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Properties

Label 1824.2.bb.a
Level $1824$
Weight $2$
Character orbit 1824.bb
Analytic conductor $14.565$
Analytic rank $0$
Dimension $40$
Inner twists $2$

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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] = [1824,2,Mod(31,1824)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1824, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 0, 5])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1824.31"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 1824 = 2^{5} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1824.bb (of order \(6\), degree \(2\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [40,0,-20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(14.5647133287\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 40 q - 20 q^{3} - 20 q^{9} - 12 q^{13} + 8 q^{19} - 12 q^{21} - 20 q^{25} + 40 q^{27} - 40 q^{31} + 24 q^{41} - 12 q^{43} + 24 q^{47} - 16 q^{49} - 24 q^{53} - 4 q^{57} - 4 q^{61} + 12 q^{63} + 4 q^{67}+ \cdots - 24 q^{97}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
31.1 0 −0.500000 − 0.866025i 0 −2.01076 − 3.48273i 0 2.77433i 0 −0.500000 + 0.866025i 0
31.2 0 −0.500000 − 0.866025i 0 −1.82034 − 3.15292i 0 − 1.74971i 0 −0.500000 + 0.866025i 0
31.3 0 −0.500000 − 0.866025i 0 −1.48231 − 2.56744i 0 1.01492i 0 −0.500000 + 0.866025i 0
31.4 0 −0.500000 − 0.866025i 0 −1.46500 − 2.53746i 0 − 3.81392i 0 −0.500000 + 0.866025i 0
31.5 0 −0.500000 − 0.866025i 0 −0.999099 − 1.73049i 0 − 4.11177i 0 −0.500000 + 0.866025i 0
31.6 0 −0.500000 − 0.866025i 0 −0.970586 − 1.68110i 0 2.58636i 0 −0.500000 + 0.866025i 0
31.7 0 −0.500000 − 0.866025i 0 −0.795479 − 1.37781i 0 − 0.191945i 0 −0.500000 + 0.866025i 0
31.8 0 −0.500000 − 0.866025i 0 −0.382920 − 0.663237i 0 − 3.54100i 0 −0.500000 + 0.866025i 0
31.9 0 −0.500000 − 0.866025i 0 −0.352093 − 0.609843i 0 − 0.0726253i 0 −0.500000 + 0.866025i 0
31.10 0 −0.500000 − 0.866025i 0 −0.0963141 − 0.166821i 0 − 3.99046i 0 −0.500000 + 0.866025i 0
31.11 0 −0.500000 − 0.866025i 0 0.0666287 + 0.115404i 0 1.13909i 0 −0.500000 + 0.866025i 0
31.12 0 −0.500000 − 0.866025i 0 0.154165 + 0.267022i 0 4.44958i 0 −0.500000 + 0.866025i 0
31.13 0 −0.500000 − 0.866025i 0 0.508588 + 0.880900i 0 1.27458i 0 −0.500000 + 0.866025i 0
31.14 0 −0.500000 − 0.866025i 0 0.680039 + 1.17786i 0 3.19193i 0 −0.500000 + 0.866025i 0
31.15 0 −0.500000 − 0.866025i 0 0.683020 + 1.18302i 0 − 3.38954i 0 −0.500000 + 0.866025i 0
31.16 0 −0.500000 − 0.866025i 0 1.27939 + 2.21597i 0 1.33892i 0 −0.500000 + 0.866025i 0
31.17 0 −0.500000 − 0.866025i 0 1.40394 + 2.43169i 0 2.53192i 0 −0.500000 + 0.866025i 0
31.18 0 −0.500000 − 0.866025i 0 1.53403 + 2.65702i 0 − 2.10047i 0 −0.500000 + 0.866025i 0
31.19 0 −0.500000 − 0.866025i 0 1.97204 + 3.41567i 0 − 3.44606i 0 −0.500000 + 0.866025i 0
31.20 0 −0.500000 − 0.866025i 0 2.09307 + 3.62530i 0 − 0.822316i 0 −0.500000 + 0.866025i 0
See all 40 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 31.20
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
76.f even 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1824.2.bb.a ✓ 40
4.b odd 2 1 1824.2.bb.b yes 40
19.d odd 6 1 1824.2.bb.b yes 40
76.f even 6 1 inner 1824.2.bb.a ✓ 40
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1824.2.bb.a ✓ 40 1.a even 1 1 trivial
1824.2.bb.a ✓ 40 76.f even 6 1 inner
1824.2.bb.b yes 40 4.b odd 2 1
1824.2.bb.b yes 40 19.d odd 6 1