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✓ label
level
weight
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relative dimension
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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
Inner twists
Rank*
Traces
Fricke sign
Coefficient ring index
Sato-Tate
$q$-expansion
$a_{2}$
$a_{3}$
$a_{5}$
$a_{7}$
4000.1.b.a
$4000$
$1$
4000.b
4.b
$2$
$4$
$4$
$1.996$
\(\Q(i, \sqrt{5})\)
$A_{5}$
None
None
$2$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$1$
\(q+(-\beta _{1}-\beta _{3})q^{3}-\beta _{3}q^{7}+(-1-\beta _{2}+\cdots)q^{9}+\cdots\)
4000.1.b.b
$4000$
$1$
4000.b
4.b
$2$
$4$
$4$
$1.996$
\(\Q(i, \sqrt{5})\)
$A_{5}$
None
None
$2$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$1$
\(q-\beta _{1}q^{3}+\beta _{3}q^{7}+\beta _{2}q^{9}-\beta _{3}q^{11}+\cdots\)
4000.1.e.a
$4000$
$1$
4000.e
40.e
$2$
$2$
$2$
$1.996$
\(\Q(\sqrt{5}) \)
$D_{5}$
\(\Q(\sqrt{-10}) \)
None
✓
$2$
$0$
\(0\)
\(0\)
\(0\)
\(-1\)
$1$
\(q-\beta q^{7}+q^{9}+(1-\beta )q^{11}+(1-\beta )q^{13}+\cdots\)
4000.1.e.b
$4000$
$1$
4000.e
40.e
$2$
$2$
$2$
$1.996$
\(\Q(\sqrt{5}) \)
$D_{5}$
\(\Q(\sqrt{-10}) \)
None
✓
$2$
$0$
\(0\)
\(0\)
\(0\)
\(1\)
$1$
\(q+\beta q^{7}+q^{9}+(1-\beta )q^{11}+(-1+\beta )q^{13}+\cdots\)
4000.1.g.a
$4000$
$1$
4000.g
8.d
$2$
$4$
$4$
$1.996$
\(\Q(i, \sqrt{5})\)
$D_{5}$
\(\Q(\sqrt{-10}) \)
None
$4$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$1$
\(q+(\beta _{1}+\beta _{3})q^{7}-q^{9}-\beta _{2}q^{11}-\beta _{1}q^{13}+\cdots\)
4000.1.h.a
$4000$
$1$
4000.h
20.d
$2$
$4$
$4$
$1.996$
\(\Q(i, \sqrt{5})\)
$A_{5}$
None
None
$2$
$0$
\(0\)
\(-2\)
\(0\)
\(4\)
$1$
\(q+(-1-\beta _{2})q^{3}+q^{7}+(1+\beta _{2})q^{9}+\cdots\)
4000.1.h.b
$4000$
$1$
4000.h
20.d
$2$
$4$
$4$
$1.996$
\(\Q(i, \sqrt{5})\)
$A_{5}$
None
None
$2$
$0$
\(0\)
\(2\)
\(0\)
\(-4\)
$1$
\(q+(1+\beta _{2})q^{3}-q^{7}+(1+\beta _{2})q^{9}+\beta _{3}q^{11}+\cdots\)
4000.1.p.a
$4000$
$1$
4000.p
5.c
$4$
$8$
$4$
$1.996$
\(\Q(\zeta_{20})\)
$D_{20}$
\(\Q(\sqrt{-5}) \)
None
$4$
$0$
\(0\)
\(-2\)
\(0\)
\(2\)
$2^{2}$
\(q+(-\zeta_{20}+\zeta_{20}^{4})q^{3}+(\zeta_{20}^{7}-\zeta_{20}^{8}+\cdots)q^{7}+\cdots\)
4000.1.p.b
$4000$
$1$
4000.p
5.c
$4$
$8$
$4$
$1.996$
\(\Q(\zeta_{20})\)
$D_{20}$
\(\Q(\sqrt{-5}) \)
None
$4$
$0$
\(0\)
\(2\)
\(0\)
\(-2\)
$2^{2}$
\(q+(\zeta_{20}^{6}+\zeta_{20}^{9})q^{3}+(-\zeta_{20}^{2}-\zeta_{20}^{3}+\cdots)q^{7}+\cdots\)
4000.1.bf.a
$4000$
$1$
4000.bf
100.h
$10$
$8$
$2$
$1.996$
\(\Q(\zeta_{20})\)
$A_{5}$
None
None
$4$
$0$
\(0\)
\(-2\)
\(0\)
