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 |
$a_{2}$ |
$a_{3}$ |
$a_{5}$ |
$a_{7}$ |
136.1.e.a |
$136$ |
$1$ |
136.e |
136.e |
$2$ |
$1$ |
$1$ |
$0.068$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-34}) \) |
\(\Q(\sqrt{17}) \) |
✓ |
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{2}+q^{4}-q^{8}+q^{9}+q^{16}-q^{17}+\cdots\) |
544.1.e.a |
$544$ |
$1$ |
544.e |
136.e |
$2$ |
$1$ |
$1$ |
$0.271$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-34}) \) |
\(\Q(\sqrt{17}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+q^{9}-q^{17}+2q^{19}-q^{25}-2q^{43}+\cdots\) |
680.1.k.e |
$680$ |
$1$ |
680.k |
680.k |
$2$ |
$4$ |
$4$ |
$0.339$ |
\(\Q(\zeta_{8})\) |
$D_{4}$ |
\(\Q(\sqrt{-34}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+\zeta_{8}^{2}q^{2}-q^{4}-\zeta_{8}q^{5}+(-\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{7}+\cdots\) |
952.1.bi.a |
$952$ |
$1$ |
952.bi |
952.ai |
$6$ |
$2$ |
$1$ |
$0.475$ |
\(\Q(\sqrt{-3}) \) |
$D_{3}$ |
\(\Q(\sqrt{-34}) \) |
None |
|
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(-1\) |
\(1\) |
$1$ |
|
\(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}+\cdots\) |
952.1.bi.b |
$952$ |
$1$ |
952.bi |
952.ai |
$6$ |
$2$ |
$1$ |
$0.475$ |
\(\Q(\sqrt{-3}) \) |
$D_{3}$ |
\(\Q(\sqrt{-34}) \) |
None |
|
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(1\) |
\(-1\) |
$1$ |
|
\(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}+\zeta_{6}^{2}q^{7}+\cdots\) |
952.1.bi.c |
$952$ |
$1$ |
952.bi |
952.ai |
$6$ |
$4$ |
$2$ |
$0.475$ |
\(\Q(\zeta_{12})\) |
$D_{6}$ |
\(\Q(\sqrt{-34}) \) |
None |
|
$8$ |
$0$ |
\(2\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{12}^{4}q^{2}-\zeta_{12}^{2}q^{4}+(-\zeta_{12}^{3}-\zeta_{12}^{5}+\cdots)q^{5}+\cdots\) |
1224.1.n.a |
$1224$ |
$1$ |
1224.n |
136.e |
$2$ |
$1$ |
$1$ |
$0.611$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-34}) \) |
\(\Q(\sqrt{17}) \) |
✓ |
$4$ |
$0$ |
\(1\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+q^{2}+q^{4}+q^{8}+q^{16}+q^{17}-2q^{19}+\cdots\) |
1224.1.n.b |
$1224$ |
$1$ |
1224.n |
136.e |
$2$ |
$2$ |
$2$ |
$0.611$ |
\(\Q(\sqrt{2}) \) |
$D_{4}$ |
\(\Q(\sqrt{-34}) \) |
None |
✓ |
$4$ |
$0$ |
\(-2\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{2}+q^{4}-\beta q^{5}-\beta q^{7}-q^{8}+\beta q^{10}+\cdots\) |
1224.1.n.c |
$1224$ |
$1$ |
1224.n |
136.e |
$2$ |
$2$ |
$2$ |
$0.611$ |
\(\Q(\sqrt{2}) \) |
$D_{4}$ |
\(\Q(\sqrt{-34}) \) |
None |
✓ |
$4$ |
$0$ |
\(2\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+q^{2}+q^{4}-\beta q^{5}+\beta q^{7}+q^{8}-\beta q^{10}+\cdots\) |
2176.1.e.a |
$2176$ |
$1$ |
2176.e |
136.e |
$2$ |
$1$ |
$1$ |
$1.086$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-34}) \) |
\(\Q(\sqrt{34}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(-2\) |
\(0\) |
$1$ |
|
\(q-2q^{5}+q^{9}-q^{17}+3q^{25}+2q^{29}+\cdots\) |
2176.1.e.b |
$2176$ |
$1$ |
