}-6q^{17}+\cdots\)
1472.2.a.d
$1472$
$2$
1472.a
1.a
$1$
$1$
$1$
$11.754$
\(\Q\)
$_{}$
None
None
✓
184.2.a.b
$1$
$1$
\(0\)
\(-1\)
\(2\)
\(4\)
$+$
$1$
$\mathrm{SU}(2)$
\(q-q^{3}+2q^{5}+4q^{7}-2q^{9}-2q^{11}+\cdots\)
1472.2.a.e
$1472$
$2$
1472.a
1.a
$1$
$1$
$1$
$11.754$
\(\Q\)
$_{}$
None
None
✓
184.2.a.a
$1$
$0$
\(0\)
\(-1\)
\(4\)
\(-2\)
$-$
$1$
$\mathrm{SU}(2)$
\(q-q^{3}+4q^{5}-2q^{7}-2q^{9}-4q^{11}+\cdots\)
1472.2.a.f
$1472$
$2$
1472.a
1.a
$1$
$1$
$1$
$11.754$
\(\Q\)
$_{}$
None
None
✓
46.2.a.a
$1$
$0$
\(0\)
\(0\)
\(-4\)
\(-4\)
$-$
$1$
$\mathrm{SU}(2)$
\(q-4q^{5}-4q^{7}-3q^{9}-2q^{11}+2q^{13}+\cdots\)
1472.2.a.g
$1472$
$2$
1472.a
1.a
$1$
$1$
$1$
$11.754$
\(\Q\)
$_{}$
None
None
✓
46.2.a.a
$1$
$0$
\(0\)
\(0\)
\(-4\)
\(4\)
$-$
$1$
$\mathrm{SU}(2)$
\(q-4q^{5}+4q^{7}-3q^{9}+2q^{11}+2q^{13}+\cdots\)
1472.2.a.h
$1472$
$2$
1472.a
1.a
$1$
$1$
$1$
$11.754$
\(\Q\)
$_{}$
None
None
✓
184.2.a.c
$1$
$0$
\(0\)
\(0\)
\(0\)
\(-4\)
$-$
$1$
$\mathrm{SU}(2)$
\(q-4q^{7}-3q^{9}+6q^{11}+2q^{13}+6q^{17}+\cdots\)
1472.2.a.i
$1472$
$2$
1472.a
1.a
$1$
$1$
$1$
$11.754$
\(\Q\)
$_{}$
None
None
✓
184.2.a.c
$1$
$0$
\(0\)
\(0\)
\(0\)
\(4\)
$-$
$1$
$\mathrm{SU}(2)$
\(q+4q^{7}-3q^{9}-6q^{11}+2q^{13}+6q^{17}+\cdots\)
1472.2.a.j
$1472$
$2$
1472.a
1.a
$1$
$1$
$1$
$11.754$
\(\Q\)
$_{}$
None
None
✓
92.2.a.b
$1$
$1$
\(0\)
\(1\)
\(0\)
\(-2\)
$+$
$1$
$\mathrm{SU}(2)$
\(q+q^{3}-2q^{7}-2q^{9}+q^{13}-6q^{17}+\cdots\)
1472.2.a.k
$1472$
$2$
1472.a
1.a
$1$
$1$
$1$
$11.754$
\(\Q\)
$_{}$
None
None
✓
184.2.a.b
$1$
$1$
\(0\)
\(1\)
\(2\)
\(-4\)
$+$
$1$
$\mathrm{SU}(2)$
\(q+q^{3}+2q^{5}-4q^{7}-2q^{9}+2q^{11}+\cdots\)
1472.2.a.l
$1472$
$2$
1472.a
1.a
$1$
$1$
$1$
$11.754$
\(\Q\)
$_{}$
None
None
✓
184.2.a.a
$1$
$0$
\(0\)
\(1\)
\(4\)
\(2\)
$-$
$1$
$\mathrm{SU}(2)$
\(q+q^{3}+4q^{5}+2q^{7}-2q^{9}+4q^{11}+\cdots\)
1472.2.a.m
$1472$
$2$
1472.a
1.a
$1$
$1$
$1$
$11.754$
\(\Q\)
$_{}$
None
None
✓
184.2.a.d
$1$
$0$
\(0\)
\(3\)
\(0\)
\(2\)
$-$
$1$
$\mathrm{SU}(2)$
\(q+3q^{3}+2q^{7}+6q^{9}+5q^{13}-6q^{17}+\cdots\)
1472.2.a.n
$1472$
$2$
1472.a
1.a
$1$
$1$
$1$
$11.754$
\(\Q\)
$_{}$
None
None
✓
92.2.a.a
$1$
$0$
\(0\)
\(3\)
\(2\)
\(-4\)
$-$
$1$
$\mathrm{SU}(2)$
\(q+3q^{3}+2q^{5}-4q^{7}+6q^{9}-2q^{11}+\cdots\)
1472.2.a.o
$1472$
$2$
1472.a
1.a
$1$
$2$
$2$
$11.754$
\(\Q(\sqrt{2}) \)
$_{}$
None
None
✓
736.2.a.a
$1$
$1$
\(0\)
\(-2\)
\(4\)
\(-4\)
$+$
$1$
$\mathrm{SU}(2)$
