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Properties

Label 1767.4.a.e
Level $1767$
Weight $4$
Character orbit 1767.a
Self dual yes
Analytic conductor $104.256$
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] = [1767,4,Mod(1,1767)] 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("1767.1"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1767, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 4, names="a")
 
Level: \( N \) \(=\) \( 1767 = 3 \cdot 19 \cdot 31 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1767.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [35] 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: \(104.256374980\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 35 q + 7 q^{2} - 105 q^{3} + 143 q^{4} + 39 q^{5} - 21 q^{6} + 21 q^{7} + 120 q^{8} + 315 q^{9} - 54 q^{10} + 178 q^{11} - 429 q^{12} + 156 q^{13} + 121 q^{14} - 117 q^{15} + 587 q^{16} + 405 q^{17} + 63 q^{18}+ \cdots + 1602 q^{99}+O(q^{100}) \) 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 −5.52698 −3.00000 22.5475 11.9705 16.5809 6.05459 −80.4040 9.00000 −66.1610
1.2 −5.01002 −3.00000 17.1003 2.59041 15.0301 −23.9646 −45.5926 9.00000 −12.9780
1.3 −4.88030 −3.00000 15.8173 −13.5501 14.6409 −14.4331 −38.1507 9.00000 66.1284
1.4 −4.58865 −3.00000 13.0557 1.31885 13.7659 −16.3406 −23.1987 9.00000 −6.05175
1.5 −4.37522 −3.00000 11.1425 12.9527 13.1256 29.4102 −13.7492 9.00000 −56.6710
1.6 −3.76709 −3.00000 6.19095 −9.05542 11.3013 33.2790 6.81485 9.00000 34.1126
1.7 −3.69308 −3.00000 5.63886 −10.2270 11.0792 2.78948 8.71989 9.00000 37.7690
1.8 −3.27794 −3.00000 2.74488 18.0880 9.83381 −15.5004 17.2260 9.00000 −59.2914
1.9 −3.20159 −3.00000 2.25017 10.0402 9.60477 19.2247 18.4086 9.00000 −32.1447
1.10 −2.49644 −3.00000 −1.76779 −18.7989 7.48932 −31.6266 24.3847 9.00000 46.9304
1.11 −2.37634 −3.00000 −2.35302 19.4559 7.12901 −32.1332 24.6023 9.00000 −46.2337
1.12 −2.03378 −3.00000 −3.86372 7.48347 6.10135 −0.835390 24.1283 9.00000 −15.2198
1.13 −1.83727 −3.00000 −4.62445 −8.04631 5.51180 −14.7214 23.1945 9.00000 14.7832
1.14 −0.818882 −3.00000 −7.32943 21.0465 2.45665 33.6845 12.5530 9.00000 −17.2346
1.15 −0.818567 −3.00000 −7.32995 −15.9606 2.45570 10.1246 12.5486 9.00000 13.0648
1.16 −0.570104 −3.00000 −7.67498 −18.7063 1.71031 17.7166 8.93637 9.00000 10.6645
1.17 −0.209323 −3.00000 −7.95618 −1.51301 0.627969 2.89019 3.34000 9.00000 0.316707
1.18 −0.0867348 −3.00000 −7.99248 3.63784 0.260204 −15.9848 1.38710 9.00000 −0.315527
1.19 0.156096 −3.00000 −7.97563 12.7057 −0.468287 19.4417 −2.49373 9.00000 1.98331
1.20 0.389416 −3.00000 −7.84835 −9.13404 −1.16825 1.33302 −6.17161 9.00000 −3.55695
See all 35 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.35
Significant digits:
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Atkin-Lehner signs

\( p \) Sign
\(3\) \( +1 \)
\(19\) \( -1 \)
\(31\) \( -1 \)

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 1767.4.a.e ✓ 35
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1767.4.a.e ✓ 35 1.a even 1 1 trivial