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Properties

Label 946.2.c.b
Level $946$
Weight $2$
Character orbit 946.c
Analytic conductor $7.554$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [946,2,Mod(945,946)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(946, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("946.945");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 946 = 2 \cdot 11 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 946.c (of order \(2\), degree \(1\), 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: \(7.55384803121\)
Analytic rank: \(0\)
Dimension: \(22\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 22 q + 22 q^{2} + 22 q^{4} + 22 q^{8} - 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 22 q + 22 q^{2} + 22 q^{4} + 22 q^{8} - 20 q^{9} + 2 q^{11} + 8 q^{15} + 22 q^{16} - 20 q^{18} + 8 q^{19} + 2 q^{22} - 26 q^{25} - 6 q^{29} + 8 q^{30} - 16 q^{31} + 22 q^{32} - 10 q^{33} - 20 q^{36} + 8 q^{38} + 36 q^{39} + 20 q^{43} + 2 q^{44} + 12 q^{47} + 38 q^{49} - 26 q^{50} - 24 q^{51} - 30 q^{53} - 14 q^{55} - 6 q^{58} - 20 q^{59} + 8 q^{60} - 6 q^{61} - 16 q^{62} + 8 q^{63} + 22 q^{64} - 52 q^{65} - 10 q^{66} - 12 q^{67} - 20 q^{72} - 26 q^{73} + 8 q^{76} + 12 q^{77} + 36 q^{78} + 10 q^{81} + 72 q^{85} + 20 q^{86} + 2 q^{88} + 12 q^{94} - 18 q^{97} + 38 q^{98} - 12 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
945.1 1.00000 − 3.07219i 1.00000 4.41514i − 3.07219i 1.80070 1.00000 −6.43837 4.41514i
945.2 1.00000 − 2.96230i 1.00000 − 2.16309i − 2.96230i 1.41074 1.00000 −5.77523 − 2.16309i
945.3 1.00000 − 2.75721i 1.00000 1.19305i − 2.75721i −5.12248 1.00000 −4.60222 1.19305i
945.4 1.00000 − 2.27291i 1.00000 − 4.00741i − 2.27291i −2.46980 1.00000 −2.16613 − 4.00741i
945.5 1.00000 − 2.20771i 1.00000 1.10463i − 2.20771i 3.06555 1.00000 −1.87400 1.10463i
945.6 1.00000 − 1.99156i 1.00000 1.14608i − 1.99156i 1.72142 1.00000 −0.966327 1.14608i
945.7 1.00000 − 1.10662i 1.00000 1.03741i − 1.10662i −4.19893 1.00000 1.77539 1.03741i
945.8 1.00000 − 0.974595i 1.00000 − 0.226054i − 0.974595i 1.36554 1.00000 2.05016 − 0.226054i
945.9 1.00000 − 0.839123i 1.00000 − 3.07360i − 0.839123i 0.0378591 1.00000 2.29587 − 3.07360i
945.10 1.00000 − 0.390118i 1.00000 − 3.02712i − 0.390118i 4.63816 1.00000 2.84781 − 3.02712i
945.11 1.00000 − 0.383366i 1.00000 2.01824i − 0.383366i −2.24878 1.00000 2.85303 2.01824i
945.12 1.00000 0.383366i 1.00000 − 2.01824i 0.383366i −2.24878 1.00000 2.85303 − 2.01824i
945.13 1.00000 0.390118i 1.00000 3.02712i 0.390118i 4.63816 1.00000 2.84781 3.02712i
945.14 1.00000 0.839123i 1.00000 3.07360i 0.839123i 0.0378591 1.00000 2.29587 3.07360i
945.15 1.00000 0.974595i 1.00000 0.226054i 0.974595i 1.36554 1.00000 2.05016 0.226054i
945.16 1.00000 1.10662i 1.00000 − 1.03741i 1.10662i −4.19893 1.00000 1.77539 − 1.03741i
945.17 1.00000 1.99156i 1.00000 − 1.14608i 1.99156i 1.72142 1.00000 −0.966327 − 1.14608i
945.18 1.00000 2.20771i 1.00000 − 1.10463i 2.20771i 3.06555 1.00000 −1.87400 − 1.10463i
945.19 1.00000 2.27291i 1.00000 4.00741i 2.27291i −2.46980 1.00000 −2.16613 4.00741i
945.20 1.00000 2.75721i 1.00000 − 1.19305i 2.75721i −5.12248 1.00000 −4.60222 − 1.19305i
See all 22 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 945.22
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
473.d even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 946.2.c.b yes 22
11.b odd 2 1 946.2.c.a ✓ 22
43.b odd 2 1 946.2.c.a ✓ 22
473.d even 2 1 inner 946.2.c.b yes 22
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
946.2.c.a ✓ 22 11.b odd 2 1
946.2.c.a ✓ 22 43.b odd 2 1
946.2.c.b yes 22 1.a even 1 1 trivial
946.2.c.b yes 22 473.d even 2 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{7}^{11} - 48 T_{7}^{9} + 30 T_{7}^{8} + 742 T_{7}^{7} - 936 T_{7}^{6} - 4096 T_{7}^{5} + 7720 T_{7}^{4} + \cdots - 384 \) acting on \(S_{2}^{\mathrm{new}}(946, [\chi])\). Copy content Toggle raw display