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Properties

Label 38025.2.a.jg
Level $38025$
Weight $2$
Character orbit 38025.a
Self dual yes
Analytic conductor $303.631$
Dimension $18$

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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] = [38025,2,Mod(1,38025)] 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("38025.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(38025, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 38025 = 3^{2} \cdot 5^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 38025.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [18,-7,0,19,0,0,12,-21,0,0,2,0,0,6,0,33,4,0,26,0,0,18,2,0,0,0, 0,34,-14,0,38,-59,0,18,0,0,46,-12,0,0,-2,0,-2,10,0,27,-28,0,6,0,0,0,0, 0,0,0,0,42,6,0,-8,-20,0,61,0,0,30,22,0,0,16,0,56,6,0,59,18,0,6,0,0,-78, -42,0,0,84,0,-24,2,0,0,26,0,20,0,0,70,-35,0,0] 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: \(303.631153686\)
Dimension: \(18\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{18} - 7 x^{17} - 3 x^{16} + 119 x^{15} - 154 x^{14} - 730 x^{13} + 1566 x^{12} + 1859 x^{11} + \cdots - 49 \) Copy content Toggle raw display
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.

\(\operatorname{Tr}(f)(q) = \) \( 18 q - 7 q^{2} + 19 q^{4} + 12 q^{7} - 21 q^{8} + 2 q^{11} + 6 q^{14} + 33 q^{16} + 4 q^{17} + 26 q^{19} + 18 q^{22} + 2 q^{23} + 34 q^{28} - 14 q^{29} + 38 q^{31} - 59 q^{32} + 18 q^{34} + 46 q^{37} - 12 q^{38}+ \cdots - 35 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(3\) \( -1 \)
\(5\) \( -1 \)
\(13\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.