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columns to display
✓ label
level
weight
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relative dimension
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Pari/GP
SageMath
Magma
Oscar
CSV
Label
Level
Weight
Char
Prim
Char order
Dim
Rel. Dim
$A$
Field
CM
Self-dual
Twist minimal
Largest
Maximal
Minimal twist
Inner twists
Rank*
Traces
Fricke sign
Coefficient ring index
Sato-Tate
$q$-expansion
$a_{2}$
$a_{3}$
$a_{5}$
$a_{7}$
1001.4.a.a
$1001$
$4$
1001.a
1.a
$1$
$18$
$18$
$59.061$
\(\mathbb{Q}[x]/(x^{18} - \cdots)\)
None
✓
✓
✓
✓
1001.4.a.a
$1$
$1$
\(-4\)
\(-12\)
\(-34\)
\(126\)
$-$
$2^{9}$
$\mathrm{SU}(2)$
\(q-\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(2+\beta _{2})q^{4}+\cdots\)
1001.4.a.b
$1001$
$4$
1001.a
1.a
$1$
$18$
$18$
$59.061$
\(\mathbb{Q}[x]/(x^{18} - \cdots)\)
None
✓
✓
✓
✓
1001.4.a.b
$1$
$1$
\(0\)
\(0\)
\(-14\)
\(-126\)
$-$
$2^{9}$
$\mathrm{SU}(2)$
\(q-\beta _{1}q^{2}-\beta _{5}q^{3}+(2+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1001.4.a.c
$1001$
$4$
1001.a
1.a
$1$
$22$
$22$
$59.061$
None
✓
✓
✓
✓
1001.4.a.c
$1$
$1$
\(-4\)
\(-2\)
\(16\)
\(-154\)
$-$
$\mathrm{SU}(2)$
1001.4.a.d
$1001$
$4$
1001.a
1.a
$1$
$22$
$22$
$59.061$
None
✓
✓
✓
✓
1001.4.a.d
$1$
$1$
\(0\)
\(-14\)
\(0\)
\(154\)
$-$
$\mathrm{SU}(2)$
1001.4.a.e
$1001$
$4$
1001.a
1.a
$1$
$25$
$25$
$59.061$
None
✓
✓
✓
✓
1001.4.a.e
$1$
$0$
\(0\)
\(-8\)
\(-42\)
\(-175\)
$+$
$\mathrm{SU}(2)$
1001.4.a.f
$1001$
$4$
1001.a
1.a
$1$
$25$
$25$
$59.061$
None
✓
✓
✓
✓
1001.4.a.f
$1$
$0$
\(0\)
\(18\)
\(48\)
\(175\)
$+$
$\mathrm{SU}(2)$
1001.4.a.g
$1001$
$4$
1001.a
1.a
$1$
$25$
$25$
$59.061$
None
✓
✓
✓
✓
1001.4.a.g
$1$
$0$
\(4\)
\(4\)
\(-2\)
\(175\)
$+$
$\mathrm{SU}(2)$
1001.4.a.h
$1001$
$4$
1001.a
1.a
$1$
$25$
$25$
$59.061$
None
✓
✓
✓
✓
1001.4.a.h
$1$
$0$
\(4\)
\(6\)
\(44\)
\(-175\)
$+$
$\mathrm{SU}(2)$
1002.4.a.a
$1002$
$4$
1002.a
1.a
$1$
$7$
$7$
$59.120$
\(\mathbb{Q}[x]/(x^{7} - \cdots)\)
None
✓
✓
✓
✓
1002.4.a.a
$1$
$1$
\(14\)
\(21\)
\(-28\)
\(-59\)
