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Properties

Label 2491.2.a.b
Level $2491$
Weight $2$
Character orbit 2491.a
Self dual yes
Analytic conductor $19.891$
Analytic rank $1$
Dimension $45$
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] = [2491,2,Mod(1,2491)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2491, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2491.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2491 = 47 \cdot 53 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2491.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: \(19.8907351435\)
Analytic rank: \(1\)
Dimension: \(45\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 45 q - 8 q^{2} + q^{3} + 38 q^{4} - 21 q^{5} - 10 q^{6} - 3 q^{7} - 24 q^{8} + 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 45 q - 8 q^{2} + q^{3} + 38 q^{4} - 21 q^{5} - 10 q^{6} - 3 q^{7} - 24 q^{8} + 20 q^{9} - 7 q^{10} - 31 q^{11} - 2 q^{12} - 20 q^{13} - 15 q^{14} - 18 q^{15} + 20 q^{16} - 17 q^{17} - 29 q^{18} - 21 q^{19} - 21 q^{20} - 55 q^{21} - 3 q^{22} - 17 q^{23} - 37 q^{24} + 28 q^{25} - 34 q^{26} + 19 q^{27} + 3 q^{28} - 76 q^{29} - 6 q^{30} - 16 q^{31} - 41 q^{32} - 2 q^{33} + 8 q^{34} - 44 q^{35} - 24 q^{36} - 25 q^{37} - 40 q^{38} - 20 q^{39} - 39 q^{40} - 59 q^{41} + 27 q^{42} - 27 q^{43} - 79 q^{44} - 47 q^{45} + 6 q^{46} - 45 q^{47} + 10 q^{48} + 20 q^{49} - 50 q^{50} - 15 q^{51} - 11 q^{52} - 45 q^{53} - 73 q^{54} + 19 q^{55} - 29 q^{56} - 37 q^{57} + 8 q^{58} - 14 q^{59} - 37 q^{60} - 20 q^{61} - 21 q^{62} - 41 q^{63} - 6 q^{64} - 34 q^{65} - 14 q^{66} - 70 q^{68} - 45 q^{69} - 6 q^{70} - 68 q^{71} - 85 q^{72} - 9 q^{73} - 12 q^{74} - 4 q^{75} - 23 q^{76} - 86 q^{77} + 39 q^{78} + 14 q^{79} + 22 q^{80} + 13 q^{81} - 28 q^{82} - 36 q^{83} - 47 q^{84} - 63 q^{85} + 4 q^{86} - 50 q^{87} + 19 q^{88} - 36 q^{89} + 71 q^{90} - 65 q^{91} - 24 q^{92} - 114 q^{93} + 8 q^{94} - 39 q^{95} - 5 q^{96} + 3 q^{97} - 20 q^{98} - 88 q^{99}+O(q^{100}) \) 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 −2.72042 0.139452 5.40068 3.96941 −0.379367 1.63252 −9.25128 −2.98055 −10.7985
1.2 −2.58989 3.40615 4.70754 0.541207 −8.82156 −4.20507 −7.01224 8.60186 −1.40167
1.3 −2.58903 0.354934 4.70310 −2.82141 −0.918936 5.08902 −6.99841 −2.87402 7.30473
1.4 −2.58210 −0.661417 4.66723 −2.22543 1.70784 −0.514264 −6.88704 −2.56253 5.74629
1.5 −2.56576 −2.19161 4.58314 1.73903 5.62314 2.35658 −6.62772 1.80314 −4.46194
1.6 −2.36398 1.86889 3.58842 1.01960 −4.41803 −2.36227 −3.75499 0.492751 −2.41031
1.7 −2.28338 2.70508 3.21384 −4.22926 −6.17673 2.06214 −2.77167 4.31744 9.65701
1.8 −2.08011 −1.54828 2.32684 −2.67746 3.22059 −3.99238 −0.679859 −0.602816 5.56939
1.9 −2.04370 −1.77731 2.17672 2.19336 3.63229 −1.51381 −0.361173 0.158820 −4.48258
1.10 −1.91361 −2.86219 1.66189 −3.41506 5.47710 1.14070 0.647001 5.19212 6.53508
1.11 −1.75833 1.43851 1.09172 0.713306 −2.52937 −1.55928 1.59705 −0.930690 −1.25423
1.12 −1.65307 −1.77519 0.732630 −0.882408 2.93451 4.04231 2.09505 0.151312 1.45868
1.13 −1.54594 1.81211 0.389933 −0.404058 −2.80142 2.99443 2.48907 0.283758 0.624650
1.14 −1.50002 −0.835536 0.250047 3.36277 1.25332 −3.06238 2.62496 −2.30188 −5.04421
1.15 −1.45795 0.290855 0.125607 0.901394 −0.424051 2.16126 2.73276 −2.91540 −1.31418
1.16 −1.25342 0.934003 −0.428941 −3.76662 −1.17070 −1.00887 3.04448 −2.12764 4.72115
1.17 −1.11957 2.27497 −0.746566 1.56652 −2.54699 −0.962558 3.07497 2.17550 −1.75383
1.18 −0.943043 3.07609 −1.11067 −3.02714 −2.90089 −3.12765 2.93350 6.46236 2.85473
1.19 −0.748691 −0.361749 −1.43946 −3.03493 0.270838 −1.14626 2.57509 −2.86914 2.27223
1.20 −0.712311 −3.08470 −1.49261 0.502631 2.19726 4.73396 2.48783 6.51535 −0.358030
See all 45 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.45
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(47\) \( +1 \)
\(53\) \( +1 \)

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 2491.2.a.b ✓ 45
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2491.2.a.b ✓ 45 1.a even 1 1 trivial