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Properties

Label 1767.4.a.h
Level $1767$
Weight $4$
Character orbit 1767.a
Self dual yes
Analytic conductor $104.256$
Analytic rank $0$
Dimension $40$
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 = [40] 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: \(40\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 40 q + 7 q^{2} + 120 q^{3} + 195 q^{4} + 5 q^{5} + 21 q^{6} + 23 q^{7} + 90 q^{8} + 360 q^{9} + 98 q^{10} + 50 q^{11} + 585 q^{12} + 222 q^{13} + 89 q^{14} + 15 q^{15} + 1155 q^{16} + 165 q^{17} + 63 q^{18}+ \cdots + 450 q^{99}+O(q^{100}) \) 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 −5.54781 3.00000 22.7782 1.89670 −16.6434 −0.127812 −81.9865 9.00000 −10.5225
1.2 −5.49495 3.00000 22.1944 −20.3845 −16.4848 8.20315 −77.9977 9.00000 112.012
1.3 −4.95203 3.00000 16.5226 20.2298 −14.8561 11.6574 −42.2043 9.00000 −100.179
1.4 −4.51047 3.00000 12.3443 −10.1780 −13.5314 −5.46846 −19.5950 9.00000 45.9077
1.5 −4.51013 3.00000 12.3413 13.4392 −13.5304 −16.4646 −19.5799 9.00000 −60.6126
1.6 −4.40288 3.00000 11.3854 4.71770 −13.2086 −32.3556 −14.9054 9.00000 −20.7715
1.7 −4.29723 3.00000 10.4661 −20.7891 −12.8917 −17.8985 −10.5976 9.00000 89.3354
1.8 −4.16616 3.00000 9.35691 −13.1815 −12.4985 31.2777 −5.65312 9.00000 54.9162
1.9 −3.97274 3.00000 7.78268 1.89956 −11.9182 30.7474 0.863350 9.00000 −7.54648
1.10 −3.35294 3.00000 3.24219 8.93548 −10.0588 −6.38413 15.9527 9.00000 −29.9601
1.11 −3.24066 3.00000 2.50189 2.54529 −9.72198 −11.2111 17.8175 9.00000 −8.24842
1.12 −2.68049 3.00000 −0.814987 −6.00477 −8.04146 −29.1707 23.6285 9.00000 16.0957
1.13 −2.12215 3.00000 −3.49649 15.8207 −6.36644 34.4325 24.3972 9.00000 −33.5738
1.14 −1.61969 3.00000 −5.37659 13.7475 −4.85908 12.5478 21.6660 9.00000 −22.2667
1.15 −1.49512 3.00000 −5.76460 −14.7200 −4.48537 19.3135 20.5798 9.00000 22.0082
1.16 −1.40586 3.00000 −6.02355 −8.70541 −4.21759 −11.3888 19.7152 9.00000 12.2386
1.17 −1.38233 3.00000 −6.08915 −16.7174 −4.14700 8.63898 19.4759 9.00000 23.1091
1.18 −0.288862 3.00000 −7.91656 21.9577 −0.866586 0.905290 4.59769 9.00000 −6.34274
1.19 −0.175340 3.00000 −7.96926 0.117908 −0.526020 −15.3486 2.80005 9.00000 −0.0206739
1.20 −0.0445748 3.00000 −7.99801 15.5179 −0.133724 −30.6741 0.713108 9.00000 −0.691707
See all 40 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.40
Significant digits:
Format:

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.h ✓ 40
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1767.4.a.h ✓ 40 1.a even 1 1 trivial