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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 (33 matches)

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Label	Dim.	$A$	Field	CM	RM	Traces				Fricke sign	$q$-expansion
Label	Dim.	$A$	Field	CM	RM	$a_2$	$a_3$	$a_5$	$a_7$	Fricke sign	$q$-expansion
1148.1.o.a	$2$	$0.573$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-41}) $	None	$-1$	$-1$	$1$	$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}+\cdots$
1148.1.o.b	$2$	$0.573$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-41}) $	None	$-1$	$1$	$1$	$-1$		$q-\zeta_{6}q^{2}-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}+\cdots$
1148.1.o.c	$4$	$0.573$	$\Q(\zeta_{12})$	$\Q(\sqrt{-41}) $	None	$-2$	$0$	$-2$	$0$		$q+\zeta_{12}^{4}q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}-\zeta_{12}^{2}q^{4}+\cdots$
1148.1.o.d	$8$	$0.573$	$\Q(\zeta_{24})$	$\Q(\sqrt{-41}) $	None	$4$	$0$	$0$	$0$		$q-\zeta_{24}^{8}q^{2}+(-\zeta_{24}^{9}+\zeta_{24}^{11})q^{3}+\cdots$
1148.1.bc.a	$8$	$0.573$	$\Q(\zeta_{20})$	None	None	$0$	$0$	$0$	$-2$		$q+\zeta_{20}^{5}q^{3}-\zeta_{20}q^{5}-\zeta_{20}^{2}q^{7}+(\zeta_{20}^{2}+\cdots)q^{11}+\cdots$
1148.1.bj.a	$8$	$0.573$	$\Q(\zeta_{24})$	None	None	$0$	$0$	$0$	$0$		$q-\zeta_{24}^{2}q^{2}-\zeta_{24}^{7}q^{3}+\zeta_{24}^{4}q^{4}+\cdots$
1148.2.a.a	$2$	$9.167$	$\Q(\sqrt{13}) $	None	None	$0$	$-3$	$-3$	$2$	$+$	$q+(-1-\beta )q^{3}+(-1-\beta )q^{5}+q^{7}+\cdots$
1148.2.a.b	$3$	$9.167$	$\Q(\zeta_{18})^+$	None	None	$0$	$-3$	$0$	$3$	$+$	$q+(-1+\beta _{1})q^{3}+(-2\beta _{1}+2\beta _{2})q^{5}+\cdots$
1148.2.a.c	$5$	$9.167$	5.5.470117.1	None	None	$0$	$-2$	$-1$	$-5$	$+$	$q-\beta _{1}q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}-q^{7}+\cdots$
1148.2.a.d	$5$	$9.167$	5.5.287349.1	None	None	$0$	$2$	$-3$	$-5$	$-$	$q+\beta _{2}q^{3}+(-1+\beta _{2}-\beta _{3})q^{5}-q^{7}+\cdots$
1148.2.a.e	$5$	$9.167$	5.5.1935333.1	None	None	$0$	$2$	$3$	$5$	$-$	$q+\beta _{1}q^{3}+(1+\beta _{4})q^{5}+q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots$
1148.2.d.a	$20$	$9.167$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None	None	$0$	$0$	$4$	$0$		$q+\beta _{12}q^{3}+\beta _{2}q^{5}-\beta _{9}q^{7}+(-1-\beta _{7}+\cdots)q^{9}+\cdots$
1148.2.i.a	$2$	$9.167$	$\Q(\sqrt{-3}) $	None	None	$0$	$-1$	$3$	$5$		$q+(-1+\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots$
1148.2.i.b	$2$	$9.167$	$\Q(\sqrt{-3}) $	None	None	$0$	$1$	$1$	$-4$		$q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-1-2\zeta_{6})q^{7}+\cdots$
1148.2.i.c	$2$	$9.167$	$\Q(\sqrt{-3}) $	None	None	$0$	$1$	$1$	$4$		$q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots$
1148.2.i.d	$16$	$9.167$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None	None	$0$	$0$	$0$	$0$		$q-\beta _{1}q^{3}+\beta _{14}q^{5}+(-\beta _{5}+\beta _{8})q^{7}+\cdots$
1148.2.i.e	$30$	$9.167$		None	None	$0$	$1$	$-3$	$3$
1148.2.k.a	$8$	$9.167$	8.0.110166016.2	None	None	$0$	$-4$	$0$	$0$		$q+(-1-\beta _{5})q^{3}+(-1+\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots$
1148.2.k.b	$36$	$9.167$		None	None	$0$	$0$	$0$	$0$
1148.2.n.a	$8$	$9.167$	8.0.64000000.2	None	None	$0$	$-4$	$-2$	$-2$		$q+(-\beta _{3}+\beta _{4}+\beta _{6}-\beta _{7})q^{3}+(-\beta _{1}+\cdots)q^{5}+\cdots$
