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 |
$a_{2}$ |
$a_{3}$ |
$a_{5}$ |
$a_{7}$ |
1512.1.e.a |
$1512$ |
$1$ |
1512.e |
168.e |
$2$ |
$1$ |
$1$ |
$0.755$ |
\(\Q\) |
$D_{3}$ |
\(\Q(\sqrt{-42}) \) |
None |
✓ |
$2$ |
$0$ |
\(-1\) |
\(0\) |
\(0\) |
\(-1\) |
$1$ |
|
\(q-q^{2}+q^{4}-q^{7}-q^{8}+q^{13}+q^{14}+\cdots\) |
1512.1.e.b |
$1512$ |
$1$ |
1512.e |
168.e |
$2$ |
$1$ |
$1$ |
$0.755$ |
\(\Q\) |
$D_{3}$ |
\(\Q(\sqrt{-42}) \) |
None |
✓ |
$2$ |
$0$ |
\(-1\) |
\(0\) |
\(0\) |
\(1\) |
$1$ |
|
\(q-q^{2}+q^{4}+q^{7}-q^{8}-q^{13}-q^{14}+\cdots\) |
1512.1.e.c |
$1512$ |
$1$ |
1512.e |
168.e |
$2$ |
$1$ |
$1$ |
$0.755$ |
\(\Q\) |
$D_{3}$ |
\(\Q(\sqrt{-42}) \) |
None |
✓ |
$2$ |
$0$ |
\(1\) |
\(0\) |
\(0\) |
\(-1\) |
$1$ |
|
\(q+q^{2}+q^{4}-q^{7}+q^{8}+q^{13}-q^{14}+\cdots\) |
1512.1.e.d |
$1512$ |
$1$ |
1512.e |
168.e |
$2$ |
$1$ |
$1$ |
$0.755$ |
\(\Q\) |
$D_{3}$ |
\(\Q(\sqrt{-42}) \) |
None |
✓ |
$2$ |
$0$ |
\(1\) |
\(0\) |
\(0\) |
\(1\) |
$1$ |
|
\(q+q^{2}+q^{4}+q^{7}+q^{8}-q^{13}+q^{14}+\cdots\) |
2184.1.bf.i |
$2184$ |
$1$ |
2184.bf |
2184.af |
$2$ |
$2$ |
$2$ |
$1.090$ |
\(\Q(\sqrt{-1}) \) |
$D_{2}$ |
\(\Q(\sqrt{-26}) \), \(\Q(\sqrt{-42}) \) |
\(\Q(\sqrt{273}) \) |
|
$8$ |
$0$ |
\(0\) |
\(-2\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-iq^{2}-q^{3}-q^{4}+iq^{6}+iq^{7}+iq^{8}+\cdots\) |
2184.1.bf.j |
$2184$ |
$1$ |
2184.bf |
2184.af |
$2$ |
$2$ |
$2$ |
$1.090$ |
\(\Q(\sqrt{-1}) \) |
$D_{2}$ |
\(\Q(\sqrt{-26}) \), \(\Q(\sqrt{-42}) \) |
\(\Q(\sqrt{273}) \) |
|
$8$ |
$0$ |
\(0\) |
\(2\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-iq^{2}+q^{3}-q^{4}-iq^{6}-iq^{7}+iq^{8}+\cdots\) |
2184.1.cj.a |
$2184$ |
$1$ |
2184.cj |
2184.bj |
$6$ |
$2$ |
$1$ |
$1.090$ |
\(\Q(\sqrt{-3}) \) |
$D_{3}$ |
\(\Q(\sqrt{-42}) \) |
None |
|
$4$ |
$0$ |
\(-1\) |
\(-1\) |
\(0\) |
\(-1\) |
$1$ |
|
\(q-\zeta_{6}q^{2}-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{6}+\cdots\) |
2184.1.cj.b |
$2184$ |
$1$ |
2184.cj |
2184.bj |
$6$ |
$2$ |
$1$ |
$1.090$ |
\(\Q(\sqrt{-3}) \) |
$D_{3}$ |
\(\Q(\sqrt{-42}) \) |
None |
|
$4$ |
$0$ |
\(-1\) |
\(1\) |
\(0\) |
\(1\) |
$1$ |
|
\(q-\zeta_{6}q^{2}+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{6}+\cdots\) |
2184.1.cj.c |
$2184$ |
$1$ |
2184.cj |
2184.bj |
$6$ |
$2$ |
$1$ |
$1.090$ |
\(\Q(\sqrt{-3}) \) |
$D_{3}$ |
\(\Q(\sqrt{-42}) \) |
None |
|
$4$ |
$0$ |
\(1\) |
\(-1\) |
\(0\) |
\(1\) |
$1$ |
|
\(q+\zeta_{6}q^{2}-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{6}+\cdots\) |
2184.1.cj.d |
$2184$ |
$1$ |
2184.cj |
2184.bj |
$6$ |
$2$ |
$1$ |
$1.090$ |
\(\Q(\sqrt{-3}) \) |
$D_{3}$ |
\(\Q(\sqrt{-42}) \) |
None |
|
$4$ |
$0$ |
\(1\) |
\(1\) |
\(0\) |
\(-1\) |
$1$ |
|