\(q+(-1+\beta )q^{3}+(2-\beta )q^{5}+(-2+\beta )q^{7}+\cdots\)
1472.2.a.p
$1472$
$2$
1472.a
1.a
$1$
$2$
$2$
$11.754$
\(\Q(\sqrt{17}) \)
$_{}$
None
None
✓
184.2.a.e
$1$
$1$
\(0\)
\(-1\)
\(-4\)
\(0\)
$+$
$1$
$\mathrm{SU}(2)$
\(q-\beta q^{3}-2q^{5}+(1+\beta )q^{9}+2\beta q^{11}+\cdots\)
1472.2.a.q
$1472$
$2$
1472.a
1.a
$1$
$2$
$2$
$11.754$
\(\Q(\sqrt{3}) \)
$_{}$
None
None
✓
736.2.a.b
$1$
$1$
\(0\)
\(0\)
\(-2\)
\(-6\)
$+$
$1$
$\mathrm{SU}(2)$
\(q+\beta q^{3}+(-1-\beta )q^{5}+(-3+\beta )q^{7}+\cdots\)
1472.2.a.r
$1472$
$2$
1472.a
1.a
$1$
$2$
$2$
$11.754$
\(\Q(\sqrt{3}) \)
$_{}$
None
None
✓
736.2.a.b
$1$
$0$
\(0\)
\(0\)
\(-2\)
\(6\)
$-$
$1$
$\mathrm{SU}(2)$
\(q+\beta q^{3}+(-1+\beta )q^{5}+(3+\beta )q^{7}+(-3+\cdots)q^{11}+\cdots\)
1472.2.a.s
$1472$
$2$
1472.a
1.a
$1$
$2$
$2$
$11.754$
\(\Q(\sqrt{5}) \)
$_{}$
None
None
✓
23.2.a.a
$1$
$0$
\(0\)
\(0\)
\(2\)
\(-2\)
$-$
$2$
$\mathrm{SU}(2)$
\(q-\beta q^{3}+(1-\beta )q^{5}+(-1-\beta )q^{7}+2q^{9}+\cdots\)
1472.2.a.t
$1472$
$2$
1472.a
1.a
$1$
$2$
$2$
$11.754$
\(\Q(\sqrt{5}) \)
$_{}$
None
None
✓
23.2.a.a
$1$
$0$
\(0\)
\(0\)
\(2\)
\(2\)
$-$
$2$
$\mathrm{SU}(2)$
\(q-\beta q^{3}+(1+\beta )q^{5}+(1-\beta )q^{7}+2q^{9}+\cdots\)
1472.2.a.u
$1472$
$2$
1472.a
1.a
$1$
$2$
$2$
$11.754$
\(\Q(\sqrt{17}) \)
$_{}$
None
None
✓
184.2.a.e
$1$
$1$
\(0\)
\(1\)
\(-4\)
\(0\)
$+$
$1$
$\mathrm{SU}(2)$
\(q+\beta q^{3}-2q^{5}+(1+\beta )q^{9}-2\beta q^{11}+\cdots\)
1472.2.a.v
$1472$
$2$
1472.a
1.a
$1$
$2$
$2$
$11.754$
\(\Q(\sqrt{2}) \)
$_{}$
None
None
✓
736.2.a.a
$1$
$0$
\(0\)
\(2\)
\(4\)
\(4\)
$-$
$1$
$\mathrm{SU}(2)$
\(q+(1+\beta )q^{3}+(2+\beta )q^{5}+(2+\beta )q^{7}+\cdots\)
1472.2.a.w
$1472$
$2$
1472.a
1.a
$1$
$3$
$3$
$11.754$
3.3.316.1
$_{}$
None
None
✓
✓
736.2.a.e
$1$
$1$
\(0\)
\(-4\)
\(2\)
\(-2\)
$+$
$1$
$\mathrm{SU}(2)$
\(q+(-1-\beta _{1})q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+\cdots\)
1472.2.a.x
$1472$
$2$
1472.a
1.a
$1$
$3$
$3$
$11.754$
3.3.316.1
$_{}$
None
None
✓
✓
736.2.a.e
$1$
$0$
\(0\)
\(4\)
\(2\)
\(2\)
$-$
$1$
$\mathrm{SU}(2)$
\(q+(1+\beta _{1})q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+(1+\cdots)q^{7}+\cdots\)
1472.2.a.y
$1472$
$2$
1472.a
1.a
$1$
$4$
$4$
$11.754$
4.4.13768.1
$_{}$
None
None
✓
✓
736.2.a.g
$1$
$1$
\(0\)
\(-2\)
\(-6\)
\(-4\)
$+$
$2$
$\mathrm{SU}(2)$
\(q+\beta _{2}q^{3}+(-2+\beta _{3})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
1472.2.a.z