\(4\)
$1$
\(q-\zeta_{20}^{2}q^{3}+(-\zeta_{20}^{4}+\zeta_{20}^{6})q^{7}+\cdots\)
4000.1.bf.b
$4000$
$1$
4000.bf
100.h
$10$
$8$
$2$
$1.996$
\(\Q(\zeta_{20})\)
$A_{5}$
None
None
$4$
$0$
\(0\)
\(2\)
\(0\)
\(-4\)
$1$
\(q+\zeta_{20}^{2}q^{3}+(\zeta_{20}^{4}-\zeta_{20}^{6})q^{7}+(-\zeta_{20}^{3}+\cdots)q^{13}+\cdots\)
4000.1.bh.a
$4000$
$1$
4000.bh
100.j
$10$
$8$
$2$
$1.996$
\(\Q(\zeta_{20})\)
$A_{5}$
None
None
$4$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$1$
\(q-\zeta_{20}q^{3}+(\zeta_{20}^{3}+\zeta_{20}^{7})q^{7}+(-1+\cdots)q^{13}+\cdots\)
4000.1.bo.a
$4000$
$1$
4000.bo
25.f
$20$
$8$
$1$
$1.996$
\(\Q(\zeta_{20})\)
$D_{20}$
\(\Q(\sqrt{-1}) \)
None
$4$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$1$
\(q-\zeta_{20}^{9}q^{9}+(-\zeta_{20}^{6}-\zeta_{20}^{7})q^{13}+\cdots\)
4000.1.bo.b
$4000$
$1$
4000.bo
25.f
$20$
$8$
$1$
$1.996$
\(\Q(\zeta_{20})\)
$D_{20}$
\(\Q(\sqrt{-1}) \)
None
$4$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$1$
\(q-\zeta_{20}^{9}q^{9}+(\zeta_{20}-\zeta_{20}^{2})q^{13}+(\zeta_{20}^{4}+\cdots)q^{17}+\cdots\)
4000.1.bo.c
$4000$
$1$
4000.bo
25.f
$20$
$8$
$1$
$1.996$
\(\Q(\zeta_{20})\)
$D_{20}$
\(\Q(\sqrt{-1}) \)
None
$4$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$1$
\(q-\zeta_{20}^{9}q^{9}+(\zeta_{20}^{6}+\zeta_{20}^{7})q^{13}+(\zeta_{20}^{2}+\cdots)q^{17}+\cdots\)
4000.1.cq.a
$4000$
$1$
4000.cq
125.i
$100$
$40$
$1$
$1.996$
\(\Q(\zeta_{100})\)
$D_{100}$
\(\Q(\sqrt{-1}) \)
None
$4$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$1$
\(q+\zeta_{100}^{13}q^{5}-\zeta_{100}^{49}q^{9}+(\zeta_{100}^{2}-\zeta_{100}^{21}+\cdots)q^{13}+\cdots\)
4000.2.a.a
$4000$
$2$
4000.a
1.a
$1$
$4$
$4$
$31.940$
\(\Q(\zeta_{20})^+\)
$_{}$
\(\Q(\sqrt{-5}) \)
None
✓
$2$
$1$
\(0\)
\(-6\)
\(0\)
\(-8\)
$+$
$1$
$N(\mathrm{U}(1))$
\(q+(-2-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(-1+2\beta _{1}+\cdots)q^{7}+\cdots\)
4000.2.a.b
$4000$
$2$
4000.a
1.a
$1$
$4$
$4$
$31.940$
\(\Q(\zeta_{20})^+\)
$_{}$
\(\Q(\sqrt{-5}) \)
None
✓
$2$
$1$
\(0\)
\(-4\)
\(0\)
\(-2\)
$+$
$1$
$N(\mathrm{U}(1))$
\(q+(-1+\beta _{1})q^{3}+(-1+\beta _{1}-\beta _{2}-\beta _{3})q^{7}+\cdots\)
4000.2.a.c
$4000$
$2$
4000.a
1.a
$1$
$4$
$4$
$31.940$
4.4.16400.1
$_{}$
None
None
✓
$2$
$0$
\(0\)
\(-2\)
\(0\)
\(-2\)
$-$
$2^{2}$
$\mathrm{SU}(2)$
\(q+\beta _{2}q^{3}+(-1-\beta _{2})q^{7}+(-2-\beta _{2}+\cdots)q^{9}+\cdots\)
4000.2.a.d
$4000$
$2$
4000.a
1.a
$1$
$4$
$4$
$31.940$
\(\Q(\zeta_{20})^+\)
$_{}$
None
None
✓
$2$
$1$
\(0\)
\(0\)
\(0\)
\(0\)
$+$
$1$
$\mathrm{SU}(2)$
