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Properties

Label 927.2.w.a
Level $927$
Weight $2$
Character orbit 927.w
Analytic conductor $7.402$
Analytic rank $0$
Dimension $576$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [927,2,Mod(80,927)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(927, base_ring=CyclotomicField(34))
 
chi = DirichletCharacter(H, H._module([17, 25]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("927.80");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 927 = 3^{2} \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 927.w (of order \(34\), degree \(16\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.40213226737\)
Analytic rank: \(0\)
Dimension: \(576\)
Relative dimension: \(36\) over \(\Q(\zeta_{34})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{34}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 576 q + 40 q^{4} - 16 q^{7}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 576 q + 40 q^{4} - 16 q^{7} - 136 q^{10} + 8 q^{13} - 64 q^{16} - 8 q^{19} - 132 q^{25} + 228 q^{28} + 180 q^{34} - 108 q^{49} - 16 q^{52} + 8 q^{55} - 96 q^{58} + 32 q^{61} - 84 q^{64} + 204 q^{73} + 80 q^{76} + 40 q^{79} + 128 q^{82} - 68 q^{85} - 68 q^{88} - 284 q^{91} - 136 q^{94} - 424 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

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.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
80.1 −2.49980 + 1.24475i 0 3.49434 − 4.62725i 2.15104 + 1.96093i 0 −3.85596 + 0.720804i −1.94910 + 10.4268i 0 −7.81805 − 2.22443i
80.2 −2.44781 + 1.21886i 0 3.30087 − 4.37106i −0.722492 − 0.658639i 0 2.59308 − 0.484731i −1.74726 + 9.34699i 0 2.57131 + 0.731602i
80.3 −2.30909 + 1.14979i 0 2.80461 − 3.71391i 1.17257 + 1.06894i 0 −2.21608 + 0.414257i −1.25792 + 6.72927i 0 −3.93663 − 1.12007i
80.4 −2.16702 + 1.07905i 0 2.32635 − 3.08059i −2.08946 − 1.90479i 0 1.23364 − 0.230607i −0.827505 + 4.42676i 0 6.58325 + 1.87310i
80.5 −2.11828 + 1.05478i 0 2.16928 − 2.87260i 0.959259 + 0.874480i 0 4.10840 − 0.767992i −0.695563 + 3.72093i 0 −2.95436 − 0.840588i
80.6 −1.87401 + 0.933146i 0 1.43588 − 1.90142i 2.61926 + 2.38777i 0 4.48209 − 0.837848i −0.147206 + 0.787484i 0 −7.13665 − 2.03055i
80.7 −1.75775 + 0.875257i 0 1.11835 − 1.48094i −1.83440 − 1.67228i 0 −3.55096 + 0.663789i 0.0520383 − 0.278380i 0 4.68810 + 1.33388i
80.8 −1.61163 + 0.802498i 0 0.748090 − 0.990631i −2.40299 − 2.19062i 0 1.67266 − 0.312675i 0.250971 − 1.34257i 0 5.63070 + 1.60207i
80.9 −1.60136 + 0.797381i 0 0.723260 − 0.957752i 0.241303 + 0.219977i 0 −4.62571 + 0.864695i 0.262914 − 1.40646i 0 −0.561818 − 0.159851i
80.10 −1.31654 + 0.655561i 0 0.0982571 − 0.130113i 1.21094 + 1.10392i 0 −0.218661 + 0.0408748i 0.496429 − 2.65566i 0 −2.31794 − 0.659512i
80.11 −1.20731 + 0.601169i 0 −0.109077 + 0.144441i 2.49118 + 2.27101i 0 0.379513 − 0.0709432i 0.540503 − 2.89144i 0 −4.37289 − 1.24419i
80.12 −1.13697 + 0.566145i 0 −0.233083 + 0.308651i 1.35540 + 1.23561i 0 0.241413 − 0.0451280i 0.557038 − 2.97989i 0 −2.24059 − 0.637502i
80.13 −0.947704 + 0.471900i 0 −0.529817 + 0.701591i −2.16711 − 1.97558i 0 2.69626 − 0.504018i 0.560097 − 2.99626i 0 2.98605 + 0.849604i
80.14 −0.664821 + 0.331042i 0 −0.872871 + 1.15587i 1.80362 + 1.64422i 0 0.707058 − 0.132172i 0.470597 − 2.51747i 0 −1.74339 − 0.496038i
80.15 −0.607968 + 0.302732i 0 −0.927291 + 1.22793i −0.905941 − 0.825874i 0 −2.56947 + 0.480316i 0.441623 − 2.36248i 0 0.800802 + 0.227848i
80.16 −0.351877 + 0.175214i 0 −1.11215 + 1.47273i −2.85149 − 2.59948i 0 −4.61082 + 0.861911i 0.277758 − 1.48587i 0 1.45884 + 0.415076i
80.17 −0.166229 + 0.0827721i 0 −1.18449 + 1.56852i −0.976774 − 0.890447i 0 4.55070 − 0.850673i 0.135310 − 0.723845i 0 0.236072 + 0.0671683i
80.18 −0.0994373 + 0.0495139i 0 −1.19783 + 1.58619i −0.133977 − 0.122136i 0 −1.34058 + 0.250598i 0.0813938 − 0.435419i 0 0.0193698 + 0.00551117i
80.19 0.0994373 − 0.0495139i 0 −1.19783 + 1.58619i 0.133977 + 0.122136i 0 −1.34058 + 0.250598i −0.0813938 + 0.435419i 0 0.0193698 + 0.00551117i
80.20 0.166229 − 0.0827721i 0 −1.18449 + 1.56852i 0.976774 + 0.890447i 0 4.55070 − 0.850673i −0.135310 + 0.723845i 0 0.236072 + 0.0671683i
See next 80 embeddings (of 576 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 80.36
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
103.f odd 34 1 inner
309.k even 34 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 927.2.w.a ✓ 576
3.b odd 2 1 inner 927.2.w.a ✓ 576
103.f odd 34 1 inner 927.2.w.a ✓ 576
309.k even 34 1 inner 927.2.w.a ✓ 576
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
927.2.w.a ✓ 576 1.a even 1 1 trivial
927.2.w.a ✓ 576 3.b odd 2 1 inner
927.2.w.a ✓ 576 103.f odd 34 1 inner
927.2.w.a ✓ 576 309.k even 34 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(927, [\chi])\).