$-$
$1$
$\mathrm{SU}(2)$
\(q+2q^{2}+3q^{3}+4q^{4}+(-4+\beta _{4}-\beta _{6})q^{5}+\cdots\)
1002.4.a.b
$1002$
$4$
1002.a
1.a
$1$
$8$
$8$
$59.120$
\(\mathbb{Q}[x]/(x^{8} - \cdots)\)
None
✓
✓
✓
✓
1002.4.a.b
$1$
$0$
\(-16\)
\(-24\)
\(2\)
\(19\)
$+$
$2\cdot 3$
$\mathrm{SU}(2)$
\(q-2q^{2}-3q^{3}+4q^{4}+\beta _{3}q^{5}+6q^{6}+\cdots\)
1002.4.a.c
$1002$
$4$
1002.a
1.a
$1$
$9$
$9$
$59.120$
\(\mathbb{Q}[x]/(x^{9} - \cdots)\)
None
✓
✓
✓
✓
1002.4.a.c
$1$
$1$
\(-18\)
\(27\)
\(2\)
\(-53\)
$-$
$1$
$\mathrm{SU}(2)$
\(q-2q^{2}+3q^{3}+4q^{4}-\beta _{5}q^{5}-6q^{6}+\cdots\)
1002.4.a.d
$1002$
$4$
1002.a
1.a
$1$
$10$
$10$
$59.120$
\(\mathbb{Q}[x]/(x^{10} - \cdots)\)
None
✓
✓
✓
✓
1002.4.a.d
$1$
$1$
\(20\)
\(-30\)
\(-22\)
\(-17\)
$-$
$5$
$\mathrm{SU}(2)$
\(q+2q^{2}-3q^{3}+4q^{4}+(-2+\beta _{5})q^{5}+\cdots\)
1002.4.a.e
$1002$
$4$
1002.a
1.a
$1$
$11$
$11$
$59.120$
\(\mathbb{Q}[x]/(x^{11} - \cdots)\)
None
✓
✓
✓
✓
1002.4.a.e
$1$
$1$
\(-22\)
\(-33\)
\(-18\)
\(5\)
$-$
$1$
$\mathrm{SU}(2)$
\(q-2q^{2}-3q^{3}+4q^{4}+(-2+\beta _{1})q^{5}+\cdots\)
1002.4.a.f
$1002$
$4$
1002.a
1.a
$1$
$11$
$11$
$59.120$
\(\mathbb{Q}[x]/(x^{11} - \cdots)\)
None
✓
✓
✓
✓
1002.4.a.f
$1$
$0$
\(22\)
\(-33\)
\(18\)
\(25\)
$+$
$2^{2}\cdot 5$
$\mathrm{SU}(2)$
\(q+2q^{2}-3q^{3}+4q^{4}+(2-\beta _{1})q^{5}+\cdots\)
1002.4.a.g
$1002$
$4$
1002.a
1.a
$1$
$12$
$12$
$59.120$
\(\mathbb{Q}[x]/(x^{12} - \cdots)\)
None
✓
✓
✓
✓
1002.4.a.g
$1$
$0$
\(-24\)
\(36\)
\(-8\)
\(45\)
$+$
$2\cdot 3$
$\mathrm{SU}(2)$
\(q-2q^{2}+3q^{3}+4q^{4}+(-1+\beta _{1})q^{5}+\cdots\)
1002.4.a.h
$1002$
$4$
1002.a
1.a
$1$
$14$
$14$
$59.120$
\(\mathbb{Q}[x]/(x^{14} - \cdots)\)
None
✓
✓
✓
✓
1002.4.a.h
$1$
$0$
\(28\)
\(42\)
\(42\)
\(67\)
$+$
$2^{2}$
$\mathrm{SU}(2)$
\(q+2q^{2}+3q^{3}+4q^{4}+(3-\beta _{1})q^{5}+\cdots\)
1003.4.a.a
$1003$
$4$
1003.a
1.a
$1$
$3$
$3$
$59.179$
3.3.75845.1
None
✓
✓
1003.4.a.a
$1$
$1$
\(-3\)
\(-5\)
\(17\)
\(-2\)
$-$
$1$
$\mathrm{SU}(2)$
\(q-q^{2}+(-2-\beta _{2})q^{3}-7q^{4}+(6+\beta _{2})q^{5}+\cdots\)
1003.4.a.b
$1003$
$4$
1003.a
1.a
$1$
$52$
$52$
