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Properties

Label 925.2.n.d
Level $925$
Weight $2$
Character orbit 925.n
Analytic conductor $7.386$
Analytic rank $0$
Dimension $28$
Inner twists $2$

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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] = [925,2,Mod(101,925)] 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("925.101"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 925 = 5^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 925.n (of order \(6\), degree \(2\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [28,6] 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: \(7.38616218697\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(14\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 185)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 28 q + 6 q^{2} + 4 q^{3} + 20 q^{4} + 2 q^{7} - 18 q^{9} + 4 q^{11} - 2 q^{12} + 30 q^{13} - 20 q^{16} - 30 q^{18} - 2 q^{21} + 30 q^{22} + 30 q^{24} + 12 q^{26} - 32 q^{27} - 2 q^{28} - 18 q^{32} - 18 q^{33}+ \cdots - 60 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
101.1 −2.29684 − 1.32608i 0.0638062 + 0.110516i 2.51697 + 4.35953i 0 − 0.338448i 1.72659 + 2.99054i − 8.04652i 1.49186 − 2.58397i 0
101.2 −2.05130 − 1.18432i 1.07393 + 1.86010i 1.80523 + 3.12676i 0 − 5.08750i −0.824280 − 1.42769i − 3.81462i −0.806637 + 1.39714i 0
101.3 −1.49679 − 0.864172i −0.833596 − 1.44383i 0.493588 + 0.854919i 0 2.88148i 0.0212161 + 0.0367474i 1.75051i 0.110234 − 0.190931i 0
101.4 −1.31801 − 0.760954i −1.33553 − 2.31321i 0.158102 + 0.273841i 0 4.06511i 0.696862 + 1.20700i 2.56258i −2.06729 + 3.58065i 0
101.5 −1.22813 − 0.709060i 1.32488 + 2.29477i 0.00553227 + 0.00958218i 0 − 3.75769i 1.47091 + 2.54770i 2.82055i −2.01063 + 3.48252i 0
101.6 −0.108589 − 0.0626936i −0.156745 − 0.271490i −0.992139 − 1.71844i 0 0.0393076i 0.790882 + 1.36985i 0.499578i 1.45086 − 2.51297i 0
101.7 0.217929 + 0.125821i 1.61547 + 2.79808i −0.968338 − 1.67721i 0 0.813045i −0.127669 − 0.221129i − 0.990637i −3.71951 + 6.44238i 0
101.8 0.596292 + 0.344270i 0.622433 + 1.07808i −0.762957 − 1.32148i 0 0.857138i 0.273058 + 0.472950i − 2.42773i 0.725155 − 1.25601i 0
101.9 0.754635 + 0.435689i −0.996238 − 1.72553i −0.620350 − 1.07448i 0 − 1.73620i −1.67414 − 2.89970i − 2.82387i −0.484979 + 0.840008i 0
101.10 1.61472 + 0.932256i 0.00733364 + 0.0127022i 0.738203 + 1.27861i 0 0.0273473i −2.28706 − 3.96130i − 0.976246i 1.49989 − 2.59789i 0
101.11 1.86389 + 1.07612i 0.823223 + 1.42586i 1.31605 + 2.27946i 0 3.54353i 2.34537 + 4.06229i 1.36041i 0.144607 − 0.250467i 0
101.12 1.91807 + 1.10740i −0.262986 − 0.455505i 1.45267 + 2.51610i 0 − 1.16492i 0.973099 + 1.68546i 2.00515i 1.36168 − 2.35849i 0
101.13 2.20795 + 1.27476i 1.58363 + 2.74293i 2.25003 + 3.89716i 0 8.07501i −2.10035 − 3.63792i 6.37394i −3.51579 + 6.08952i 0
101.14 2.32618 + 1.34302i −1.52962 − 2.64937i 2.60740 + 4.51616i 0 − 8.21722i −0.284485 − 0.492742i 8.63511i −3.17945 + 5.50697i 0
751.1 −2.29684 + 1.32608i 0.0638062 − 0.110516i 2.51697 − 4.35953i 0 0.338448i 1.72659 − 2.99054i 8.04652i 1.49186 + 2.58397i 0
751.2 −2.05130 + 1.18432i 1.07393 − 1.86010i 1.80523 − 3.12676i 0 5.08750i −0.824280 + 1.42769i 3.81462i −0.806637 − 1.39714i 0
751.3 −1.49679 + 0.864172i −0.833596 + 1.44383i 0.493588 − 0.854919i 0 − 2.88148i 0.0212161 − 0.0367474i − 1.75051i 0.110234 + 0.190931i 0
751.4 −1.31801 + 0.760954i −1.33553 + 2.31321i 0.158102 − 0.273841i 0 − 4.06511i 0.696862 − 1.20700i − 2.56258i −2.06729 − 3.58065i 0
751.5 −1.22813 + 0.709060i 1.32488 − 2.29477i 0.00553227 − 0.00958218i 0 3.75769i 1.47091 − 2.54770i − 2.82055i −2.01063 − 3.48252i 0
751.6 −0.108589 + 0.0626936i −0.156745 + 0.271490i −0.992139 + 1.71844i 0 − 0.0393076i 0.790882 − 1.36985i − 0.499578i 1.45086 + 2.51297i 0
See all 28 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 101.14
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
37.e even 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 925.2.n.d 28
5.b even 2 1 185.2.m.a ✓ 28
5.c odd 4 1 925.2.m.c 28
5.c odd 4 1 925.2.m.d 28
37.e even 6 1 inner 925.2.n.d 28
185.l even 6 1 185.2.m.a ✓ 28
185.q odd 12 1 6845.2.a.n 14
185.q odd 12 1 6845.2.a.o 14
185.r odd 12 1 925.2.m.c 28
185.r odd 12 1 925.2.m.d 28
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
185.2.m.a ✓ 28 5.b even 2 1
185.2.m.a ✓ 28 185.l even 6 1
925.2.m.c 28 5.c odd 4 1
925.2.m.c 28 185.r odd 12 1
925.2.m.d 28 5.c odd 4 1
925.2.m.d 28 185.r odd 12 1
925.2.n.d 28 1.a even 1 1 trivial
925.2.n.d 28 37.e even 6 1 inner
6845.2.a.n 14 185.q odd 12 1
6845.2.a.o 14 185.q odd 12 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{28} - 6 T_{2}^{27} - 6 T_{2}^{26} + 108 T_{2}^{25} - 27 T_{2}^{24} - 1260 T_{2}^{23} + 1484 T_{2}^{22} + \cdots + 729 \) acting on \(S_{2}^{\mathrm{new}}(925, [\chi])\). Copy content Toggle raw display