The results below are complete, since the LMFDB contains all newforms with $Nk^2$ at most 4000

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Level Weight Analytic conductor Analytic rank Dim.
Bad \(p\) Char. Primitive character Character order Is maximal/largest
Coefficient field Self-twists CM/RM discriminant Inner twist count Is self-dual
Coefficient ring index Coefficient ring gens. Is twist minimal Projective image
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Results (5 matches)

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Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 11 19
418.2.a.b 418.a 1.a $1$ $3.338$ \(\Q\) None 418.2.a.b \(1\) \(0\) \(2\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{5}+2q^{7}+q^{8}-3q^{9}+\cdots\)
418.2.a.c 418.a 1.a $1$ $3.338$ \(\Q\) None 418.2.a.c \(1\) \(3\) \(-2\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+3q^{3}+q^{4}-2q^{5}+3q^{6}+q^{7}+\cdots\)
418.2.a.e 418.a 1.a $2$ $3.338$ \(\Q(\sqrt{17}) \) None 418.2.a.e \(-2\) \(1\) \(4\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-\beta )q^{3}+q^{4}+2q^{5}+(-1+\cdots)q^{6}+\cdots\)
418.2.a.f 418.a 1.a $2$ $3.338$ \(\Q(\sqrt{21}) \) None 418.2.a.f \(2\) \(-1\) \(3\) \(-5\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta q^{3}+q^{4}+(2-\beta )q^{5}-\beta q^{6}+\cdots\)
418.2.a.h 418.a 1.a $3$ $3.338$ 3.3.469.1 None 418.2.a.h \(3\) \(1\) \(5\) \(1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(2-\beta _{1})q^{5}+\beta _{1}q^{6}+\cdots\)
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