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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twist	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (21 matches)

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Label	Dim.	$A$	Field	CM	Traces				Fricke sign	$q$-expansion
Label	Dim.	$A$	Field	CM	$a_2$	$a_3$	$a_5$	$a_7$	Fricke sign	$q$-expansion
1334.2.a.a	$1$	$10.652$	$\Q$	None	$-1$	$0$	$0$	$4$	$-$	$q-q^{2}+q^{4}+4q^{7}-q^{8}-3q^{9}+2q^{11}+\cdots$
1334.2.a.b	$1$	$10.652$	$\Q$	None	$-1$	$1$	$-3$	$-4$	$-$	$q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-4q^{7}+\cdots$
1334.2.a.c	$1$	$10.652$	$\Q$	None	$-1$	$1$	$1$	$0$	$+$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots$
1334.2.a.d	$4$	$10.652$	4.4.37108.1	None	$-4$	$1$	$-1$	$0$	$+$	$q-q^{2}-\beta _{2}q^{3}+q^{4}+\beta _{2}q^{5}+\beta _{2}q^{6}+\cdots$
1334.2.a.e	$4$	$10.652$	4.4.4352.1	None	$4$	$-4$	$0$	$-4$	$+$	$q+q^{2}+(-1-\beta _{3})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
1334.2.a.f	$5$	$10.652$	5.5.207184.1	None	$-5$	$1$	$-5$	$-2$	$+$	$q-q^{2}-\beta _{3}q^{3}+q^{4}+(-1+\beta _{4})q^{5}+\cdots$
1334.2.a.g	$5$	$10.652$	5.5.978400.1	None	$-5$	$1$	$3$	$4$	$-$	$q-q^{2}+(\beta _{1}-\beta _{2})q^{3}+q^{4}+(\beta _{1}+\beta _{4})q^{5}+\cdots$
1334.2.a.h	$5$	$10.652$	5.5.179024.1	None	$5$	$-3$	$-5$	$-6$	$+$	$q+q^{2}+(-1+\beta _{3})q^{3}+q^{4}+(-1-\beta _{4})q^{5}+\cdots$
1334.2.a.i	$8$	$10.652$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	$8$	$4$	$0$	$8$	$-$	$q+q^{2}-\beta _{4}q^{3}+q^{4}-\beta _{1}q^{5}-\beta _{4}q^{6}+\cdots$
1334.2.a.j	$9$	$10.652$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	$-9$	$-3$	$5$	$6$	$-$	$q-q^{2}-\beta _{1}q^{3}+q^{4}+(1-\beta _{6})q^{5}+\beta _{1}q^{6}+\cdots$
1334.2.a.k	$10$	$10.652$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	$10$	$5$	$-1$	$2$	$-$	$q+q^{2}+(1-\beta _{1})q^{3}+q^{4}-\beta _{5}q^{5}+(1+\cdots)q^{6}+\cdots$
1334.2.c.a	$28$	$10.652$		None	$0$	$0$	$-2$	$16$
1334.2.c.b	$28$	$10.652$		None	$0$	$0$	$2$	$-8$
1334.4.a.a	$15$	$78.709$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	$30$	$-18$	$-25$	$-55$	$-$	$q+2q^{2}+(-1-\beta _{1})q^{3}+4q^{4}+(-2+\cdots)q^{5}+\cdots$
1334.4.a.b	$17$	$78.709$	$\mathbb{Q}[x]/(x^{17} - \cdots)$	None	$-34$	$10$	$-25$	$-27$	$-$	$q-2q^{2}+(1-\beta _{1})q^{3}+4q^{4}+(-1-\beta _{4}+\cdots)q^{5}+\cdots$
1334.4.a.c	$18$	$78.709$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	$36$	$-3$	$0$	$-41$	$-$	$q+2q^{2}-\beta _{1}q^{3}+4q^{4}+(\beta _{1}+\beta _{8})q^{5}+\cdots$
1334.4.a.d	$19$	$78.709$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	None	$-38$	$-5$	$0$	$-13$	$-$	$q-2q^{2}-\beta _{1}q^{3}+4q^{4}-\beta _{6}q^{5}+2\beta _{1}q^{6}+\cdots$
1334.4.a.e	$21$	$78.709$		None	$-42$	$-5$	$0$	$15$	$+$
1334.4.a.f	$21$	$78.709$		None	$-42$	$-2$	$25$	$29$	$+$
1334.4.a.g	$21$	$78.709$		None	$42$	$18$	$25$	$57$	$+$
1334.4.a.h	$22$	$78.709$		None	$44$	$21$	$0$	$43$	$+$

