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Properties

Label 454.6.a.c
Level $454$
Weight $6$
Character orbit 454.a
Self dual yes
Analytic conductor $72.814$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $1$

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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] = [454,6,Mod(1,454)] 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("454.1"); S:= CuspForms(chi, 6); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(454, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 6, names="a")
 
Level: \( N \) \(=\) \( 454 = 2 \cdot 227 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 454.a (trivial)

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: yes
Analytic conductor: \(72.8142541951\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 96 q^{2} - q^{3} + 384 q^{4} + 131 q^{5} + 4 q^{6} - 270 q^{7} - 1536 q^{8} + 2237 q^{9} - 524 q^{10} + 1071 q^{11} - 16 q^{12} + 1435 q^{13} + 1080 q^{14} - 818 q^{15} + 6144 q^{16} + 2344 q^{17}+ \cdots + 515613 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −4.00000 −28.7432 16.0000 −44.8015 114.973 −36.2675 −64.0000 583.173 179.206
1.2 −4.00000 −28.1338 16.0000 93.5426 112.535 −158.491 −64.0000 548.512 −374.170
1.3 −4.00000 −27.7470 16.0000 −73.0204 110.988 −116.542 −64.0000 526.897 292.082
1.4 −4.00000 −20.1664 16.0000 80.2136 80.6654 −123.689 −64.0000 163.682 −320.854
1.5 −4.00000 −20.1509 16.0000 −21.0107 80.6037 108.611 −64.0000 163.060 84.0429
1.6 −4.00000 −15.7818 16.0000 −30.5216 63.1273 −30.2899 −64.0000 6.06625 122.086
1.7 −4.00000 −14.0484 16.0000 97.0319 56.1937 127.503 −64.0000 −45.6416 −388.128
1.8 −4.00000 −13.6701 16.0000 −20.1284 54.6802 73.3752 −64.0000 −56.1295 80.5134
1.9 −4.00000 −9.30305 16.0000 33.9393 37.2122 −213.506 −64.0000 −156.453 −135.757
1.10 −4.00000 −8.37307 16.0000 53.9317 33.4923 104.744 −64.0000 −172.892 −215.727
1.11 −4.00000 −2.12992 16.0000 −37.8978 8.51966 55.6897 −64.0000 −238.463 151.591
1.12 −4.00000 −2.04191 16.0000 91.3578 8.16765 144.717 −64.0000 −238.831 −365.431
1.13 −4.00000 −1.07544 16.0000 33.4233 4.30178 −40.9714 −64.0000 −241.843 −133.693
1.14 −4.00000 −0.282811 16.0000 −88.6813 1.13124 128.637 −64.0000 −242.920 354.725
1.15 −4.00000 9.73175 16.0000 −39.5216 −38.9270 −110.386 −64.0000 −148.293 158.086
1.16 −4.00000 11.5870 16.0000 −54.6103 −46.3478 −253.932 −64.0000 −108.742 218.441
1.17 −4.00000 11.9411 16.0000 −66.4848 −47.7643 −75.1343 −64.0000 −100.411 265.939
1.18 −4.00000 16.2623 16.0000 66.1555 −65.0494 170.078 −64.0000 21.4638 −264.622
1.19 −4.00000 17.5594 16.0000 −47.3097 −70.2374 240.265 −64.0000 65.3310 189.239
1.20 −4.00000 18.6402 16.0000 17.9640 −74.5606 −134.451 −64.0000 104.455 −71.8558
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.24
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(227\) \( -1 \)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 454.6.a.c ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
454.6.a.c ✓ 24 1.a even 1 1 trivial