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Properties

Label 580.2.be.d
Level $580$
Weight $2$
Character orbit 580.be
Analytic conductor $4.631$
Analytic rank $0$
Dimension $24$
CM discriminant -20
Inner twists $4$

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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] = [580,2,Mod(19,580)] 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("580.19"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(580, base_ring=CyclotomicField(28)) chi = DirichletCharacter(H, H._module([14, 14, 9])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 580 = 2^{2} \cdot 5 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 580.be (of order \(28\), degree \(12\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [24,4] 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: no
Analytic conductor: \(4.63132331723\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(2\) over \(\Q(\zeta_{28})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{28}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 4 q^{2} + 4 q^{3} - 30 q^{7} - 8 q^{8} - 8 q^{12} - 12 q^{14} + 70 q^{15} + 16 q^{16} + 4 q^{18} - 12 q^{21} - 10 q^{23} - 40 q^{24} + 20 q^{25} + 58 q^{27} + 12 q^{29} - 16 q^{32} + 104 q^{36} + 24 q^{41}+ \cdots + 84 q^{98}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
19.1 −0.752407 − 1.19745i −1.12218 + 3.20702i −0.867767 + 1.80194i −2.18001 − 0.497572i 4.68458 − 1.06922i −3.95172 + 1.90305i 2.81064 − 0.316683i −6.68017 − 5.32726i 1.04443 + 2.98482i
19.2 −0.752407 − 1.19745i 0.914312 − 2.61295i −0.867767 + 1.80194i 2.18001 + 0.497572i −3.81681 + 0.871162i 1.42674 − 0.687083i 2.81064 − 0.316683i −3.64606 − 2.90764i −1.04443 − 2.98482i
39.1 1.19745 − 0.752407i −3.20702 − 1.12218i 0.867767 − 1.80194i −2.18001 − 0.497572i −4.68458 + 1.06922i −2.66698 + 1.28435i −0.316683 − 2.81064i 6.68017 + 5.32726i −2.98482 + 1.04443i
39.2 1.19745 − 0.752407i 2.61295 + 0.914312i 0.867767 − 1.80194i 2.18001 + 0.497572i 3.81681 − 0.871162i −4.54898 + 2.19068i −0.316683 − 2.81064i 3.64606 + 2.90764i 2.98482 − 1.04443i
79.1 0.467085 − 1.33485i −0.0972829 − 0.0109612i −1.56366 − 1.24698i 0.970194 + 2.01463i −0.0600709 + 0.124739i −2.84936 − 3.57299i −2.39490 + 1.50481i −2.91544 − 0.665430i 3.14239 − 0.354063i
79.2 0.467085 − 1.33485i 2.62958 + 0.296283i −1.56366 − 1.24698i −0.970194 − 2.01463i 1.62373 − 3.37172i −2.40786 − 3.01936i −2.39490 + 1.50481i 3.90215 + 0.890639i −3.14239 + 0.354063i
119.1 1.19745 + 0.752407i −3.20702 + 1.12218i 0.867767 + 1.80194i −2.18001 + 0.497572i −4.68458 − 1.06922i −2.66698 − 1.28435i −0.316683 + 2.81064i 6.68017 − 5.32726i −2.98482 − 1.04443i
119.2 1.19745 + 0.752407i 2.61295 − 0.914312i 0.867767 + 1.80194i 2.18001 − 0.497572i 3.81681 + 0.871162i −4.54898 − 2.19068i −0.316683 + 2.81064i 3.64606 − 2.90764i 2.98482 + 1.04443i
159.1 0.158342 + 1.40532i −1.78450 − 2.84001i −1.94986 + 0.445042i 1.74823 + 1.39417i 3.70857 − 2.95748i −0.0935380 + 0.409817i −0.934170 − 2.66971i −3.57958 + 7.43308i −1.68243 + 2.67758i