\(q+\zeta_{6}q^{2}+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{6}+\cdots\) |
2184.1.gf.a |
$2184$ |
$1$ |
2184.gf |
2184.ff |
$6$ |
$4$ |
$2$ |
$1.090$ |
\(\Q(\zeta_{12})\) |
$D_{6}$ |
\(\Q(\sqrt{-42}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(-2\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+\zeta_{12}q^{2}+\zeta_{12}^{4}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{5}q^{6}+\cdots\) |
2184.1.gf.b |
$2184$ |
$1$ |
2184.gf |
2184.ff |
$6$ |
$4$ |
$2$ |
$1.090$ |
\(\Q(\zeta_{12})\) |
$D_{6}$ |
\(\Q(\sqrt{-42}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(2\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{12}q^{2}-\zeta_{12}^{4}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{5}q^{6}+\cdots\) |
2688.1.e.a |
$2688$ |
$1$ |
2688.e |
168.e |
$2$ |
$1$ |
$1$ |
$1.341$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-42}) \) |
\(\Q(\sqrt{7}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(-1\) |
\(0\) |
\(-1\) |
$1$ |
|
\(q-q^{3}-q^{7}+q^{9}+q^{21}+q^{25}-q^{27}+\cdots\) |
2688.1.e.b |
$2688$ |
$1$ |
2688.e |
168.e |
$2$ |
$1$ |
$1$ |
$1.341$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-42}) \) |
\(\Q(\sqrt{7}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(-1\) |
\(0\) |
\(1\) |
$1$ |
|
\(q-q^{3}+q^{7}+q^{9}-q^{21}+q^{25}-q^{27}+\cdots\) |
2688.1.e.c |
$2688$ |
$1$ |
2688.e |
168.e |
$2$ |
$1$ |
$1$ |
$1.341$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-42}) \) |
\(\Q(\sqrt{7}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(1\) |
\(0\) |
\(-1\) |
$1$ |
|
\(q+q^{3}-q^{7}+q^{9}-q^{21}+q^{25}+q^{27}+\cdots\) |
2688.1.e.d |
$2688$ |
$1$ |
2688.e |
168.e |
$2$ |
$1$ |
$1$ |
$1.341$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-42}) \) |
\(\Q(\sqrt{7}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(1\) |
\(0\) |
\(1\) |
$1$ |
|
\(q+q^{3}+q^{7}+q^{9}+q^{21}+q^{25}+q^{27}+\cdots\) |
2856.1.bd.i |
$2856$ |
$1$ |
2856.bd |
2856.ad |
$2$ |
$2$ |
$2$ |
$1.425$ |
\(\Q(\sqrt{-1}) \) |
$D_{2}$ |
\(\Q(\sqrt{-119}) \), \(\Q(\sqrt{-42}) \) |
\(\Q(\sqrt{102}) \) |
|
$8$ |
$0$ |
\(-2\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{2}-iq^{3}+q^{4}+iq^{6}+iq^{7}-q^{8}+\cdots\) |
2856.1.bd.j |
$2856$ |
$1$ |
2856.bd |
2856.ad |
$2$ |
$2$ |
$2$ |
$1.425$ |
\(\Q(\sqrt{-1}) \) |
$D_{2}$ |
\(\Q(\sqrt{-119}) \), \(\Q(\sqrt{-42}) \) |
\(\Q(\sqrt{102}) \) |
|
$8$ |
$0$ |
\(2\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+q^{2}-iq^{3}+q^{4}-iq^{6}-iq^{7}+q^{8}+\cdots\) |
2856.1.bt.a |
$2856$ |
$1$ |
2856.bt |
2856.at |
$4$ |
$4$ |
$2$ |
$1.425$ |
\(\Q(\zeta_{8})\) |
$D_{4}$ |
\(\Q(\sqrt{-42}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-q^{4}-\zeta_{8}^{3}q^{6}+\cdots\) |
2856.1.bt.b |
