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Properties

Label 1.276.a.a
Level $1$
Weight $276$
Character orbit 1.a
Self dual yes
Analytic conductor $478.903$
Dimension $23$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1,276,Mod(1,1)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1, base_ring=CyclotomicField(1))
 
chi = DirichletCharacter(H, H._module([]))
 
N = Newforms(chi, 276, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1.1");
 
S:= CuspForms(chi, 276);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 276 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

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: yes
Analytic conductor: \(478.903017903\)
Dimension: \(23\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 23 q + 75\!\cdots\!56 q^{2}+ \cdots + 15\!\cdots\!91 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 23 q + 75\!\cdots\!56 q^{2}+ \cdots + 31\!\cdots\!32 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −4.63882e41 6.73147e65 1.54478e83 −1.71003e96 −3.12260e107 −2.06023e116 −4.34980e124 2.91562e131 7.93251e137
1.2 −4.49206e41 −7.75875e65 1.41078e83 1.54940e96 3.48528e107 −1.83420e116 −3.61025e124 4.40418e131 −6.96001e137
1.3 −4.32163e41 −1.10731e64 1.26057e83 4.65053e94 4.78540e105 1.45852e116 −2.82411e124 −1.61442e131 −2.00979e136
1.4 −3.74837e41 −2.24898e65 7.97941e82 −8.51578e95 8.42999e106 7.88848e115 −7.15400e123 −1.10985e131 3.19203e137
1.5 −3.72693e41 3.90357e65 7.81920e82 2.39385e96 −1.45483e107 −3.37913e115 −6.51603e123 −9.18587e129 −8.92171e137
1.6 −2.80349e41 −3.00532e65 1.78870e82 −1.45498e96 8.42538e106 −3.10839e116 1.20049e124 −7.12446e130 4.07902e137
1.7 −2.24211e41 4.27784e65 −1.04378e82 1.80200e94 −9.59139e106 −1.09259e116 1.59518e124 2.14352e130 −4.04027e135
1.8 −2.11665e41 5.73969e65 −1.59065e82 −8.75354e95 −1.21489e107 2.58666e116 1.62167e124 1.67876e131 1.85281e137
1.9 −1.81035e41 −7.69268e65 −2.79347e82 −1.20384e96 1.39265e107 2.43373e116 1.60475e124 4.30210e131 2.17938e137
1.10 −1.55434e41 −3.31336e65 −3.65485e82 1.47242e96 5.15011e106 1.81392e115 1.51171e124 −5.17804e130 −2.28864e137
1.11 −6.43334e39 −2.14976e64 −6.06670e82 −2.41759e96 1.38302e104 5.41101e115 7.80849e122 −1.61102e131 1.55531e136
1.12 2.12261e40 3.32277e65 −6.02579e82 8.33630e94 7.05295e105 −1.68990e116 −2.56764e123 −5.11562e130 1.76947e135
1.13 1.08630e41 1.36341e64 −4.89080e82 9.91910e95 1.48107e105 2.28125e116 −1.19076e124 −1.61378e131 1.07751e137
1.14 1.11485e41 7.66699e65 −4.82794e82 1.91922e96 8.54758e106 6.34140e115 −1.21506e124 4.26263e131 2.13965e137
1.15 1.31768e41 −5.62903e65 −4.33457e82 5.54110e93 −7.41725e106 −1.44261e116 −1.37110e124 1.55296e131 7.30138e134
1.16 2.53728e41 7.00866e65 3.66973e81 −2.16796e96 1.77830e107 −7.85368e115 −1.44723e124 3.29650e131 −5.50072e137
1.17 2.87403e41 −4.33382e65 2.18920e82 −1.34668e96 −1.24555e107 8.27697e115 −1.11559e124 2.62555e130 −3.87039e137
1.18 3.15674e41 2.13523e65 3.89415e82 −2.24250e95 6.74037e106 1.65868e116 −6.87124e123 −1.15972e131 −7.07897e136
1.19 3.29438e41 8.43122e63 4.78211e82 2.44412e96 2.77757e105 −2.70401e116 −4.24557e123 −1.61493e131 8.05188e137
1.20 3.49627e41 3.15238e65 6.15304e82 −3.21024e95 1.10215e107 −1.21314e116 2.87390e122 −6.21895e130 −1.12239e137
See all 23 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.23
Significant digits:
Format:

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 1.276.a.a ✓ 23
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1.276.a.a ✓ 23 1.a even 1 1 trivial

Hecke kernels

This newform subspace is the entire newspace \(S_{276}^{\mathrm{new}}(\Gamma_0(1))\).