2176.e |
136.e |
$2$ |
$1$ |
$1$ |
$1.086$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-17}) \), \(\Q(\sqrt{-34}) \) |
\(\Q(\sqrt{2}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(-2\) |
$1$ |
|
\(q-2q^{7}+q^{9}+q^{17}+2q^{23}-q^{25}+\cdots\) |
2176.1.e.c |
$2176$ |
$1$ |
2176.e |
136.e |
$2$ |
$1$ |
$1$ |
$1.086$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-17}) \), \(\Q(\sqrt{-34}) \) |
\(\Q(\sqrt{2}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(2\) |
$1$ |
|
\(q+2q^{7}+q^{9}+q^{17}-2q^{23}-q^{25}+\cdots\) |
2176.1.e.d |
$2176$ |
$1$ |
2176.e |
136.e |
$2$ |
$1$ |
$1$ |
$1.086$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-34}) \) |
\(\Q(\sqrt{34}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(2\) |
\(0\) |
$1$ |
|
\(q+2q^{5}+q^{9}-q^{17}+3q^{25}-2q^{29}+\cdots\) |
2312.1.f.a |
$2312$ |
$1$ |
2312.f |
8.d |
$2$ |
$1$ |
$1$ |
$1.154$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-34}) \) |
\(\Q(\sqrt{17}) \) |
✓ |
$4$ |
$0$ |
\(1\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+q^{2}+q^{4}+q^{8}-q^{9}+q^{16}-q^{18}+\cdots\) |
2312.1.j.a |
$2312$ |
$1$ |
2312.j |
136.j |
$4$ |
$2$ |
$1$ |
$1.154$ |
\(\Q(\sqrt{-1}) \) |
$D_{2}$ |
\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-34}) \) |
\(\Q(\sqrt{17}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+iq^{2}-q^{4}-iq^{8}+iq^{9}+q^{16}+\cdots\) |
2312.1.p.c |
$2312$ |
$1$ |
2312.p |
136.p |
$8$ |
$4$ |
$1$ |
$1.154$ |
\(\Q(\zeta_{8})\) |
$D_{2}$ |
\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-34}) \) |
\(\Q(\sqrt{17}) \) |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}-\zeta_{8}q^{8}-\zeta_{8}q^{9}+\cdots\) |
2584.1.bi.a |
$2584$ |
$1$ |
2584.bi |
2584.ai |
$6$ |
$2$ |
$1$ |
$1.290$ |
\(\Q(\sqrt{-3}) \) |
$D_{3}$ |
\(\Q(\sqrt{-34}) \) |
None |
|
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(-1\) |
\(-4\) |
$1$ |
|
\(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}-q^{7}+q^{8}+\cdots\) |
2584.1.bi.b |
$2584$ |
$1$ |
2584.bi |
2584.ai |
$6$ |
$2$ |
$1$ |
$1.290$ |
\(\Q(\sqrt{-3}) \) |
$D_{3}$ |
\(\Q(\sqrt{-34}) \) |
None |
|
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(1\) |
\(4\) |
$1$ |
|
\(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}+q^{7}+q^{8}+\cdots\) |
2584.1.bi.e |
$2584$ |
$1$ |
2584.bi |
2584.ai |
$6$ |
$4$ |
$2$ |
$1.290$ |
\(\Q(\zeta_{12})\) |
$D_{6}$ |
\(\Q(\sqrt{-34}) \) |
None |
|
$8$ |
$0$ |
\(2\) |
\(0\) |
\(0\) |
\(0\) |
$3$ |
|
\(q-\zeta_{12}^{4}q^{2}-\zeta_{12}^{2}q^{4}+(-\zeta_{12}^{3}-\zeta_{12}^{5}+\cdots)q^{5}+\cdots\) |
2584.1.ct.b |
$2584$ |
$1$ |
2584.ct |
2584.bt |
$18$ |
$6$ |
$1$ |
$1.290$ |
\(\Q(\zeta_{18})\) |
$D_{9}$ |
\(\Q(\sqrt{-34}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(-6\) |
\(-3\) |
$1$ |
|
\(q+\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}+(-1-\zeta_{18}^{2}+\cdots)q^{5}+\cdots\) |
2584.1.ct.c |
$2584$ |
$1$ |