$2856$ |
$1$ |
2856.bt |
2856.at |
$4$ |
$4$ |
$2$ |
$1.425$ |
\(\Q(\zeta_{8})\) |
$D_{4}$ |
\(\Q(\sqrt{-42}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-q^{4}+\zeta_{8}^{3}q^{6}+\cdots\) |
2856.1.dg.a |
$2856$ |
$1$ |
2856.dg |
2856.cg |
$8$ |
$8$ |
$2$ |
$1.425$ |
\(\Q(\zeta_{16})\) |
$D_{8}$ |
\(\Q(\sqrt{-42}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{16}^{6}q^{2}+\zeta_{16}^{5}q^{3}-\zeta_{16}^{4}q^{4}+\cdots\) |
2856.1.dg.b |
$2856$ |
$1$ |
2856.dg |
2856.cg |
$8$ |
$8$ |
$2$ |
$1.425$ |
\(\Q(\zeta_{16})\) |
$D_{8}$ |
\(\Q(\sqrt{-42}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+\zeta_{16}^{6}q^{2}+\zeta_{16}^{5}q^{3}-\zeta_{16}^{4}q^{4}+\cdots\) |
3528.1.g.b |
$3528$ |
$1$ |
3528.g |
8.d |
$2$ |
$2$ |
$2$ |
$1.761$ |
\(\Q(\sqrt{-1}) \) |
$D_{2}$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-42}) \) |
\(\Q(\sqrt{6}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-iq^{2}-q^{4}+iq^{8}+q^{16}-iq^{23}+\cdots\) |
3528.1.bx.c |
$3528$ |
$1$ |
3528.bx |
56.k |
$6$ |
$4$ |
$2$ |
$1.761$ |
\(\Q(\zeta_{12})\) |
$D_{2}$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-42}) \) |
\(\Q(\sqrt{6}) \) |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{8}+\zeta_{12}^{4}q^{16}+\cdots\) |
3864.1.dl.a |
$3864$ |
$1$ |
3864.dl |
3864.cl |
$22$ |
$10$ |
$1$ |
$1.928$ |
\(\Q(\zeta_{22})\) |
$D_{11}$ |
\(\Q(\sqrt{-42}) \) |
None |
|
$4$ |
$0$ |
\(-1\) |
\(-1\) |
\(0\) |
\(-1\) |
$1$ |
|
\(q-\zeta_{22}^{5}q^{2}-\zeta_{22}^{7}q^{3}+\zeta_{22}^{10}q^{4}+\cdots\) |
3864.1.dl.b |
$3864$ |
$1$ |
3864.dl |
3864.cl |
$22$ |
$10$ |
$1$ |
$1.928$ |
\(\Q(\zeta_{22})\) |
$D_{11}$ |
\(\Q(\sqrt{-42}) \) |
None |
|
$4$ |
$0$ |
\(-1\) |
\(1\) |
\(0\) |
\(1\) |
$1$ |
|
\(q-\zeta_{22}^{5}q^{2}+\zeta_{22}^{7}q^{3}+\zeta_{22}^{10}q^{4}+\cdots\) |
3864.1.dl.c |
$3864$ |
$1$ |
3864.dl |
3864.cl |
$22$ |
$10$ |
$1$ |
$1.928$ |
\(\Q(\zeta_{22})\) |
$D_{11}$ |
\(\Q(\sqrt{-42}) \) |
None |
|
$4$ |
$0$ |
\(1\) |
\(-1\) |
\(0\) |
\(1\) |
$1$ |
|
\(q+\zeta_{22}^{5}q^{2}-\zeta_{22}^{7}q^{3}+\zeta_{22}^{10}q^{4}+\cdots\) |
3864.1.dl.d |
$3864$ |
$1$ |
3864.dl |
3864.cl |
$22$ |
$10$ |
$1$ |
$1.928$ |
\(\Q(\zeta_{22})\) |
$D_{11}$ |
\(\Q(\sqrt{-42}) \) |
None |
|
$4$ |
$0$ |
\(1\) |
\(1\) |
\(0\) |
\(-1\) |
$1$ |
|
\(q+\zeta_{22}^{5}q^{2}+\zeta_{22}^{7}q^{3}+\zeta_{22}^{10}q^{4}+\cdots\) |
504.2.p.c |
$504$ |
$2$ |
504.p |
56.e |
$2$ |
$4$ |
$4$ |
$4.024$ |
\(\Q(\sqrt{-2}, \sqrt{7})\) |
$_{}$ |
\(\Q(\sqrt{-42}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+\beta _{1}q^{2}-2q^{4}-\beta _{3}q^{7}-2\beta _{1}q^{8}+\cdots\) |
168.3.e.a |
$168$ |
$3$ |
168.e |
168.e |
$2$ |
$1$ |
$1$ |
$4.578$ |
\(\Q\) |
$_{}$ |
\(\Q(\sqrt{-42}) \) |
None |
✓ |
$2$ |