$59.179$
None
✓
✓
✓
1003.4.a.b
$1$
$1$
\(-8\)
\(-19\)
\(-95\)
\(-50\)
$-$
$\mathrm{SU}(2)$
1003.4.a.c
$1003$
$4$
1003.a
1.a
$1$
$57$
$57$
$59.179$
None
✓
✓
✓
✓
1003.4.a.c
$1$
$1$
\(-11\)
\(-18\)
\(-132\)
\(-52\)
$-$
$\mathrm{SU}(2)$
1003.4.a.d
$1003$
$4$
1003.a
1.a
$1$
$59$
$59$
$59.179$
None
✓
✓
✓
✓
1003.4.a.d
$1$
$0$
\(13\)
\(12\)
\(102\)
\(-24\)
$+$
$\mathrm{SU}(2)$
1003.4.a.e
$1003$
$4$
1003.a
1.a
$1$
$61$
$61$
$59.179$
None
✓
✓
✓
✓
1003.4.a.e
$1$
$0$
\(13\)
\(30\)
\(128\)
\(116\)
$+$
$\mathrm{SU}(2)$
1004.4.a.a
$1004$
$4$
1004.a
1.a
$1$
$28$
$28$
$59.238$
None
✓
✓
✓
✓
1004.4.a.a
$1$
$1$
\(0\)
\(-6\)
\(0\)
\(-57\)
$-$
$\mathrm{SU}(2)$
1004.4.a.b
$1004$
$4$
1004.a
1.a
$1$
$35$
$35$
$59.238$
None
✓
✓
✓
✓
1004.4.a.b
$1$
$0$
\(0\)
\(12\)
\(0\)
\(41\)
$+$
$\mathrm{SU}(2)$
1005.4.a.a
$1005$
$4$
1005.a
1.a
$1$
$2$
$2$
$59.297$
\(\Q(\sqrt{19}) \)
None
✓
✓
1005.4.a.a
$1$
$1$
\(6\)
\(6\)
\(10\)
\(-12\)
$-$
$1$
$\mathrm{SU}(2)$
\(q+3q^{2}+3q^{3}+q^{4}+5q^{5}+9q^{6}+\cdots\)
1005.4.a.b
$1005$
$4$
1005.a
1.a
$1$
$12$
$12$
$59.297$
\(\mathbb{Q}[x]/(x^{12} - \cdots)\)
None
✓
✓
✓
1005.4.a.b
$1$
$1$
\(-16\)
\(36\)
\(60\)
\(-45\)
$-$
$2^{3}\cdot 5$
$\mathrm{SU}(2)$
\(q+(-1-\beta _{1})q^{2}+3q^{3}+(3+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1005.4.a.c
$1005$
$4$
1005.a
1.a
$1$
$14$
$14$
$59.297$
\(\mathbb{Q}[x]/(x^{14} - \cdots)\)
None
✓
✓
✓
✓
1005.4.a.c
$1$
$1$
\(2\)
\(-42\)
\(-70\)
\(1\)
$-$
$2^{6}$
$\mathrm{SU}(2)$
\(q+\beta _{1}q^{2}-3q^{3}+(3+\beta _{2})q^{4}-5q^{5}+\cdots\)
1005.4.a.d
$1005$
$4$
1005.a
1.a
$1$
$17$
$17$
$59.297$
\(\mathbb{Q}[x]/(x^{17} - \cdots)\)
None
✓
✓
✓
✓
1005.4.a.d
$1$
$1$
\(-5\)
\(-51\)
\(85\)
\(-57\)
$-$
$2^{3}$
$\mathrm{SU}(2)$
\(q-\beta _{1}q^{2}-3q^{3}+(3+\beta _{1}+\beta _{2})q^{4}+\cdots\)
1005.4.a.e
$1005$
$4$
1005.a
1.a
$1$
$17$
$17$
$59.297$
\(\mathbb{Q}[x]/(x^{17} - \cdots)\)
None
✓
✓
✓
✓
1005.4.a.e
$1$
$1$
\(-3\)
\(51\)
\(-85\)
\(1\)
$-$
$2^{4}$
$\mathrm{SU}(2)$
\(q-\beta _{1}q^{2}+3q^{3}+(3+\beta _{2})q^{4}-5q^{5}+\cdots\)
1005.4.a.f