2584.ct |
2584.bt |
$18$ |
$6$ |
$1$ |
$1.290$ |
\(\Q(\zeta_{18})\) |
$D_{9}$ |
\(\Q(\sqrt{-34}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(6\) |
\(3\) |
$1$ |
|
\(q+\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}+(1+\zeta_{18}^{2}+\cdots)q^{5}+\cdots\) |
2584.1.ct.e |
$2584$ |
$1$ |
2584.ct |
2584.bt |
$18$ |
$12$ |
$2$ |
$1.290$ |
\(\Q(\zeta_{36})\) |
$D_{18}$ |
\(\Q(\sqrt{-34}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$3$ |
|
\(q-\zeta_{36}^{8}q^{2}+\zeta_{36}^{16}q^{4}+(\zeta_{36}^{9}-\zeta_{36}^{13}+\cdots)q^{5}+\cdots\) |
2720.1.k.e |
$2720$ |
$1$ |
2720.k |
680.k |
$2$ |
$4$ |
$4$ |
$1.357$ |
\(\Q(\zeta_{8})\) |
$D_{4}$ |
\(\Q(\sqrt{-34}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+\zeta_{8}^{3}q^{5}+(-\zeta_{8}-\zeta_{8}^{3})q^{7}-q^{9}+\cdots\) |
3128.1.bx.a |
$3128$ |
$1$ |
3128.bx |
3128.ax |
$22$ |
$10$ |
$1$ |
$1.561$ |
\(\Q(\zeta_{22})\) |
$D_{11}$ |
\(\Q(\sqrt{-34}) \) |
None |
|
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(-9\) |
\(2\) |
$1$ |
|
\(q-\zeta_{22}^{9}q^{2}-\zeta_{22}^{7}q^{4}+(-1+\zeta_{22}^{9}+\cdots)q^{5}+\cdots\) |
3128.1.bx.b |
$3128$ |
$1$ |
3128.bx |
3128.ax |
$22$ |
$10$ |
$1$ |
$1.561$ |
\(\Q(\zeta_{22})\) |
$D_{11}$ |
\(\Q(\sqrt{-34}) \) |
None |
|
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(9\) |
\(-2\) |
$1$ |
|
\(q-\zeta_{22}^{9}q^{2}-\zeta_{22}^{7}q^{4}+(1-\zeta_{22}^{9}+\cdots)q^{5}+\cdots\) |
3128.1.bx.c |
$3128$ |
$1$ |
3128.bx |
3128.ax |
$22$ |
$20$ |
$2$ |
$1.561$ |
\(\Q(\zeta_{44})\) |
$D_{22}$ |
\(\Q(\sqrt{-34}) \) |
None |
|
$8$ |
$0$ |
\(2\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+\zeta_{44}^{10}q^{2}+\zeta_{44}^{20}q^{4}+(-\zeta_{44}^{11}+\cdots)q^{5}+\cdots\) |
3400.1.g.a |
$3400$ |
$1$ |
3400.g |
136.e |
$2$ |
$1$ |
$1$ |
$1.697$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-34}) \) |
\(\Q(\sqrt{17}) \) |
✓ |
$4$ |
$0$ |
\(1\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+q^{2}+q^{4}+q^{8}+q^{9}+q^{16}+q^{17}+\cdots\) |
3400.1.g.c |
$3400$ |
$1$ |
3400.g |
136.e |
$2$ |
$2$ |
$2$ |
$1.697$ |
\(\Q(\sqrt{2}) \) |
$D_{4}$ |
\(\Q(\sqrt{-34}) \) |
None |
✓ |
$4$ |
$0$ |
\(-2\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{2}+q^{4}-\beta q^{7}-q^{8}+q^{9}+\beta q^{14}+\cdots\) |
3400.1.g.g |
$3400$ |
$1$ |
3400.g |
136.e |
$2$ |
$2$ |
$2$ |
$1.697$ |
\(\Q(\sqrt{2}) \) |
$D_{4}$ |
\(\Q(\sqrt{-34}) \) |
None |
✓ |
$4$ |
$0$ |
\(2\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+q^{2}+q^{4}-\beta q^{7}+q^{8}+q^{9}-\beta q^{14}+\cdots\) |
3400.1.k.a |
$3400$ |
$1$ |
3400.k |
680.k |
$2$ |
$2$ |
$2$ |
$1.697$ |
\(\Q(\sqrt{-1}) \) |
$D_{2}$ |
\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-34}) \) |
\(\Q(\sqrt{17}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-iq^{2}-q^{4}+iq^{8}-q^{9}+q^{16}-iq^{17}+\cdots\) |
3400.1.ch.a |
$3400$ |
$1$ |
3400.ch |
3400.bh |
$10$ |
$16$ |
$4$ |
$1.697$ |