$0$ |
\(-2\) |
\(-3\) |
\(0\) |
\(-7\) |
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-2q^{2}-3q^{3}+4q^{4}+6q^{6}-7q^{7}+\cdots\) |
168.3.e.b |
$168$ |
$3$ |
168.e |
168.e |
$2$ |
$1$ |
$1$ |
$4.578$ |
\(\Q\) |
$_{}$ |
\(\Q(\sqrt{-42}) \) |
None |
✓ |
$2$ |
$0$ |
\(-2\) |
\(3\) |
\(0\) |
\(7\) |
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-2q^{2}+3q^{3}+4q^{4}-6q^{6}+7q^{7}+\cdots\) |
168.3.e.c |
$168$ |
$3$ |
168.e |
168.e |
$2$ |
$1$ |
$1$ |
$4.578$ |
\(\Q\) |
$_{}$ |
\(\Q(\sqrt{-42}) \) |
None |
✓ |
$2$ |
$0$ |
\(2\) |
\(-3\) |
\(0\) |
\(7\) |
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+2q^{2}-3q^{3}+4q^{4}-6q^{6}+7q^{7}+\cdots\) |
168.3.e.d |
$168$ |
$3$ |
168.e |
168.e |
$2$ |
$1$ |
$1$ |
$4.578$ |
\(\Q\) |
$_{}$ |
\(\Q(\sqrt{-42}) \) |
None |
✓ |
$2$ |
$0$ |
\(2\) |
\(3\) |
\(0\) |
\(-7\) |
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+2q^{2}+3q^{3}+4q^{4}+6q^{6}-7q^{7}+\cdots\) |
1344.2.i.c |
$1344$ |
$2$ |
1344.i |
168.i |
$2$ |
$8$ |
$8$ |
$10.732$ |
8.0.49787136.1 |
$_{}$ |
\(\Q(\sqrt{-42}) \) |
None |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{12}$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-\beta _{1}q^{3}+\beta _{3}q^{7}-3q^{9}+\beta _{7}q^{13}+\cdots\) |
2016.2.p.c |
$2016$ |
$2$ |
2016.p |
56.e |
$2$ |
$4$ |
$4$ |
$16.098$ |
\(\Q(\sqrt{-2}, \sqrt{7})\) |
$_{}$ |
\(\Q(\sqrt{-42}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{3}$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+\beta _{3}q^{7}-2\beta _{3}q^{13}+\beta _{2}q^{17}+\beta _{1}q^{23}+\cdots\) |
672.3.e.a |
$672$ |
$3$ |
672.e |
168.e |
$2$ |
$1$ |
$1$ |
$18.311$ |
\(\Q\) |
$_{}$ |
\(\Q(\sqrt{-42}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(-3\) |
\(0\) |
\(-7\) |
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-3q^{3}-7q^{7}+9q^{9}+2q^{13}-22q^{17}+\cdots\) |
672.3.e.b |
$672$ |
$3$ |
672.e |
168.e |
$2$ |
$1$ |
$1$ |
$18.311$ |
\(\Q\) |
$_{}$ |
\(\Q(\sqrt{-42}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(-3\) |
\(0\) |
\(7\) |
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-3q^{3}+7q^{7}+9q^{9}-2q^{13}-22q^{17}+\cdots\) |
672.3.e.c |
$672$ |
$3$ |
672.e |
168.e |
$2$ |
$1$ |
$1$ |
$18.311$ |
\(\Q\) |
$_{}$ |
\(\Q(\sqrt{-42}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(3\) |
\(0\) |
\(-7\) |
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+3q^{3}-7q^{7}+9q^{9}+2q^{13}+22q^{17}+\cdots\) |
672.3.e.d |
$672$ |
$3$ |
672.e |
168.e |
$2$ |
$1$ |
$1$ |
$18.311$ |
\(\Q\) |
$_{}$ |
\(\Q(\sqrt{-42}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(3\) |
\(0\) |
\(7\) |
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+3q^{3}+7q^{7}+9q^{9}-2q^{13}+22q^{17}+\cdots\) |