1148.2.n.b	$8$	$9.167$	8.0.64000000.2	None	None	$0$	$8$	$-2$	$-2$		$q+(1+\beta _{5})q^{3}+(\beta _{2}+\beta _{7})q^{5}+\beta _{4}q^{7}+\cdots$
1148.2.n.c	$16$	$9.167$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	None	$0$	$-2$	$-13$	$4$		$q+(-\beta _{1}-\beta _{2}+\beta _{5}-\beta _{6})q^{3}+(-1+\cdots)q^{5}+\cdots$
1148.2.n.d	$24$	$9.167$		None	None	$0$	$-10$	$4$	$-6$
1148.2.n.e	$24$	$9.167$		None	None	$0$	$12$	$17$	$6$
1148.2.r.a	$56$	$9.167$		None	None	$0$	$0$	$4$	$0$
1148.2.ba.a	$80$	$9.167$		None	None	$0$	$0$	$-4$	$0$
1148.3.b.a	$52$	$31.281$		None	None	$0$	$0$	$0$	$-20$
1148.3.g.a	$56$	$31.281$		None	None	$0$	$0$	$0$	$0$
1148.4.a.a	$15$	$67.734$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	None	$0$	$-14$	$-24$	$105$	$-$	$q+(-1+\beta _{1})q^{3}+(-2-\beta _{3})q^{5}+7q^{7}+\cdots$
1148.4.a.b	$15$	$67.734$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	None	$0$	$0$	$6$	$-105$	$-$	$q+\beta _{1}q^{3}-\beta _{4}q^{5}-7q^{7}+(6+\beta _{2})q^{9}+\cdots$
1148.4.a.c	$15$	$67.734$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	None	$0$	$10$	$6$	$105$	$+$	$q+(1-\beta _{1})q^{3}+\beta _{3}q^{5}+7q^{7}+(11-\beta _{1}+\cdots)q^{9}+\cdots$
1148.4.a.d	$15$	$67.734$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	None	$0$	$12$	$-4$	$-105$	$+$	$q+(1-\beta _{1})q^{3}+\beta _{4}q^{5}-7q^{7}+(6-\beta _{1}+\cdots)q^{9}+\cdots$
1148.4.d.a	$64$	$67.734$		None	None	$0$	$0$	$20$	$0$

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Label	Dim.	\(A\)	Field	CM	RM	Traces				Fricke sign	$q$-expansion
Label	Dim.	\(A\)	Field	CM	RM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	Fricke sign	$q$-expansion
1148.1.o.a	\(2\)	\(0.573\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-41}) \)	None	\(-1\)	\(-1\)	\(1\)	\(1\)		\(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}+\cdots\)
1148.1.o.b	\(2\)	\(0.573\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-41}) \)	None	\(-1\)	\(1\)	\(1\)	\(-1\)		\(q-\zeta_{6}q^{2}-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}+\cdots\)
1148.1.o.c	\(4\)	\(0.573\)	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-41}) \)	None	\(-2\)	\(0\)	\(-2\)	\(0\)		\(q+\zeta_{12}^{4}q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
1148.1.o.d	\(8\)	\(0.573\)	\(\Q(\zeta_{24})\)	\(\Q(\sqrt{-41}) \)	None	\(4\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{24}^{8}q^{2}+(-\zeta_{24}^{9}+\zeta_{24}^{11})q^{3}+\cdots\)
1148.1.bc.a	\(8\)	\(0.573\)	\(\Q(\zeta_{20})\)	None	None	\(0\)	\(0\)	\(0\)	\(-2\)		\(q+\zeta_{20}^{5}q^{3}-\zeta_{20}q^{5}-\zeta_{20}^{2}q^{7}+(\zeta_{20}^{2}+\cdots)q^{11}+\cdots\)
1148.1.bj.a	\(8\)	\(0.573\)	\(\Q(\zeta_{24})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{24}^{2}q^{2}-\zeta_{24}^{7}q^{3}+\zeta_{24}^{4}q^{4}+\cdots\)
1148.2.a.a	\(2\)	\(9.167\)	\(\Q(\sqrt{13}) \)	None	None	\(0\)	\(-3\)	\(-3\)	\(2\)	\(+\)	\(q+(-1-\beta )q^{3}+(-1-\beta )q^{5}+q^{7}+\cdots\)
1148.2.a.b	\(3\)	\(9.167\)	\(\Q(\zeta_{18})^+\)	None	None	\(0\)	\(-3\)	\(0\)	\(3\)	\(+\)	\(q+(-1+\beta _{1})q^{3}+(-2\beta _{1}+2\beta _{2})q^{5}+\cdots\)
1148.2.a.c	\(5\)	\(9.167\)	5.5.470117.1	None	None	\(0\)	\(-2\)	\(-1\)	\(-5\)	\(+\)	\(q-\beta _{1}q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}-q^{7}+\cdots\)
1148.2.a.d	\(5\)	\(9.167\)	5.5.287349.1	None	None	\(0\)	\(2\)	\(-3\)	\(-5\)	\(-\)	\(q+\beta _{2}q^{3}+(-1+\beta _{2}-\beta _{3})q^{5}-q^{7}+\cdots\)