\(\Q(\zeta_{40})\) |
$D_{20}$ |
\(\Q(\sqrt{-34}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{40}^{18}q^{2}-\zeta_{40}^{16}q^{4}+\zeta_{40}^{15}q^{5}+\cdots\) |
3400.1.cs.a |
$3400$ |
$1$ |
3400.cs |
3400.bs |
$10$ |
$4$ |
$1$ |
$1.697$ |
\(\Q(\zeta_{10})\) |
$D_{5}$ |
\(\Q(\sqrt{-34}) \) |
None |
|
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(-4\) |
\(2\) |
$1$ |
|
\(q+\zeta_{10}^{2}q^{2}+\zeta_{10}^{4}q^{4}-q^{5}+(-\zeta_{10}^{2}+\cdots)q^{7}+\cdots\) |
3400.1.cs.b |
$3400$ |
$1$ |
3400.cs |
3400.bs |
$10$ |
$4$ |
$1$ |
$1.697$ |
\(\Q(\zeta_{10})\) |
$D_{5}$ |
\(\Q(\sqrt{-34}) \) |
None |
|
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(4\) |
\(-2\) |
$1$ |
|
\(q+\zeta_{10}^{2}q^{2}+\zeta_{10}^{4}q^{4}+q^{5}+(\zeta_{10}^{2}+\cdots)q^{7}+\cdots\) |
3400.1.cs.c |
$3400$ |
$1$ |
3400.cs |
3400.bs |
$10$ |
$8$ |
$2$ |
$1.697$ |
\(\Q(\zeta_{20})\) |
$D_{10}$ |
\(\Q(\sqrt{-34}) \) |
None |
|
$8$ |
$0$ |
\(2\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{20}^{4}q^{2}+\zeta_{20}^{8}q^{4}+\zeta_{20}^{5}q^{5}+\cdots\) |
3808.1.by.a |
$3808$ |
$1$ |
3808.by |
952.ai |
$6$ |
$2$ |
$1$ |
$1.900$ |
\(\Q(\sqrt{-3}) \) |
$D_{3}$ |
\(\Q(\sqrt{-34}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(-1\) |
\(-1\) |
$1$ |
|
\(q+\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}-\zeta_{6}q^{17}+\cdots\) |
3808.1.by.b |
$3808$ |
$1$ |
3808.by |
952.ai |
$6$ |
$2$ |
$1$ |
$1.900$ |
\(\Q(\sqrt{-3}) \) |
$D_{3}$ |
\(\Q(\sqrt{-34}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(1\) |
\(1\) |
$1$ |
|
\(q-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}-\zeta_{6}q^{17}+\cdots\) |
3808.1.by.c |
$3808$ |
$1$ |
3808.by |
952.ai |
$6$ |
$4$ |
$2$ |
$1.900$ |
\(\Q(\zeta_{12})\) |
$D_{6}$ |
\(\Q(\sqrt{-34}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+(-\zeta_{12}-\zeta_{12}^{3})q^{5}+\zeta_{12}q^{7}-\zeta_{12}^{2}q^{9}+\cdots\) |
3944.1.p.a |
$3944$ |
$1$ |
3944.p |
3944.p |
$2$ |
$4$ |
$4$ |
$1.968$ |
\(\Q(\zeta_{8})\) |
$D_{4}$ |
\(\Q(\sqrt{-34}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+\zeta_{8}^{2}q^{2}-q^{4}+(\zeta_{8}-\zeta_{8}^{3})q^{5}+(-\zeta_{8}+\cdots)q^{7}+\cdots\) |
3944.1.cf.a |
$3944$ |
$1$ |
3944.cf |
3944.bf |
$14$ |
$24$ |
$4$ |
$1.968$ |
\(\Q(\zeta_{56})\) |
$D_{28}$ |
\(\Q(\sqrt{-34}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{56}^{6}q^{2}+\zeta_{56}^{12}q^{4}+(\zeta_{56}^{15}+\zeta_{56}^{25}+\cdots)q^{5}+\cdots\) |
3944.1.cn.a |
$3944$ |
$1$ |
3944.cn |
3944.bn |
$14$ |
$6$ |
$1$ |
$1.968$ |
\(\Q(\zeta_{14})\) |
$D_{7}$ |
\(\Q(\sqrt{-34}) \) |
None |
|
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(-2\) |
\(-2\) |
$1$ |
|
\(q+\zeta_{14}^{6}q^{2}-\zeta_{14}^{5}q^{4}+(-\zeta_{14}+\zeta_{14}^{4}+\cdots)q^{5}+\cdots\) |
3944.1.cn.b |
$3944$ |
$1$ |
3944.cn |
3944.bn |
$14$ |
$6$ |
$1$ |
$1.968$ |
\(\Q(\zeta_{14})\) |
$D_{7}$ |
\(\Q(\sqrt{-34}) \) |
None |
|
