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Level	Weight	Analytic conductor	\(Nk^2\)	Dim.
Bad \(p\)	Char.	Primitive character	Character order	Coefficient field
Self-twists	CM/RM discriminant	Inner twist count*	Is self-dual?	Analytic rank
Coefficient ring index	Coefficient ring gens.	Only for weight 1:	Projective image	Projective image type
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Results (displaying all 16 matches)

Label	Dim.	\(A\)	Field	CM	Traces				Fricke sign	$q$-expansion
					\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)
4004.2.a.a	\(1\)	\(31.972\)	\(\Q\)	None	\(0\)	\(-2\)	\(0\)	\(1\)	\(-\)	\(q-2q^{3}+q^{7}+q^{9}-q^{11}+q^{13}+6q^{17}+\cdots\)
4004.2.a.b	\(1\)	\(31.972\)	\(\Q\)	None	\(0\)	\(-1\)	\(-3\)	\(-1\)	\(+\)	\(q-q^{3}-3q^{5}-q^{7}-2q^{9}-q^{11}+q^{13}+\cdots\)
4004.2.a.c	\(1\)	\(31.972\)	\(\Q\)	None	\(0\)	\(2\)	\(4\)	\(1\)	\(-\)	\(q+2q^{3}+4q^{5}+q^{7}+q^{9}+q^{11}-q^{13}+\cdots\)
4004.2.a.d	\(4\)	\(31.972\)	4.4.3981.1	None	\(0\)	\(-3\)	\(-1\)	\(4\)	\(+\)	\(q+(-1-\beta _{3})q^{3}+(\beta _{2}+\beta _{3})q^{5}+q^{7}+\cdots\)
4004.2.a.e	\(4\)	\(31.972\)	\(\Q(\zeta_{15})^+\)	None	\(0\)	\(1\)	\(1\)	\(-4\)	\(+\)	\(q+(-\beta _{2}-\beta _{3})q^{3}+(1-\beta _{1}+\beta _{3})q^{5}+\cdots\)
4004.2.a.f	\(5\)	\(31.972\)	5.5.463341.1	None	\(0\)	\(3\)	\(0\)	\(-5\)	\(+\)	\(q+(1-\beta _{1})q^{3}-\beta _{2}q^{5}-q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
4004.2.a.g	\(6\)	\(31.972\)	6.6.246302029.1	None	\(0\)	\(-2\)	\(-3\)	\(6\)	\(+\)	\(q-\beta _{1}q^{3}+(-1-\beta _{4})q^{5}+q^{7}+(1+\beta _{3}+\cdots)q^{9}+\cdots\)
4004.2.a.h	\(9\)	\(31.972\)	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	\(0\)	\(3\)	\(0\)	\(9\)	\(-\)	\(q+\beta _{1}q^{3}-\beta _{4}q^{5}+q^{7}+(2+\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
4004.2.a.i	\(9\)	\(31.972\)	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	\(0\)	\(4\)	\(4\)	\(9\)	\(-\)	\(q+\beta _{1}q^{3}-\beta _{7}q^{5}+q^{7}+(1+\beta _{3}+\beta _{4}+\cdots)q^{9}+\cdots\)
4004.2.a.j	\(10\)	\(31.972\)	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	\(0\)	\(-2\)	\(-2\)	\(-10\)	\(-\)	\(q-\beta _{1}q^{3}+\beta _{3}q^{5}-q^{7}+(1+\beta _{2})q^{9}+\cdots\)
4004.2.a.k	\(10\)	\(31.972\)	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	\(0\)	\(1\)	\(4\)	\(-10\)	\(-\)	\(q+\beta _{1}q^{3}-\beta _{4}q^{5}-q^{7}+(2+\beta _{2})q^{9}+\cdots\)
4004.2.e.a	\(48\)	\(31.972\)		None	\(0\)	\(0\)	\(0\)	\(-4\)
4004.2.e.b	\(48\)	\(31.972\)		None	\(0\)	\(0\)	\(0\)	\(4\)
4004.2.m.a	\(2\)	\(31.972\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(4\)	\(0\)	\(0\)		\(q+2q^{3}+iq^{5}+iq^{7}+q^{9}-iq^{11}+\cdots\)
4004.2.m.b	\(30\)	\(31.972\)		None	\(0\)	\(0\)	\(0\)	\(0\)
4004.2.m.c	\(36\)	\(31.972\)		None	\(0\)	\(-4\)	\(0\)	\(0\)