Properties

Label 277.2.b.a
Level $277$
Weight $2$
Character orbit 277.b
Analytic conductor $2.212$
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] = [277,2,Mod(276,277)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(277, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("277.276");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 277 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 277.b (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: \(2.21185613599\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 22 q - 24 q^{4} + 4 q^{7} + 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 22 q - 24 q^{4} + 4 q^{7} + 18 q^{9} + 2 q^{12} - 12 q^{13} + 12 q^{16} - 14 q^{19} - 12 q^{21} + 10 q^{22} + 20 q^{23} - 18 q^{25} - 28 q^{28} - 4 q^{30} + 10 q^{34} - 42 q^{36} + 18 q^{39} + 20 q^{40} - 18 q^{41} - 8 q^{47} - 56 q^{48} + 2 q^{49} + 58 q^{52} + 48 q^{55} + 26 q^{57} - 42 q^{59} - 10 q^{62} - 44 q^{63} - 34 q^{64} + 60 q^{66} + 22 q^{67} - 12 q^{69} + 58 q^{70} + 34 q^{71} + 46 q^{74} - 42 q^{75} + 26 q^{76} - 10 q^{81} - 58 q^{83} - 10 q^{84} + 42 q^{85} - 6 q^{86} - 20 q^{87} + 22 q^{88} + 24 q^{89} + 36 q^{90} + 24 q^{91} - 32 q^{92}+O(q^{100}) \) 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.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
276.1 2.68652i −2.60737 −5.21740 1.33248i 7.00475i 1.65648 8.64361i 3.79837 3.57973
276.2 2.56713i 0.633441 −4.59016 3.09865i 1.62613i 0.825668 6.64928i −2.59875 −7.95463
276.3 2.18038i 1.68863 −2.75407 2.77637i 3.68186i 5.06490 1.64417i −0.148525 6.05355
276.4 2.08361i 3.11952 −2.34144 1.38208i 6.49986i −1.57376 0.711419i 6.73139 −2.87971
276.5 2.06854i −0.276722 −2.27884 0.357229i 0.572410i −3.43105 0.576785i −2.92342 0.738940
276.6 1.48073i −2.72109 −0.192568 2.57972i 4.02921i −2.42120 2.67632i 4.40434 −3.81987
276.7 1.36148i −2.29126 0.146365 1.83057i 3.11951i 2.23488 2.92224i 2.24986 2.49229
276.8 1.02645i 1.27949 0.946398 1.00561i 1.31333i −0.808050 3.02433i −1.36290 −1.03221
276.9 0.939915i 2.45709 1.11656 4.02488i 2.30946i −3.10332 2.92930i 3.03729 3.78305
276.10 0.873504i 0.0630325 1.23699 2.12471i 0.0550591i 3.67656 2.82753i −2.99603 −1.85594
276.11 0.268026i −1.34476 1.92816 3.33851i 0.360432i −0.121112 1.05285i −1.19161 0.894808
276.12 0.268026i −1.34476 1.92816 3.33851i 0.360432i −0.121112 1.05285i −1.19161 0.894808
276.13 0.873504i 0.0630325 1.23699 2.12471i 0.0550591i 3.67656 2.82753i −2.99603 −1.85594
276.14 0.939915i 2.45709 1.11656 4.02488i 2.30946i −3.10332 2.92930i 3.03729 3.78305
276.15 1.02645i 1.27949 0.946398 1.00561i 1.31333i −0.808050 3.02433i −1.36290 −1.03221
276.16 1.36148i −2.29126 0.146365 1.83057i 3.11951i 2.23488 2.92224i 2.24986 2.49229
276.17 1.48073i −2.72109 −0.192568 2.57972i 4.02921i −2.42120 2.67632i 4.40434 −3.81987
276.18 2.06854i −0.276722 −2.27884 0.357229i 0.572410i −3.43105 0.576785i −2.92342 0.738940
276.19 2.08361i 3.11952 −2.34144 1.38208i 6.49986i −1.57376 0.711419i 6.73139 −2.87971
276.20 2.18038i 1.68863 −2.75407 2.77637i 3.68186i 5.06490 1.64417i −0.148525 6.05355
See all 22 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 276.22
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
277.b even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 277.2.b.a 22
277.b even 2 1 inner 277.2.b.a 22
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
277.2.b.a 22 1.a even 1 1 trivial
277.2.b.a 22 277.b even 2 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(277, [\chi])\).