\(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{7}+\beta _{2}q^{9}+\cdots\)
4000.2.a.e
$4000$
$2$
4000.a
1.a
$1$
$4$
$4$
$31.940$
\(\Q(\zeta_{20})^+\)
$_{}$
None
None
✓
$2$
$1$
\(0\)
\(0\)
\(0\)
\(0\)
$+$
$1$
$\mathrm{SU}(2)$
\(q+\beta _{1}q^{3}+\beta _{3}q^{7}+\beta _{2}q^{9}-2\beta _{3}q^{11}+\cdots\)
4000.2.a.f
$4000$
$2$
4000.a
1.a
$1$
$4$
$4$
$31.940$
\(\Q(\zeta_{20})^+\)
$_{}$
None
None
✓
$2$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$-$
$1$
$\mathrm{SU}(2)$
\(q+\beta _{1}q^{3}+\beta _{3}q^{7}+\beta _{2}q^{9}+2\beta _{3}q^{11}+\cdots\)
4000.2.a.g
$4000$
$2$
4000.a
1.a
$1$
$4$
$4$
$31.940$
\(\Q(\zeta_{20})^+\)
$_{}$
None
None
✓
$2$
$1$
\(0\)
\(0\)
\(0\)
\(0\)
$+$
$1$
$\mathrm{SU}(2)$
\(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{7}+\beta _{2}q^{9}+\cdots\)
4000.2.a.h
$4000$
$2$
4000.a
1.a
$1$
$4$
$4$
$31.940$
4.4.16400.1
$_{}$
None
None
✓
$2$
$1$
\(0\)
\(2\)
\(0\)
\(2\)
$+$
$2^{2}$
$\mathrm{SU}(2)$
\(q-\beta _{2}q^{3}+(1+\beta _{2})q^{7}+(-2-\beta _{2})q^{9}+\cdots\)
4000.2.a.i
$4000$
$2$
4000.a
1.a
$1$
$4$
$4$
$31.940$
\(\Q(\zeta_{20})^+\)
$_{}$
\(\Q(\sqrt{-5}) \)
None
✓
$2$
$0$
\(0\)
\(4\)
\(0\)
\(2\)
$-$
$1$
$N(\mathrm{U}(1))$
\(q+(1+\beta _{1})q^{3}+(1+\beta _{1}+\beta _{2}-\beta _{3})q^{7}+\cdots\)
4000.2.a.j
$4000$
$2$
4000.a
1.a
$1$
$4$
$4$
$31.940$
\(\Q(\zeta_{20})^+\)
$_{}$
\(\Q(\sqrt{-5}) \)
None
✓
$2$
$0$
\(0\)
\(6\)
\(0\)
\(8\)
$-$
$1$
$N(\mathrm{U}(1))$
\(q+(2-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(1+2\beta _{1}+\cdots)q^{7}+\cdots\)
4000.2.a.k
$4000$
$2$
4000.a
1.a
$1$
$6$
$6$
$31.940$
6.6.30040000.1
$_{}$
None
None
✓
$1$
$1$
\(0\)
\(0\)
\(0\)
\(-3\)
$+$
$1$
$\mathrm{SU}(2)$
\(q+\beta _{1}q^{3}+(-1+\beta _{5})q^{7}+(1+\beta _{1}+\beta _{3}+\cdots)q^{9}+\cdots\)
4000.2.a.l
$4000$
$2$
4000.a
1.a
$1$
$6$
$6$
$31.940$
6.6.30040000.1
$_{}$
None
None
✓
$1$
$0$
\(0\)
\(0\)
\(0\)
\(-3\)
$-$
$1$
$\mathrm{SU}(2)$
\(q+\beta _{1}q^{3}+(-1+\beta _{5})q^{7}+(1+\beta _{1}+\beta _{3}+\cdots)q^{9}+\cdots\)
4000.2.a.m
$4000$
$2$
4000.a
1.a
$1$
$6$
$6$
$31.940$
6.6.30040000.1
$_{}$
None
None
✓
$1$
$1$
\(0\)
\(0\)
\(0\)
\(3\)
$+$
$1$
$\mathrm{SU}(2)$
\(q-\beta _{1}q^{3}+(1-\beta _{5})q^{7}+(1+\beta _{1}+\beta _{3}+\cdots)q^{9}+\cdots\)
4000.2.a.n
$4000$
$2$
4000.a
1.a
$1$
$6$
$6$
$31.940$
6.6.30040000.1
$_{}$
None
None
✓
$1$
$0$
\(0\)
\(0\)
\(0\)
\(3\)
$-$
$1$
$\mathrm{SU}(2)$
\(q-\beta _{1}q^{3}+(1-\beta _{5})q^{7}+(1+\beta _{1}+\beta _{3}+\cdots)q^{9}+\cdots\)
4000.2.a.o
$4000$
$2$
4000.a
1.a
$1$
$8$
$8$
$31.940$