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(2\) |
\(2\) |
$1$ |
|
\(q+\zeta_{14}^{6}q^{2}-\zeta_{14}^{5}q^{4}+(\zeta_{14}-\zeta_{14}^{4}+\cdots)q^{5}+\cdots\) |
3944.1.cn.c |
$3944$ |
$1$ |
3944.cn |
3944.bn |
$14$ |
$12$ |
$2$ |
$1.968$ |
\(\Q(\zeta_{28})\) |
$D_{14}$ |
\(\Q(\sqrt{-34}) \) |
None |
|
$8$ |
$0$ |
\(2\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{28}^{12}q^{2}-\zeta_{28}^{10}q^{4}+(\zeta_{28}-\zeta_{28}^{9}+\cdots)q^{5}+\cdots\) |
136.3.e.a |
$136$ |
$3$ |
136.e |
136.e |
$2$ |
$2$ |
$2$ |
$3.706$ |
\(\Q(\sqrt{17}) \) |
$_{}$ |
\(\Q(\sqrt{-34}) \) |
None |
✓ |
$4$ |
$0$ |
\(-4\) |
\(0\) |
\(0\) |
\(0\) |
$2^{2}$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-2q^{2}+4q^{4}+\beta q^{5}-\beta q^{7}-8q^{8}+\cdots\) |
136.3.e.c |
$136$ |
$3$ |
136.e |
136.e |
$2$ |
$2$ |
$2$ |
$3.706$ |
\(\Q(\sqrt{2}) \) |
$_{}$ |
\(\Q(\sqrt{-34}) \) |
None |
✓ |
$4$ |
$0$ |
\(4\) |
\(0\) |
\(0\) |
\(0\) |
$2^{2}$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+2q^{2}+4q^{4}+\beta q^{5}-2\beta q^{7}+8q^{8}+\cdots\) |
680.2.u.b |
$680$ |
$2$ |
680.u |
680.u |
$4$ |
$8$ |
$4$ |
$5.430$ |
8.0.\(\cdots\).13 |
$_{}$ |
\(\Q(\sqrt{-34}) \) |
None |
|
$8$ |
$0$ |
\(-8\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{U}(1)[D_{4}]$ |
\(q+(-1+\beta _{2})q^{2}-2\beta _{2}q^{4}-\beta _{1}q^{5}+\cdots\) |
680.2.u.c |
$680$ |
$2$ |
680.u |
680.u |
$4$ |
$8$ |
$4$ |
$5.430$ |
8.0.\(\cdots\).13 |
$_{}$ |
\(\Q(\sqrt{-34}) \) |
None |
|
$8$ |
$0$ |
\(8\) |
\(0\) |
\(0\) |
\(0\) |
$5$ |
$\mathrm{U}(1)[D_{4}]$ |
\(q+(1+\beta _{2})q^{2}+2\beta _{2}q^{4}-\beta _{5}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\) |
952.2.k.a |
$952$ |
$2$ |
952.k |
952.k |
$2$ |
$8$ |
$8$ |
$7.602$ |
8.0.5473632256.3 |
$_{}$ |
\(\Q(\sqrt{-34}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{6}$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+\beta _{3}q^{2}+2q^{4}+(-\beta _{1}-\beta _{6})q^{5}+\beta _{4}q^{7}+\cdots\) |
952.2.bf.a |
$952$ |
$2$ |
952.bf |
952.af |
$6$ |
$16$ |
$8$ |
$7.602$ |
\(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
$_{}$ |
\(\Q(\sqrt{-34}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{12}\cdot 7$ |
$\mathrm{U}(1)[D_{6}]$ |
\(q+(\beta _{2}+\beta _{6})q^{2}-2\beta _{5}q^{4}+(-\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\) |
1088.2.h.b |
$1088$ |
$2$ |
1088.h |
136.h |
$2$ |
$8$ |
$8$ |
$8.688$ |
8.0.342102016.5 |
$_{}$ |
\(\Q(\sqrt{-34}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{13}$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+\beta _{2}q^{5}-\beta _{4}q^{7}-3q^{9}+\beta _{1}q^{17}+\cdots\) |
1224.2.h.a |
$1224$ |
$2$ |
1224.h |
408.h |
$2$ |
$8$ |
$8$ |
$9.774$ |
8.0.\(\cdots\).11 |
$_{}$ |
\(\Q(\sqrt{-34}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{3}$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}-\beta _{4}q^{7}+2\beta _{1}q^{8}+\cdots\) |