↑

Properties

Label 1334.2.c.b
Level $1334$
Weight $2$
Character orbit 1334.c
Analytic conductor $10.652$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1334,2,Mod(231,1334)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1334, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1334.231");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1334 = 2 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1334.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: \(10.6520436296\)
Analytic rank: \(0\)
Dimension: \(28\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 28 q - 28 q^{4} + 2 q^{5} + 2 q^{6} - 8 q^{7} - 54 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 28 q - 28 q^{4} + 2 q^{5} + 2 q^{6} - 8 q^{7} - 54 q^{9} - 2 q^{13} + 28 q^{16} - 2 q^{20} + 6 q^{22} - 28 q^{23} - 2 q^{24} + 38 q^{25} + 8 q^{28} - 2 q^{29} + 2 q^{30} + 30 q^{33} + 12 q^{34} + 56 q^{35} + 54 q^{36} + 12 q^{38} + 16 q^{42} - 52 q^{45} + 76 q^{49} - 60 q^{51} + 2 q^{52} - 22 q^{53} - 14 q^{54} + 72 q^{57} - 18 q^{58} - 12 q^{59} + 14 q^{62} + 24 q^{63} - 28 q^{64} - 42 q^{65} - 16 q^{67} - 4 q^{71} - 32 q^{74} - 34 q^{78} + 2 q^{80} + 116 q^{81} - 68 q^{82} - 48 q^{83} + 46 q^{86} + 12 q^{87} - 6 q^{88} + 96 q^{91} + 28 q^{92} + 70 q^{93} - 10 q^{94} + 2 q^{96}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
231.1 − 1.00000i − 3.33101i −1.00000 3.07426 −3.33101 −2.74084 1.00000i −8.09562 − 3.07426i
231.2 − 1.00000i − 2.92171i −1.00000 1.71359 −2.92171 4.94068 1.00000i −5.53640 − 1.71359i
231.3 − 1.00000i − 2.46607i −1.00000 −3.00520 −2.46607 −4.12629 1.00000i −3.08153 3.00520i
231.4 − 1.00000i − 2.03717i −1.00000 −3.43292 −2.03717 0.221932 1.00000i −1.15006 3.43292i
231.5 − 1.00000i − 1.50644i −1.00000 2.58695 −1.50644 −0.901133 1.00000i 0.730640 − 2.58695i
231.6 − 1.00000i − 0.549299i −1.00000 −1.94586 −0.549299 −0.582420 1.00000i 2.69827 1.94586i
231.7 − 1.00000i − 0.403192i −1.00000 0.661843 −0.403192 −5.15327 1.00000i 2.83744 − 0.661843i
231.8 − 1.00000i 0.464907i −1.00000 −1.92613 0.464907 1.50697 1.00000i 2.78386 1.92613i
231.9 − 1.00000i 0.761460i −1.00000 −0.684530 0.761460 4.35995 1.00000i 2.42018 0.684530i
231.10 − 1.00000i 1.54533i −1.00000 2.82162 1.54533 0.523514 1.00000i 0.611963 − 2.82162i
231.11 − 1.00000i 2.38000i −1.00000 0.00138862 2.38000 −1.62782 1.00000i −2.66440 − 0.00138862i
231.12 − 1.00000i 2.71709i −1.00000 1.23317 2.71709 −2.56392 1.00000i −4.38260 − 1.23317i
231.13 − 1.00000i 3.04036i −1.00000 3.90148 3.04036 4.69219 1.00000i −6.24380 − 3.90148i
231.14 − 1.00000i 3.30575i −1.00000 −3.99966 3.30575 −2.54954 1.00000i −7.92795 3.99966i
231.15 1.00000i − 3.30575i −1.00000 −3.99966 3.30575 −2.54954 − 1.00000i −7.92795 − 3.99966i
231.16 1.00000i − 3.04036i −1.00000 3.90148 3.04036 4.69219 − 1.00000i −6.24380 3.90148i
231.17 1.00000i − 2.71709i −1.00000 1.23317 2.71709 −2.56392 − 1.00000i −4.38260 1.23317i
231.18 1.00000i − 2.38000i −1.00000 0.00138862 2.38000 −1.62782 − 1.00000i −2.66440 0.00138862i
231.19 1.00000i − 1.54533i −1.00000 2.82162 1.54533 0.523514 − 1.00000i 0.611963 2.82162i
231.20 1.00000i − 0.761460i −1.00000 −0.684530 0.761460 4.35995 − 1.00000i 2.42018 − 0.684530i
See all 28 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 231.28
Significant digits:
Format:

Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1334.2.c.b ✓ 28
29.b even 2 1 inner 1334.2.c.b ✓ 28
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1334.2.c.b ✓ 28 1.a even 1 1 trivial
1334.2.c.b ✓ 28 29.b even 2 1 inner