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 3 37
222.2.a.a 222.a 1.a $1$ $1.773$ \(\Q\) None 222.2.a.a \(-1\) \(-1\) \(-4\) \(3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}+3q^{7}+\cdots\)
222.2.a.b 222.a 1.a $1$ $1.773$ \(\Q\) None 222.2.a.b \(-1\) \(-1\) \(2\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{8}+\cdots\)
222.2.a.c 222.a 1.a $1$ $1.773$ \(\Q\) None 222.2.a.c \(-1\) \(1\) \(4\) \(-1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+4q^{5}-q^{6}-q^{7}+\cdots\)
222.2.a.d 222.a 1.a $1$ $1.773$ \(\Q\) None 222.2.a.d \(1\) \(-1\) \(0\) \(3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+3q^{7}+q^{8}+\cdots\)
222.2.a.e 222.a 1.a $1$ $1.773$ \(\Q\) None 222.2.a.e \(1\) \(1\) \(0\) \(-1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}-q^{7}+q^{8}+\cdots\)
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