8.8.\(\cdots\).1
$_{}$
None
None
✓
$2$
$1$
\(0\)
\(0\)
\(0\)
\(0\)
$+$
$2^{4}$
$\mathrm{SU}(2)$
\(q-\beta _{4}q^{3}-\beta _{6}q^{7}+(1-\beta _{5})q^{9}+(\beta _{4}+\cdots)q^{11}+\cdots\)
4000.2.a.p
$4000$
$2$
4000.a
1.a
$1$
$8$
$8$
$31.940$
8.8.\(\cdots\).1
$_{}$
None
None
✓
$2$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$-$
$2^{4}$
$\mathrm{SU}(2)$
\(q-\beta _{4}q^{3}-\beta _{6}q^{7}+(1-\beta _{5})q^{9}+(-\beta _{4}+\cdots)q^{11}+\cdots\)
4000.2.a.q
$4000$
$2$
4000.a
1.a
$1$
$8$
$8$
$31.940$
8.8.\(\cdots\).1
$_{}$
None
None
✓
$2$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$-$
$2^{2}$
$\mathrm{SU}(2)$
\(q-\beta _{1}q^{3}+\beta _{7}q^{7}+(2+\beta _{2})q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
4000.2.a.r
$4000$
$2$
4000.a
1.a
$1$
$8$
$8$
$31.940$
8.8.\(\cdots\).1
$_{}$
None
None
✓
$2$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$-$
$2^{2}$
$\mathrm{SU}(2)$
\(q-\beta _{1}q^{3}+\beta _{7}q^{7}+(2+\beta _{2})q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
4000.2.c.a
$4000$
$2$
4000.c
5.b
$2$
$8$
$8$
$31.940$
\(\Q(\zeta_{20})\)
$_{}$
\(\Q(\sqrt{-5}) \)
None
$4$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$2^{8}$
$\mathrm{U}(1)[D_{2}]$
\(q+(\zeta_{20}^{3}+\zeta_{20}^{7})q^{3}+(\zeta_{20}^{2}-2\zeta_{20}^{3}+\cdots)q^{7}+\cdots\)
4000.2.c.b
$4000$
$2$
4000.c
5.b
$2$
$8$
$8$
$31.940$
\(\Q(\zeta_{20})\)
$_{}$
\(\Q(\sqrt{-5}) \)
None
$4$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$2^{8}$
$\mathrm{U}(1)[D_{2}]$
\(q-\zeta_{20}^{3}q^{3}+(\zeta_{20}^{3}-\zeta_{20}^{7})q^{7}+(-1+\cdots)q^{9}+\cdots\)
4000.2.c.c
$4000$
$2$
4000.c
5.b
$2$
$8$
$8$
$31.940$
\(\Q(\zeta_{20})\)
$_{}$
None
None
$4$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$2^{4}$
$\mathrm{SU}(2)[C_{2}]$
\(q-\zeta_{20}^{7}q^{3}+(\zeta_{20}^{2}-\zeta_{20}^{7})q^{7}+(1+\cdots)q^{9}+\cdots\)
4000.2.c.d
$4000$
$2$
4000.c
5.b
$2$
$8$
$8$
$31.940$
\(\Q(\zeta_{20})\)
$_{}$
None
None
$4$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$2^{8}$
$\mathrm{SU}(2)[C_{2}]$
\(q+\zeta_{20}^{2}q^{3}-\zeta_{20}^{7}q^{7}-\zeta_{20}^{5}q^{9}+\cdots\)
4000.2.c.e
$4000$
$2$
4000.c
5.b
$2$
$8$
$8$
$31.940$
8.0.268960000.3
$_{}$
None
None
$4$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$2^{8}$
$\mathrm{SU}(2)[C_{2}]$
\(q+(-\beta _{1}+\beta _{3})q^{3}+\beta _{3}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
4000.2.c.f
$4000$
$2$
4000.c
5.b
$2$
$12$
$12$
$31.940$
\(\mathbb{Q}[x]/(x^{12} + \cdots)\)
$_{}$
None
None
$2$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$2^{2}$