$1005$
$4$
1005.a
1.a
$1$
$17$
$17$
$59.297$
\(\mathbb{Q}[x]/(x^{17} - \cdots)\)
None
✓
✓
✓
✓
1005.4.a.f
$1$
$0$
\(3\)
\(51\)
\(-85\)
\(-27\)
$+$
$2^{3}$
$\mathrm{SU}(2)$
\(q+\beta _{1}q^{2}+3q^{3}+(4+\beta _{2})q^{4}-5q^{5}+\cdots\)
1005.4.a.g
$1005$
$4$
1005.a
1.a
$1$
$17$
$17$
$59.297$
\(\mathbb{Q}[x]/(x^{17} - \cdots)\)
None
✓
✓
✓
✓
1005.4.a.g
$1$
$0$
\(5\)
\(-51\)
\(85\)
\(83\)
$+$
$2^{4}$
$\mathrm{SU}(2)$
\(q+\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}+5q^{5}+\cdots\)
1005.4.a.h
$1005$
$4$
1005.a
1.a
$1$
$18$
$18$
$59.297$
\(\mathbb{Q}[x]/(x^{18} - \cdots)\)
None
✓
✓
✓
✓
1005.4.a.h
$1$
$0$
\(-4\)
\(-54\)
\(-90\)
\(-27\)
$+$
$2^{2}$
$\mathrm{SU}(2)$
\(q-\beta _{1}q^{2}-3q^{3}+(5+\beta _{2})q^{4}-5q^{5}+\cdots\)
1005.4.a.i
$1005$
$4$
1005.a
1.a
$1$
$18$
$18$
$59.297$
\(\mathbb{Q}[x]/(x^{18} - \cdots)\)
None
✓
✓
✓
✓
1005.4.a.i
$1$
$0$
\(12\)
\(54\)
\(90\)
\(83\)
$+$
$2^{3}\cdot 5$
$\mathrm{SU}(2)$
\(q+(1-\beta _{1})q^{2}+3q^{3}+(5-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1006.4.a.a
$1006$
$4$
1006.a
1.a
$1$
$29$
$29$
$59.356$
None
✓
✓
✓
✓
1006.4.a.a
$1$
$1$
\(-58\)
\(7\)
\(-34\)
\(-3\)
$-$
$\mathrm{SU}(2)$
1006.4.a.b
$1006$
$4$
1006.a
1.a
$1$
$29$
$29$
$59.356$
None
✓
✓
✓
✓
1006.4.a.b
$1$
$1$
\(58\)
\(-25\)
\(-54\)
\(-77\)
$-$
$\mathrm{SU}(2)$
1006.4.a.c
$1006$
$4$
1006.a
1.a
$1$
$34$
$34$
$59.356$
None
✓
✓
✓
✓
1006.4.a.c
$1$
$0$
\(-68\)
\(-5\)
\(26\)
\(-17\)
$+$
$\mathrm{SU}(2)$
1006.4.a.d
$1006$
$4$
1006.a
1.a
$1$
$34$
$34$
$59.356$
None
✓
✓
✓
✓
1006.4.a.d
$1$
$0$
\(68\)
\(23\)
\(36\)
\(105\)
$+$
$\mathrm{SU}(2)$
1007.4.a.a
$1007$
$4$
1007.a
1.a
$1$
$1$
$1$
$59.415$
\(\Q\)
None
✓
✓
1007.4.a.a
$1$
$0$
\(-3\)
\(10\)
\(11\)
\(10\)
$+$
$1$
$\mathrm{SU}(2)$
\(q-3q^{2}+10q^{3}+q^{4}+11q^{5}-30q^{6}+\cdots\)
1007.4.a.b
$1007$
$4$
1007.a
1.a
$1$
$50$
$50$
$59.415$
None
✓
✓
✓
✓
1007.4.a.b
$1$
$1$
\(-6\)
\(3\)
\(-16\)
\(-62\)
$-$
$\mathrm{SU}(2)$
1007.4.a.c
$1007$
$4$
1007.a
1.a
$1$
$52$
$52$
$59.415$
None
✓
✓
✓
✓
1007.4.a.c
$1$
$1$
\(-12\)
\(-27\)
\(-30\)