159.2 0.158342 + 1.40532i 0.846261 + 1.34682i −1.94986 + 0.445042i −1.74823 − 1.39417i −1.75871 + 1.40253i 1.09810 − 4.81107i −0.934170 − 2.66971i 0.203893 − 0.423389i 1.68243 − 2.67758i
259.1 0.158342 − 1.40532i −1.78450 + 2.84001i −1.94986 − 0.445042i 1.74823 − 1.39417i 3.70857 + 2.95748i −0.0935380 − 0.409817i −0.934170 + 2.66971i −3.57958 − 7.43308i −1.68243 − 2.67758i
259.2 0.158342 − 1.40532i 0.846261 − 1.34682i −1.94986 − 0.445042i −1.74823 + 1.39417i −1.75871 − 1.40253i 1.09810 + 4.81107i −0.934170 + 2.66971i 0.203893 + 0.423389i 1.68243 + 2.67758i
279.1 0.467085 + 1.33485i −0.0972829 + 0.0109612i −1.56366 + 1.24698i 0.970194 − 2.01463i −0.0600709 − 0.124739i −2.84936 + 3.57299i −2.39490 − 1.50481i −2.91544 + 0.665430i 3.14239 + 0.354063i
279.2 0.467085 + 1.33485i 2.62958 − 0.296283i −1.56366 + 1.24698i −0.970194 + 2.01463i 1.62373 + 3.37172i −2.40786 + 3.01936i −2.39490 − 1.50481i 3.90215 − 0.890639i −3.14239 − 0.354063i
359.1 1.33485 − 0.467085i −0.296283 − 2.62958i 1.56366 − 1.24698i −0.970194 + 2.01463i −1.62373 − 3.37172i 2.25542 − 2.82821i 1.50481 − 2.39490i −3.90215 + 0.890639i −0.354063 + 3.14239i
359.2 1.33485 − 0.467085i 0.0109612 + 0.0972829i 1.56366 − 1.24698i 0.970194 − 2.01463i 0.0600709 + 0.124739i −1.66308 + 2.08543i 1.50481 − 2.39490i 2.91544 − 0.665430i 0.354063 − 3.14239i
379.1 −1.40532 − 0.158342i −1.34682 − 0.846261i 1.94986 + 0.445042i −1.74823 + 1.39417i 1.75871 + 1.40253i −0.424996 − 1.86203i −2.66971 − 0.934170i −0.203893 − 0.423389i 2.67758 − 1.68243i
379.2 −1.40532 − 0.158342i 2.84001 + 1.78450i 1.94986 + 0.445042i 1.74823 − 1.39417i −3.70857 − 2.95748i −1.17375 − 5.14253i −2.66971 − 0.934170i 3.57958 + 7.43308i −2.67758 + 1.68243i
479.1 −1.40532 + 0.158342i −1.34682 + 0.846261i 1.94986 − 0.445042i −1.74823 − 1.39417i 1.75871 − 1.40253i −0.424996 + 1.86203i −2.66971 + 0.934170i −0.203893 + 0.423389i 2.67758 + 1.68243i
479.2 −1.40532 + 0.158342i 2.84001 − 1.78450i 1.94986 − 0.445042i 1.74823 + 1.39417i −3.70857 + 2.95748i −1.17375 + 5.14253i −2.66971 + 0.934170i 3.57958 − 7.43308i −2.67758 − 1.68243i
See all 24 embeddings
\(n\): e.g. 2-40 or 80-90
Embeddings: e.g. 1-3 or 19.2
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
20.d odd 2 1 CM by \(\Q(\sqrt{-5}) \)
29.f odd 28 1 inner
580.be even 28 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 580.2.be.d yes 24
4.b odd 2 1 580.2.be.c ✓ 24
5.b even 2 1 580.2.be.c ✓ 24
20.d odd 2 1 CM 580.2.be.d yes 24
29.f odd 28 1 inner 580.2.be.d yes 24
116.l even 28 1 580.2.be.c ✓ 24
145.s odd 28 1 580.2.be.c ✓ 24
580.be even 28 1 inner 580.2.be.d yes 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
580.2.be.c ✓ 24 4.b odd 2 1
580.2.be.c ✓ 24 5.b even 2 1
580.2.be.c ✓ 24 116.l even 28 1
580.2.be.c ✓ 24 145.s odd 28 1
580.2.be.d yes 24 1.a even 1 1 trivial
580.2.be.d yes 24 20.d odd 2 1 CM
580.2.be.d yes 24 29.f odd 28 1 inner
580.2.be.d yes 24 580.be even 28 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(580, [\chi])\):

\( T_{3}^{24} - 4 T_{3}^{23} + 8 T_{3}^{22} - 50 T_{3}^{21} + 164 T_{3}^{20} - 10 T_{3}^{19} - 22 T_{3}^{18} + \cdots + 28561 \) Copy content Toggle raw display
\( T_{13} \) Copy content Toggle raw display