$\mathrm{SU}(2)[C_{2}]$
\(q+\beta _{1}q^{3}-\beta _{11}q^{7}+(\beta _{3}+\beta _{4}+\beta _{6}+\cdots)q^{9}+\cdots\)
4000.2.c.g
$4000$
$2$
4000.c
5.b
$2$
$12$
$12$
$31.940$
\(\mathbb{Q}[x]/(x^{12} + \cdots)\)
$_{}$
None
None
$2$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$2^{2}$
$\mathrm{SU}(2)[C_{2}]$
\(q+\beta _{1}q^{3}-\beta _{11}q^{7}+(\beta _{3}+\beta _{4}+\beta _{6}+\cdots)q^{9}+\cdots\)
4000.2.c.h
$4000$
$2$
4000.c
5.b
$2$
$16$
$16$
$31.940$
\(\mathbb{Q}[x]/(x^{16} - \cdots)\)
$_{}$
None
None
$4$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$2^{8}$
$\mathrm{SU}(2)[C_{2}]$
\(q-\beta _{3}q^{3}-\beta _{15}q^{7}+(-2+\beta _{4})q^{9}+\cdots\)
4000.2.c.i
$4000$
$2$
4000.c
5.b
$2$
$16$
$16$
$31.940$
\(\mathbb{Q}[x]/(x^{16} - \cdots)\)
$_{}$
None
None
$4$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$2^{20}$
$\mathrm{SU}(2)[C_{2}]$
\(q-\beta _{1}q^{3}-\beta _{12}q^{7}+(-1+\beta _{6})q^{9}+\cdots\)
4000.2.d.a
$4000$
$2$
4000.d
8.b
$2$
$4$
$4$
$31.940$
\(\Q(i, \sqrt{5})\)
$_{}$
None
None
$2$
$0$
\(0\)
\(0\)
\(0\)
\(-2\)
$1$
$\mathrm{SU}(2)[C_{2}]$
\(q+2\beta _{1}q^{3}+(1+3\beta _{2})q^{7}+(-1+4\beta _{2}+\cdots)q^{9}+\cdots\)
4000.2.d.b
$4000$
$2$
4000.d
8.b
$2$
$4$
$4$
$31.940$
\(\Q(i, \sqrt{5})\)
$_{}$
None
None
$2$
$0$
\(0\)
\(0\)
\(0\)
\(2\)
$1$
$\mathrm{SU}(2)[C_{2}]$
\(q+2\beta _{1}q^{3}+(-1-3\beta _{2})q^{7}+(-1+4\beta _{2}+\cdots)q^{9}+\cdots\)
4000.2.d.c
$4000$
$2$
4000.d
8.b
$2$
$40$
$40$
$31.940$
$_{}$
None
None
$4$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$\mathrm{SU}(2)[C_{2}]$
4000.2.d.d
$4000$
$2$
4000.d
8.b
$2$
$48$
$48$
$31.940$
$_{}$
None
None
$4$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$\mathrm{SU}(2)[C_{2}]$
4000.2.f.a
$4000$
$2$
4000.f
40.f
$2$
$4$
$4$
$31.940$
\(\Q(i, \sqrt{5})\)
$_{}$
None
None
$2$
$0$
\(0\)
\(-4\)
\(0\)
\(0\)
$1$
$\mathrm{SU}(2)[C_{2}]$
\(q+(-2-2\beta _{2})q^{3}+(3\beta _{1}+2\beta _{3})q^{7}+\cdots\)
4000.2.f.b
$4000$
$2$
4000.f
40.f
$2$
$4$
$4$
$31.940$
\(\Q(i, \sqrt{5})\)
$_{}$
None
None
$2$
$0$
\(0\)
\(4\)
\(0\)
\(0\)
$1$
$\mathrm{SU}(2)[C_{2}]$
\(q+(2+2\beta _{2})q^{3}+(3\beta _{1}+2\beta _{3})q^{7}+(5+\cdots)q^{9}+\cdots\)
4000.2.f.c
$4000$
$2$
4000.f
40.f
$2$
$20$
$20$
$31.940$
\(\mathbb{Q}[x]/(x^{20} - \cdots)\)
$_{}$
None
None
$2$
$0$
\(0\)
\(-4\)
\(0\)
\(0\)
$2^{14}$
$\mathrm{SU}(2)[C_{2}]$
\(q-\beta _{9}q^{3}+\beta _{5}q^{7}+(\beta _{1}-\beta _{7}+\beta _{10}+\cdots)q^{9}+\cdots\)
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