\(-108\)
$-$
$\mathrm{SU}(2)$
1007.4.a.d
$1007$
$4$
1007.a
1.a
$1$
$64$
$64$
$59.415$
None
✓
✓
✓
1007.4.a.d
$1$
$0$
\(9\)
\(-13\)
\(33\)
\(96\)
$+$
$\mathrm{SU}(2)$
1007.4.a.e
$1007$
$4$
1007.a
1.a
$1$
$67$
$67$
$59.415$
None
✓
✓
✓
✓
1007.4.a.e
$1$
$0$
\(12\)
\(27\)
\(30\)
\(60\)
$+$
$\mathrm{SU}(2)$
1008.4.a.a
$1008$
$4$
1008.a
1.a
$1$
$1$
$1$
$59.474$
\(\Q\)
None
✓
126.4.a.e
$1$
$0$
\(0\)
\(0\)
\(-22\)
\(7\)
$+$
$1$
$\mathrm{SU}(2)$
\(q-22q^{5}+7q^{7}+26q^{11}-54q^{13}+\cdots\)
1008.4.a.b
$1008$
$4$
1008.a
1.a
$1$
$1$
$1$
$59.474$
\(\Q\)
None
✓
42.4.a.a
$1$
$0$
\(0\)
\(0\)
\(-18\)
\(-7\)
$+$
$1$
$\mathrm{SU}(2)$
\(q-18q^{5}-7q^{7}-72q^{11}-34q^{13}+\cdots\)
1008.4.a.c
$1008$
$4$
1008.a
1.a
$1$
$1$
$1$
$59.474$
\(\Q\)
None
✓
7.4.a.a
$1$
$1$
\(0\)
\(0\)
\(-16\)
\(7\)
$-$
$1$
$\mathrm{SU}(2)$
\(q-2^{4}q^{5}+7q^{7}-8q^{11}+28q^{13}+\cdots\)
1008.4.a.d
$1008$
$4$
1008.a
1.a
$1$
$1$
$1$
$59.474$
\(\Q\)
None
✓
84.4.a.b
$1$
$1$
\(0\)
\(0\)
\(-14\)
\(7\)
$-$
$1$
$\mathrm{SU}(2)$
\(q-14q^{5}+7q^{7}+4q^{11}+54q^{13}+\cdots\)
1008.4.a.e
$1008$
$4$
1008.a
1.a
$1$
$1$
$1$
$59.474$
\(\Q\)
None
✓
56.4.a.b
$1$
$0$
\(0\)
\(0\)
\(-8\)
\(7\)
$+$
$1$
$\mathrm{SU}(2)$
\(q-8q^{5}+7q^{7}+56q^{11}-28q^{13}+\cdots\)
1008.4.a.f
$1008$
$4$
1008.a
1.a
$1$
$1$
$1$
$59.474$
\(\Q\)
None
✓
28.4.a.b
$1$
$0$
\(0\)
\(0\)
\(-6\)
\(-7\)
$+$
$1$
$\mathrm{SU}(2)$
\(q-6q^{5}-7q^{7}-12q^{11}-82q^{13}+\cdots\)
1008.4.a.g
$1008$
$4$
1008.a
1.a
$1$
$1$
$1$
$59.474$
\(\Q\)
None
✓
126.4.a.b
$1$
$1$
\(0\)
\(0\)
\(-6\)
\(-7\)
$-$
$1$
$\mathrm{SU}(2)$
\(q-6q^{5}-7q^{7}+30q^{11}+2q^{13}-66q^{17}+\cdots\)
1008.4.a.h
$1008$
$4$
1008.a
1.a
$1$
$1$
$1$
$59.474$
\(\Q\)
None
✓
84.4.a.a
$1$
$0$
\(0\)
\(0\)
\(-6\)
\(-7\)
$+$
$1$
$\mathrm{SU}(2)$
\(q-6q^{5}-7q^{7}+6^{2}q^{11}+62q^{13}+\cdots\)
1008.4.a.i
$1008$
$4$
1008.a
1.a
$1$
$1$
$1$
$59.474$
\(\Q\)
None
✓
168.4.a.c
$1$
$0$
\(0\)
\(0\)
\(-4\)
\(7\)
$+$
$1$
$\mathrm{SU}(2)$
\(q-4q^{5}+7q^{7}-26q^{11}+2q^{13}+6^{2}q^{17}+\cdots\)
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