$1472$
$2$
1472.a
1.a
$1$
$4$
$4$
$11.754$
4.4.13768.1
$_{}$
None
None
✓
✓
736.2.a.g
$1$
$0$
\(0\)
\(2\)
\(-6\)
\(4\)
$-$
$2$
$\mathrm{SU}(2)$
\(q-\beta _{2}q^{3}+(-2+\beta _{3})q^{5}+(1-\beta _{1})q^{7}+\cdots\)
1472.2.b.a
$1472$
$2$
1472.b
8.b
$2$
$6$
$6$
$11.754$
6.0.399424.1
$_{}$
None
None
✓
1472.2.b.a
$2$
$0$
\(0\)
\(0\)
\(0\)
\(-4\)
$2^{3}$
$\mathrm{SU}(2)[C_{2}]$
\(q-\beta _{3}q^{3}+(-\beta _{3}-\beta _{5})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
1472.2.b.b
$1472$
$2$
1472.b
8.b
$2$
$6$
$6$
$11.754$
6.0.399424.1
$_{}$
None
None
✓
1472.2.b.a
$2$
$0$
\(0\)
\(0\)
\(0\)
\(4\)
$2^{3}$
$\mathrm{SU}(2)[C_{2}]$
\(q-\beta _{3}q^{3}+(\beta _{3}+\beta _{5})q^{5}+(1-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
1472.2.b.c
$1472$
$2$
1472.b
8.b
$2$
$16$
$16$
$11.754$
\(\mathbb{Q}[x]/(x^{16} + \cdots)\)
$_{}$
None
None
✓
1472.2.b.c
$2$
$0$
\(0\)
\(0\)
\(0\)
\(-4\)
$2^{17}$
$\mathrm{SU}(2)[C_{2}]$
\(q+\beta _{1}q^{3}+\beta _{11}q^{5}-\beta _{9}q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots\)
1472.2.b.d
$1472$
$2$
1472.b
8.b
$2$
$16$
$16$
$11.754$
\(\mathbb{Q}[x]/(x^{16} + \cdots)\)
$_{}$
None
None
✓
1472.2.b.c
$2$
$0$
\(0\)
\(0\)
\(0\)
\(4\)
$2^{17}$
$\mathrm{SU}(2)[C_{2}]$
\(q+\beta _{1}q^{3}-\beta _{11}q^{5}+\beta _{9}q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots\)
1472.2.c.a
$1472$
$2$
1472.c
92.b
$2$
$4$
$4$
$11.754$
\(\Q(\sqrt{2}, \sqrt{-5})\)
$_{}$
None
None
368.2.c.a
$4$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$2$
$\mathrm{SU}(2)[C_{2}]$
\(q+\beta _{3}q^{3}-\beta _{2}q^{5}-\beta _{1}q^{7}-2q^{9}+3\beta _{1}q^{11}+\cdots\)
1472.2.c.b
$1472$
$2$
1472.c
92.b
$2$
$4$
$4$
$11.754$
\(\Q(i, \sqrt{14})\)
$_{}$
None
None
92.2.b.a
$4$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$2$
$\mathrm{SU}(2)[C_{2}]$
\(q+\beta _{1}q^{3}+\beta _{2}q^{5}-\beta _{3}q^{7}+2q^{9}-\beta _{3}q^{11}+\cdots\)
1472.2.c.c
$1472$
$2$
1472.c
92.b
$2$
$6$
$6$
$11.754$
6.0.8869743.1
$_{}$
\(\Q(\sqrt{-23}) \)
None
92.2.b.b
$4$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$2^{7}$
$\mathrm{U}(1)[D_{2}]$
\(q-\beta _{1}q^{3}+(-3-\beta _{2})q^{9}+(-\beta _{2}-\beta _{4}+\cdots)q^{13}+\cdots\)
1472.2.c.d
$1472$
$2$
1472.c
92.b
$2$
$8$
$8$
$11.754$
8.0.303595776.1
$_{}$
None
None
368.2.c.b
$4$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$2^{8}$
$\mathrm{SU}(2)[C_{2}]$
