↑

Properties

Label 8003.2.a.b
Level $8003$
Weight $2$
Character orbit 8003.a
Self dual yes
Analytic conductor $63.904$
Analytic rank $1$
Dimension $153$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [8003,2,Mod(1,8003)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("8003.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8003, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 8003 = 53 \cdot 151 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8003.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [153] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(63.9042767376\)
Analytic rank: \(1\)
Dimension: \(153\)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 153 q - 9 q^{2} - 17 q^{3} + 137 q^{4} - 31 q^{5} - 10 q^{6} - 17 q^{7} - 30 q^{8} + 136 q^{9} - 34 q^{10} - q^{11} - 60 q^{12} - 101 q^{13} - 16 q^{14} - 14 q^{15} + 97 q^{16} - 12 q^{17} - 45 q^{18}+ \cdots - 11 q^{99}+O(q^{100}) \) 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.

Copy content comment:embeddings in the coefficient field
 
Copy content gp:mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −2.82377 0.0811365 5.97367 1.22528 −0.229111 1.93678 −11.2207 −2.99342 −3.45990
1.2 −2.76122 −1.93941 5.62432 −0.205414 5.35515 −1.99038 −10.0076 0.761331 0.567192
1.3 −2.72579 2.89515 5.42994 −2.27822 −7.89157 −3.84210 −9.34930 5.38188 6.20996
1.4 −2.71996 −3.40952 5.39818 0.859174 9.27375 3.37109 −9.24292 8.62480 −2.33692
1.5 −2.64082 1.90424 4.97394 2.87158 −5.02877 0.865912 −7.85365 0.626146 −7.58334
1.6 −2.62408 −2.48215 4.88578 −3.25865 6.51336 0.610888 −7.57250 3.16108 8.55094
1.7 −2.55787 −0.498344 4.54269 3.86602 1.27470 −1.47646 −6.50388 −2.75165 −9.88878
1.8 −2.55291 −0.169380 4.51736 −0.762748 0.432413 0.998481 −6.42660 −2.97131 1.94723
1.9 −2.54449 −2.75216 4.47442 −0.0821866 7.00285 −2.51361 −6.29612 4.57441 0.209123
1.10 −2.53517 1.42230 4.42707 −0.780530 −3.60576 3.78955 −6.15303 −0.977076 1.97877
1.11 −2.49383 −0.270355 4.21918 −2.99495 0.674220 −3.80387 −5.53426 −2.92691 7.46890
1.12 −2.46809 2.55539 4.09144 0.103837 −6.30691 0.172456 −5.16186 3.53000 −0.256278
1.13 −2.45028 −2.96227 4.00387 −1.96635 7.25838 −3.26353 −4.91003 5.77502 4.81810
1.14 −2.41716 −1.38399 3.84266 1.63498 3.34533 −3.98295 −4.45401 −1.08457 −3.95202
1.15 −2.40368 2.42213 3.77770 1.57847 −5.82205 −3.75128 −4.27303 2.86673 −3.79414
1.16 −2.36991 −1.12262 3.61648 0.983312 2.66051 2.71051 −3.83091 −1.73972 −2.33036
1.17 −2.35186 2.82673 3.53125 2.18646 −6.64808 0.649269 −3.60130 4.99041 −5.14224
1.18 −2.34979 −2.55203 3.52153 3.27958 5.99675 4.82178 −3.57528 3.51287 −7.70633
1.19 −2.34552 3.15214 3.50145 −3.97132 −7.39341 −1.04283 −3.52168 6.93601 9.31479
1.20 −2.32654 −0.105675 3.41278 −1.05522 0.245856 0.945293 −3.28688 −2.98883 2.45502
See next 80 embeddings (of 153 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.153
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(53\) \( +1 \)
\(151\) \( +1 \)

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 8003.2.a.b ✓ 153
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8003.2.a.b ✓ 153 1.a even 1 1 trivial