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Properties

Label 30345.2.a.ed
Level $30345$
Weight $2$
Character orbit 30345.a
Self dual yes
Analytic conductor $242.306$
Dimension $30$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [30345,2,Mod(1,30345)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("30345.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(30345, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 30345 = 3 \cdot 5 \cdot 7 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 30345.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [30,3,-30,39,-30,-3,30,9,30,-3,3,-39,12,3,30,57,0,3,12,-39,-30, -3,-18,-9,30,6,-30,39,-18,3,-3,51,-3,0,-30,39,12,24,-12,-9,-15,-3,36,6, -30,21,27,-57,30,3,0,15,24,-3,-3,9,-12,0,-18,39,6,-72,30,147,-12,3,30, 0,18,-3,-18,9,-24,-6,-30,60,3,-6,24,-57,30,-24,0,-39,0,39,18,24,21,-3, 12,9,3,72,-12,-51,-75,3,3,39] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(None)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(242.306044934\)
Dimension: \(30\)
Twist minimal: not computed
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 30 q + 3 q^{2} - 30 q^{3} + 39 q^{4} - 30 q^{5} - 3 q^{6} + 30 q^{7} + 9 q^{8} + 30 q^{9} - 3 q^{10} + 3 q^{11} - 39 q^{12} + 12 q^{13} + 3 q^{14} + 30 q^{15} + 57 q^{16} + 3 q^{18} + 12 q^{19} - 39 q^{20}+ \cdots + 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(3\) \( +1 \)
\(5\) \( +1 \)
\(7\) \( -1 \)
\(17\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.