1148.2.a.e	\(5\)	\(9.167\)	5.5.1935333.1	None	None	\(0\)	\(2\)	\(3\)	\(5\)	\(-\)	\(q+\beta _{1}q^{3}+(1+\beta _{4})q^{5}+q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
1148.2.d.a	\(20\)	\(9.167\)	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None	None	\(0\)	\(0\)	\(4\)	\(0\)		\(q+\beta _{12}q^{3}+\beta _{2}q^{5}-\beta _{9}q^{7}+(-1-\beta _{7}+\cdots)q^{9}+\cdots\)
1148.2.i.a	\(2\)	\(9.167\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(-1\)	\(3\)	\(5\)		\(q+(-1+\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots\)
1148.2.i.b	\(2\)	\(9.167\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(1\)	\(1\)	\(-4\)		\(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-1-2\zeta_{6})q^{7}+\cdots\)
1148.2.i.c	\(2\)	\(9.167\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(1\)	\(1\)	\(4\)		\(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
1148.2.i.d	\(16\)	\(9.167\)	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{1}q^{3}+\beta _{14}q^{5}+(-\beta _{5}+\beta _{8})q^{7}+\cdots\)
1148.2.i.e	\(30\)	\(9.167\)		None	None	\(0\)	\(1\)	\(-3\)	\(3\)
1148.2.k.a	\(8\)	\(9.167\)	8.0.110166016.2	None	None	\(0\)	\(-4\)	\(0\)	\(0\)		\(q+(-1-\beta _{5})q^{3}+(-1+\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots\)
1148.2.k.b	\(36\)	\(9.167\)		None	None	\(0\)	\(0\)	\(0\)	\(0\)
1148.2.n.a	\(8\)	\(9.167\)	8.0.64000000.2	None	None	\(0\)	\(-4\)	\(-2\)	\(-2\)		\(q+(-\beta _{3}+\beta _{4}+\beta _{6}-\beta _{7})q^{3}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
1148.2.n.b	\(8\)	\(9.167\)	8.0.64000000.2	None	None	\(0\)	\(8\)	\(-2\)	\(-2\)		\(q+(1+\beta _{5})q^{3}+(\beta _{2}+\beta _{7})q^{5}+\beta _{4}q^{7}+\cdots\)
1148.2.n.c	\(16\)	\(9.167\)	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	None	\(0\)	\(-2\)	\(-13\)	\(4\)		\(q+(-\beta _{1}-\beta _{2}+\beta _{5}-\beta _{6})q^{3}+(-1+\cdots)q^{5}+\cdots\)
1148.2.n.d	\(24\)	\(9.167\)		None	None	\(0\)	\(-10\)	\(4\)	\(-6\)
1148.2.n.e	\(24\)	\(9.167\)		None	None	\(0\)	\(12\)	\(17\)	\(6\)
1148.2.r.a	\(56\)	\(9.167\)		None	None	\(0\)	\(0\)	\(4\)	\(0\)
1148.2.ba.a	\(80\)	\(9.167\)		None	None	\(0\)	\(0\)	\(-4\)	\(0\)
1148.3.b.a	\(52\)	\(31.281\)		None	None	\(0\)	\(0\)	\(0\)	\(-20\)
1148.3.g.a	\(56\)	\(31.281\)		None	None	\(0\)	\(0\)	\(0\)	\(0\)
1148.4.a.a	\(15\)	\(67.734\)	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	None	\(0\)	\(-14\)	\(-24\)	\(105\)	\(-\)	\(q+(-1+\beta _{1})q^{3}+(-2-\beta _{3})q^{5}+7q^{7}+\cdots\)
1148.4.a.b	\(15\)	\(67.734\)	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	None	\(0\)	\(0\)	\(6\)	\(-105\)	\(-\)	\(q+\beta _{1}q^{3}-\beta _{4}q^{5}-7q^{7}+(6+\beta _{2})q^{9}+\cdots\)
1148.4.a.c	\(15\)	\(67.734\)	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	None	\(0\)	\(10\)	\(6\)	\(105\)	\(+\)	\(q+(1-\beta _{1})q^{3}+\beta _{3}q^{5}+7q^{7}+(11-\beta _{1}+\cdots)q^{9}+\cdots\)
1148.4.a.d	\(15\)	\(67.734\)	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	None	\(0\)	\(12\)	\(-4\)	\(-105\)	\(+\)	\(q+(1-\beta _{1})q^{3}+\beta _{4}q^{5}-7q^{7}+(6-\beta _{1}+\cdots)q^{9}+\cdots\)
1148.4.d.a	\(64\)	\(67.734\)		None	None	\(0\)	\(0\)	\(20\)	\(0\)

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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.