\(q-\beta _{1}q^{3}+\beta _{4}q^{5}-\beta _{6}q^{7}+\beta _{7}q^{9}+\cdots\)
1472.2.c.e
$1472$
$2$
1472.c
92.b
$2$
$24$
$24$
$11.754$
$_{}$
None
None
✓
736.2.c.a
$4$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$\mathrm{SU}(2)[C_{2}]$
1472.2.h.a
$1472$
$2$
1472.h
184.h
$2$
$8$
$8$
$11.754$
8.0.\(\cdots\).3
$_{}$
\(\Q(\sqrt{-46}) \)
None
✓
1472.2.h.a
$8$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$2^{10}$
$\mathrm{U}(1)[D_{2}]$
\(q+\beta _{3}q^{5}-3q^{9}-\beta _{4}q^{11}+\beta _{7}q^{19}+\cdots\)
1472.2.h.b
$1472$
$2$
1472.h
184.h
$2$
$8$
$8$
$11.754$
8.0.157351936.1
$_{}$
None
None
✓
1472.2.h.b
$8$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$2^{6}$
$\mathrm{SU}(2)[C_{2}]$
\(q+\beta _{4}q^{3}+\beta _{3}q^{5}+\beta _{7}q^{7}+4q^{9}-\beta _{5}q^{11}+\cdots\)
1472.2.h.c
$1472$
$2$
1472.h
184.h
$2$
$32$
$32$
$11.754$
$_{}$
None
None
✓
✓
1472.2.h.c
$8$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$\mathrm{SU}(2)[C_{2}]$
1472.2.i.a
$1472$
$2$
1472.i
368.i
$4$
$12$
$6$
$11.754$
12.0.\(\cdots\).1
$_{}$
\(\Q(\sqrt{-23}) \)
None
368.2.i.a
$4$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$2^{8}$
$\mathrm{U}(1)[D_{4}]$
\(q+\beta _{3}q^{3}+(-3\beta _{1}-\beta _{3}+\beta _{4}+\beta _{11})q^{9}+\cdots\)
1472.2.i.b
$1472$
$2$
1472.i
368.i
$4$
$80$
$40$
$11.754$
$_{}$
None
None
✓
368.2.i.b
$4$
$0$
\(0\)
\(4\)
\(0\)
\(0\)
$\mathrm{SU}(2)[C_{4}]$
1472.2.j.a
$1472$
$2$
1472.j
16.e
$4$
$2$
$1$
$11.754$
\(\Q(\sqrt{-1}) \)
$_{}$
None
None
368.2.j.a
$2$
$1$
\(0\)
\(-2\)
\(0\)
\(0\)
$1$
$\mathrm{SU}(2)[C_{4}]$
\(q+(-1+i)q^{3}+4iq^{7}+iq^{9}+(-4+\cdots)q^{11}+\cdots\)
1472.2.j.b
$1472$
$2$
1472.j
16.e
$4$
$4$
$2$
$11.754$
\(\Q(\zeta_{12})\)
$_{}$
None
None
368.2.j.b
$2$
$0$
\(0\)
\(6\)
\(-4\)
\(0\)
$2$
$\mathrm{SU}(2)[C_{4}]$
\(q+(1-\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+(-1-\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
1472.2.j.c
$1472$
$2$
1472.j
16.e
$4$
$12$
$6$
$11.754$
12.0.\(\cdots\).1
$_{}$
None
None
368.2.j.c
$2$
$0$
\(0\)
\(-2\)
\(-4\)
\(0\)
$2^{3}$
$\mathrm{SU}(2)[C_{4}]$
\(q+\beta _{1}q^{3}+(-1+\beta _{2}+\beta _{3}+\beta _{5}-\beta _{6}+\cdots)q^{5}+\cdots\)
1472.2.j.d
$1472$
$2$
1472.j
16.e
$4$
$24$
$12$
$11.754$
$_{}$
None
None
368.2.j.d
$2$
$0$
\(0\)
\(4\)
\(4\)
\(0\)
$\mathrm{SU}(2)[C_{4}]$
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