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Properties

Label 1589.2.a.d
Level $1589$
Weight $2$
Character orbit 1589.a
Self dual yes
Analytic conductor $12.688$
Analytic rank $0$
Dimension $35$
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] = [1589,2,Mod(1,1589)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1589, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) 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("1589.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 1589 = 7 \cdot 227 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1589.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [35,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(12.6882288812\)
Analytic rank: \(0\)
Dimension: \(35\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 35 q + 2 q^{2} + 3 q^{3} + 50 q^{4} - 7 q^{5} + q^{6} - 35 q^{7} + 6 q^{8} + 50 q^{9} + 14 q^{10} + 18 q^{11} - 3 q^{12} - 15 q^{13} - 2 q^{14} + 15 q^{15} + 84 q^{16} - 2 q^{17} + 14 q^{18} + 56 q^{19}+ \cdots + 112 q^{99}+O(q^{100}) \) 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 −2.81115 1.26957 5.90256 −1.53317 −3.56897 −1.00000 −10.9707 −1.38818 4.30996
1.2 −2.65388 −1.31711 5.04306 −0.499094 3.49545 −1.00000 −8.07590 −1.26521 1.32453
1.3 −2.61565 2.57280 4.84161 −3.94761 −6.72954 −1.00000 −7.43264 3.61930 10.3256
1.4 −2.50815 −2.40693 4.29079 3.73521 6.03692 −1.00000 −5.74564 2.79330 −9.36845
1.5 −2.41051 −3.19192 3.81057 −4.02520 7.69417 −1.00000 −4.36440 7.18838 9.70280
1.6 −2.30078 2.40038 3.29359 1.91728 −5.52274 −1.00000 −2.97627 2.76182 −4.41123
1.7 −2.19228 −1.28813 2.80611 2.27203 2.82394 −1.00000 −1.76722 −1.34073 −4.98092
1.8 −1.67290 0.647104 0.798589 −2.18294 −1.08254 −1.00000 2.00984 −2.58126 3.65183
1.9 −1.60890 3.20939 0.588551 0.250712 −5.16358 −1.00000 2.27088 7.30018 −0.403369
1.10 −1.51408 −1.10474 0.292441 −2.22241 1.67266 −1.00000 2.58538 −1.77955 3.36490
1.11 −1.43752 −2.67770 0.0664512 −1.44229 3.84924 −1.00000 2.77951 4.17009 2.07331
1.12 −1.20096 0.826066 −0.557698 0.315473 −0.992071 −1.00000 3.07169 −2.31762 −0.378870
1.13 −1.07664 2.23788 −0.840839 2.23110 −2.40940 −1.00000 3.05857 2.00810 −2.40210
1.14 −0.952142 1.41398 −1.09343 −2.32847 −1.34631 −1.00000 2.94538 −1.00067 2.21703
1.15 −0.693131 −0.510616 −1.51957 0.240976 0.353923 −1.00000 2.43952 −2.73927 −0.167028
1.16 0.104408 −3.31183 −1.98910 1.06818 −0.345780 −1.00000 −0.416492 7.96822 0.111526
1.17 0.145967 −0.518848 −1.97869 −2.92663 −0.0757347 −1.00000 −0.580759 −2.73080 −0.427192
1.18 0.148093 1.10112 −1.97807 4.11134 0.163068 −1.00000 −0.589125 −1.78754 0.608862
1.19 0.299503 2.78324 −1.91030 3.31729 0.833589 −1.00000 −1.17115 4.74644 0.993537
1.20 0.417333 3.18300 −1.82583 −3.79061 1.32837 −1.00000 −1.59665 7.13147 −1.58195
See all 35 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.35
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(7\) \( +1 \)
\(227\) \( -1 \)

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 1589.2.a.d ✓ 35
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1589.2.a.d ✓ 35 1.a even 1 1 trivial