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Properties

Label 35700.2.a.dl
Level $35700$
Weight $2$
Character orbit 35700.a
Self dual yes
Analytic conductor $285.066$
Dimension $10$

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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] = [35700,2,Mod(1,35700)] 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("35700.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(35700, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 35700 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 35700.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [10,0,10,0,0,0,-10,0,10,0,2,0,9,0,0,0,-10,0,-2,0,-10,0,-1,0,0, 0,10,0,0,0,9,0,2,0,0,0,17,0,9,0,-3,0,0,0,0,0,19,0,10,0,-10,0,8,0,0,0,-2, 0,10,0,-1,0,-10,0,0,0,-4,0,-1,0,-4,0,8,0,0,0,-2,0,-16,0,10,0,1,0,0,0,0, 0,-2,0,-9,0,9,0,0,0,0,0,2,0] 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: \(285.065935216\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 22x^{8} - 21x^{7} + 81x^{6} + 84x^{5} - 98x^{4} - 97x^{3} + 32x^{2} + 30x + 4 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 10 q + 10 q^{3} - 10 q^{7} + 10 q^{9} + 2 q^{11} + 9 q^{13} - 10 q^{17} - 2 q^{19} - 10 q^{21} - q^{23} + 10 q^{27} + 9 q^{31} + 2 q^{33} + 17 q^{37} + 9 q^{39} - 3 q^{41} + 19 q^{47} + 10 q^{49} - 10 q^{51}+ \cdots + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(3\) \( -1 \)
\(5\) \( -1 \)
\(7\) \( +1 \)
\(17\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.