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Properties

Label 1134.3.b.c
Level $1134$
Weight $3$
Character orbit 1134.b
Analytic conductor $30.899$
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] = [1134,3,Mod(323,1134)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1134, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 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("1134.323"); S:= CuspForms(chi, 3); N := Newforms(S);
 
Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1134.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(30.8992619785\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: no (minimal twist has level 126)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 48 q^{4} + 96 q^{16} + 24 q^{19} - 48 q^{22} - 144 q^{25} + 120 q^{31} + 96 q^{34} - 168 q^{37} - 120 q^{43} + 168 q^{49} + 264 q^{55} - 192 q^{64} - 144 q^{67} + 24 q^{73} - 48 q^{76} - 24 q^{79}+ \cdots - 96 q^{97}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
323.1 − 1.41421i 0 −2.00000 − 7.74628i 0 −2.64575 2.82843i 0 −10.9549
323.2 − 1.41421i 0 −2.00000 − 6.37459i 0 −2.64575 2.82843i 0 −9.01503
323.3 − 1.41421i 0 −2.00000 − 6.01006i 0 2.64575 2.82843i 0 −8.49950
323.4 − 1.41421i 0 −2.00000 − 4.16679i 0 2.64575 2.82843i 0 −5.89274
323.5 − 1.41421i 0 −2.00000 − 3.19697i 0 2.64575 2.82843i 0 −4.52120
323.6 − 1.41421i 0 −2.00000 − 2.65693i 0 −2.64575 2.82843i 0 −3.75747
323.7 − 1.41421i 0 −2.00000 0.768169i 0 2.64575 2.82843i 0 1.08636
323.8 − 1.41421i 0 −2.00000 2.95738i 0 −2.64575 2.82843i 0 4.18237
323.9 − 1.41421i 0 −2.00000 4.01088i 0 2.64575 2.82843i 0 5.67224
323.10 − 1.41421i 0 −2.00000 5.20706i 0 −2.64575 2.82843i 0 7.36389
323.11 − 1.41421i 0 −2.00000 8.59478i 0 2.64575 2.82843i 0 12.1548
323.12 − 1.41421i 0 −2.00000 8.61336i 0 −2.64575 2.82843i 0 12.1811
323.13 1.41421i 0 −2.00000 − 8.61336i 0 −2.64575 − 2.82843i 0 12.1811
323.14 1.41421i 0 −2.00000 − 8.59478i 0 2.64575 − 2.82843i 0 12.1548
323.15 1.41421i 0 −2.00000 − 5.20706i 0 −2.64575 − 2.82843i 0 7.36389
323.16 1.41421i 0 −2.00000 − 4.01088i 0 2.64575 − 2.82843i 0 5.67224
323.17 1.41421i 0 −2.00000 − 2.95738i 0 −2.64575 − 2.82843i 0 4.18237
323.18 1.41421i 0 −2.00000 − 0.768169i 0 2.64575 − 2.82843i 0 1.08636
323.19 1.41421i 0 −2.00000 2.65693i 0 −2.64575 − 2.82843i 0 −3.75747
323.20 1.41421i 0 −2.00000 3.19697i 0 2.64575 − 2.82843i 0 −4.52120
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 323.24
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1134.3.b.c 24
3.b odd 2 1 inner 1134.3.b.c 24
9.c even 3 1 126.3.q.a ✓ 24
9.c even 3 1 378.3.q.a 24
9.d odd 6 1 126.3.q.a ✓ 24
9.d odd 6 1 378.3.q.a 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
126.3.q.a ✓ 24 9.c even 3 1
126.3.q.a ✓ 24 9.d odd 6 1
378.3.q.a 24 9.c even 3 1
378.3.q.a 24 9.d odd 6 1
1134.3.b.c 24 1.a even 1 1 trivial
1134.3.b.c 24 3.b odd 2 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5}^{24} + 372 T_{5}^{22} + 59670 T_{5}^{20} + 5428672 T_{5}^{18} + 310334277 T_{5}^{16} + \cdots + 13\!\cdots\!69 \) acting on \(S_{3}^{\mathrm{new}}(1134, [\chi])\). Copy content Toggle raw display