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Properties

Label 672.3.g.a
Level $672$
Weight $3$
Character orbit 672.g
Analytic conductor $18.311$
Analytic rank $0$
Dimension $24$
Inner twists $2$

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Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [672,3,Mod(463,672)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(672, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0, 0])) N = Newforms(chi, 3, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("672.463"); S:= CuspForms(chi, 3); N := Newforms(S);
 
Level: \( N \) \(=\) \( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 672.g (of order \(2\), degree \(1\), not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(18.3106737650\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: no (minimal twist has level 168)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 72 q^{9} - 32 q^{11} + 16 q^{17} + 64 q^{19} - 72 q^{25} - 80 q^{41} - 32 q^{43} - 168 q^{49} - 192 q^{51} - 192 q^{65} + 32 q^{67} - 240 q^{73} + 384 q^{75} + 216 q^{81} + 320 q^{83} + 400 q^{89}+ \cdots - 96 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Copy content comment:embeddings in the coefficient field
 
Copy content gp:mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
463.1 0 −1.73205 0 − 9.26683i 0 − 2.64575i 0 3.00000 0
463.2 0 −1.73205 0 − 7.47825i 0 2.64575i 0 3.00000 0
463.3 0 −1.73205 0 − 6.16432i 0 − 2.64575i 0 3.00000 0
463.4 0 −1.73205 0 − 5.94177i 0 2.64575i 0 3.00000 0
463.5 0 −1.73205 0 − 2.78060i 0 2.64575i 0 3.00000 0
463.6 0 −1.73205 0 − 0.769463i 0 − 2.64575i 0 3.00000 0
463.7 0 −1.73205 0 0.769463i 0 2.64575i 0 3.00000 0
463.8 0 −1.73205 0 2.78060i 0 − 2.64575i 0 3.00000 0
463.9 0 −1.73205 0 5.94177i 0 − 2.64575i 0 3.00000 0
463.10 0 −1.73205 0 6.16432i 0 2.64575i 0 3.00000 0
463.11 0 −1.73205 0 7.47825i 0 − 2.64575i 0 3.00000 0
463.12 0 −1.73205 0 9.26683i 0 2.64575i 0 3.00000 0
463.13 0 1.73205 0 − 8.04930i 0 − 2.64575i 0 3.00000 0
463.14 0 1.73205 0 − 4.09875i 0 2.64575i 0 3.00000 0
463.15 0 1.73205 0 − 3.78720i 0 2.64575i 0 3.00000 0
463.16 0 1.73205 0 − 3.19600i 0 2.64575i 0 3.00000 0
463.17 0 1.73205 0 − 2.47223i 0 − 2.64575i 0 3.00000 0
463.18 0 1.73205 0 − 0.560422i 0 − 2.64575i 0 3.00000 0
463.19 0 1.73205 0 0.560422i 0 2.64575i 0 3.00000 0
463.20 0 1.73205 0 2.47223i 0 2.64575i 0 3.00000 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 463.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
8.d odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 672.3.g.a 24
3.b odd 2 1 2016.3.g.d 24
4.b odd 2 1 168.3.g.a ✓ 24
8.b even 2 1 168.3.g.a ✓ 24
8.d odd 2 1 inner 672.3.g.a 24
12.b even 2 1 504.3.g.d 24
24.f even 2 1 2016.3.g.d 24
24.h odd 2 1 504.3.g.d 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
168.3.g.a ✓ 24 4.b odd 2 1
168.3.g.a ✓ 24 8.b even 2 1
504.3.g.d 24 12.b even 2 1
504.3.g.d 24 24.h odd 2 1
672.3.g.a 24 1.a even 1 1 trivial
672.3.g.a 24 8.d odd 2 1 inner
2016.3.g.d 24 3.b odd 2 1
2016.3.g.d 24 24.f even 2 1

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(672, [\chi])\).