The results below are complete, since the LMFDB contains all newforms with trivial character and $Nk^2$ at most 40000

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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 (4 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 23
736.4.a.f 736.a 1.a $8$ $43.425$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 736.4.a.e \(0\) \(12\) \(-12\) \(-14\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(2-\beta _{1})q^{3}+(-1-\beta _{3})q^{5}+(-2+\cdots)q^{7}+\cdots\)
736.4.a.g 736.a 1.a $9$ $43.425$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None 736.4.a.g \(0\) \(-14\) \(30\) \(28\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-2+\beta _{1})q^{3}+(3-\beta _{4})q^{5}+(3-\beta _{6}+\cdots)q^{7}+\cdots\)
736.4.a.i 736.a 1.a $9$ $43.425$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None 736.4.a.h \(0\) \(0\) \(0\) \(42\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}-\beta _{5}q^{5}+(5-\beta _{3})q^{7}+(8-\beta _{3}+\cdots)q^{9}+\cdots\)
736.4.a.j 736.a 1.a $9$ $43.425$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None 736.4.a.g \(0\) \(14\) \(30\) \(-28\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(2-\beta _{1})q^{3}+(3-\beta _{4})q^{5}+(-3+\beta _{6}+\cdots)q^{7}+\cdots\)
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