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Label	Dim.	\(A\)	Field	CM	Traces				Fricke sign	$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	Fricke sign	$q$-expansion
1334.2.a.a	\(1\)	\(10.652\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(4\)	\(-\)	\(q-q^{2}+q^{4}+4q^{7}-q^{8}-3q^{9}+2q^{11}+\cdots\)
1334.2.a.b	\(1\)	\(10.652\)	\(\Q\)	None	\(-1\)	\(1\)	\(-3\)	\(-4\)	\(-\)	\(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-4q^{7}+\cdots\)
1334.2.a.c	\(1\)	\(10.652\)	\(\Q\)	None	\(-1\)	\(1\)	\(1\)	\(0\)	\(+\)	\(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots\)
1334.2.a.d	\(4\)	\(10.652\)	4.4.37108.1	None	\(-4\)	\(1\)	\(-1\)	\(0\)	\(+\)	\(q-q^{2}-\beta _{2}q^{3}+q^{4}+\beta _{2}q^{5}+\beta _{2}q^{6}+\cdots\)
1334.2.a.e	\(4\)	\(10.652\)	4.4.4352.1	None	\(4\)	\(-4\)	\(0\)	\(-4\)	\(+\)	\(q+q^{2}+(-1-\beta _{3})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
1334.2.a.f	\(5\)	\(10.652\)	5.5.207184.1	None	\(-5\)	\(1\)	\(-5\)	\(-2\)	\(+\)	\(q-q^{2}-\beta _{3}q^{3}+q^{4}+(-1+\beta _{4})q^{5}+\cdots\)
1334.2.a.g	\(5\)	\(10.652\)	5.5.978400.1	None	\(-5\)	\(1\)	\(3\)	\(4\)	\(-\)	\(q-q^{2}+(\beta _{1}-\beta _{2})q^{3}+q^{4}+(\beta _{1}+\beta _{4})q^{5}+\cdots\)
1334.2.a.h	\(5\)	\(10.652\)	5.5.179024.1	None	\(5\)	\(-3\)	\(-5\)	\(-6\)	\(+\)	\(q+q^{2}+(-1+\beta _{3})q^{3}+q^{4}+(-1-\beta _{4})q^{5}+\cdots\)
1334.2.a.i	\(8\)	\(10.652\)	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	\(8\)	\(4\)	\(0\)	\(8\)	\(-\)	\(q+q^{2}-\beta _{4}q^{3}+q^{4}-\beta _{1}q^{5}-\beta _{4}q^{6}+\cdots\)
1334.2.a.j	\(9\)	\(10.652\)	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	\(-9\)	\(-3\)	\(5\)	\(6\)	\(-\)	\(q-q^{2}-\beta _{1}q^{3}+q^{4}+(1-\beta _{6})q^{5}+\beta _{1}q^{6}+\cdots\)
1334.2.a.k	\(10\)	\(10.652\)	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	\(10\)	\(5\)	\(-1\)	\(2\)	\(-\)	\(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}-\beta _{5}q^{5}+(1+\cdots)q^{6}+\cdots\)
1334.2.c.a	\(28\)	\(10.652\)		None	\(0\)	\(0\)	\(-2\)	\(16\)
1334.2.c.b	\(28\)	\(10.652\)		None	\(0\)	\(0\)	\(2\)	\(-8\)
1334.4.a.a	\(15\)	\(78.709\)	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	\(30\)	\(-18\)	\(-25\)	\(-55\)	\(-\)	\(q+2q^{2}+(-1-\beta _{1})q^{3}+4q^{4}+(-2+\cdots)q^{5}+\cdots\)
1334.4.a.b	\(17\)	\(78.709\)	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	\(-34\)	\(10\)	\(-25\)	\(-27\)	\(-\)	\(q-2q^{2}+(1-\beta _{1})q^{3}+4q^{4}+(-1-\beta _{4}+\cdots)q^{5}+\cdots\)
1334.4.a.c	\(18\)	\(78.709\)	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	\(36\)	\(-3\)	\(0\)	\(-41\)	\(-\)	\(q+2q^{2}-\beta _{1}q^{3}+4q^{4}+(\beta _{1}+\beta _{8})q^{5}+\cdots\)
1334.4.a.d	\(19\)	\(78.709\)	\(\mathbb{Q}[x]/(x^{19} - \cdots)\)	None	\(-38\)	\(-5\)	\(0\)	\(-13\)	\(-\)	\(q-2q^{2}-\beta _{1}q^{3}+4q^{4}-\beta _{6}q^{5}+2\beta _{1}q^{6}+\cdots\)
1334.4.a.e	\(21\)	\(78.709\)		None	\(-42\)	\(-5\)	\(0\)	\(15\)	\(+\)
1334.4.a.f	\(21\)	\(78.709\)		None	\(-42\)	\(-2\)	\(25\)	\(29\)	\(+\)
1334.4.a.g	\(21\)	\(78.709\)		None	\(42\)	\(18\)	\(25\)	\(57\)	\(+\)
1334.4.a.h	\(22\)	\(78.709\)		None	\(44\)	\(21\)	\(0\)	\(43\)	\(+\)

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.