↑

Properties

Label 2151.4.a.f
Level $2151$
Weight $4$
Character orbit 2151.a
Self dual yes
Analytic conductor $126.913$
Analytic rank $0$
Dimension $37$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2151,4,Mod(1,2151)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2151, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2151.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2151 = 3^{2} \cdot 239 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2151.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: \(126.913108422\)
Analytic rank: \(0\)
Dimension: \(37\)
Twist minimal: no (minimal twist has level 239)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 37 q - 4 q^{2} + 170 q^{4} - 43 q^{5} + 60 q^{7} - 27 q^{8}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 37 q - 4 q^{2} + 170 q^{4} - 43 q^{5} + 60 q^{7} - 27 q^{8} + 147 q^{10} - 55 q^{11} + 250 q^{13} - 169 q^{14} + 918 q^{16} - 189 q^{17} + 550 q^{19} - 486 q^{20} + 226 q^{22} - 74 q^{23} + 1604 q^{25} - 560 q^{26} + 829 q^{28} - 389 q^{29} + 1107 q^{31} - 125 q^{32} + 1423 q^{34} - 270 q^{35} + 1002 q^{37} - 1037 q^{38} + 1536 q^{40} - 1518 q^{41} + 1098 q^{43} - 1037 q^{44} + 1030 q^{46} - 1214 q^{47} + 4663 q^{49} - 929 q^{50} + 2895 q^{52} - 904 q^{53} + 1350 q^{55} - 2556 q^{56} + 1396 q^{58} - 1658 q^{59} + 2313 q^{61} + 4519 q^{62} + 3807 q^{64} + 56 q^{65} + 1535 q^{67} + 6526 q^{68} - 4099 q^{70} + 3255 q^{71} + 3154 q^{73} + 2629 q^{74} + 1981 q^{76} + 3734 q^{77} + 2260 q^{79} + 8242 q^{80} - 9898 q^{82} + 939 q^{83} + 1272 q^{85} + 3457 q^{86} - 1808 q^{88} - 1486 q^{89} + 174 q^{91} + 14076 q^{92} - 984 q^{94} + 1828 q^{95} + 6148 q^{97} + 6243 q^{98}+O(q^{100}) \) 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 −5.58089 0 23.1463 10.0408 0 25.4163 −84.5299 0 −56.0363
1.2 −5.29599 0 20.0475 −6.13814 0 −8.89768 −63.8037 0 32.5075
1.3 −5.11871 0 18.2012 −0.668880 0 7.37421 −52.2167 0 3.42380
1.4 −4.90101 0 16.0199 −18.8248 0 −10.8883 −39.3055 0 92.2607
1.5 −4.79841 0 15.0248 14.4400 0 1.92684 −33.7078 0 −69.2892
1.6 −4.53815 0 12.5948 −19.7043 0 34.6627 −20.8518 0 89.4211
1.7 −4.41344 0 11.4784 −16.6195 0 −34.6158 −15.3518 0 73.3492
1.8 −3.91247 0 7.30741 2.39092 0 22.0359 2.70973 0 −9.35442
1.9 −3.84652 0 6.79575 −10.3358 0 2.00272 4.63218 0 39.7568
1.10 −3.37030 0 3.35895 1.43026 0 27.2799 15.6418 0 −4.82040
1.11 −2.83758 0 0.0518438 9.05330 0 −30.7893 22.5535 0 −25.6894
1.12 −2.73040 0 −0.544930 −10.5995 0 15.6616 23.3311 0 28.9408
1.13 −2.40786 0 −2.20221 19.1943 0 10.9735 24.5655 0 −46.2171
1.14 −1.50491 0 −5.73525 −18.0796 0 −23.9080 20.6703 0 27.2082
1.15 −1.28174 0 −6.35714 −12.7359 0 11.6522 18.4021 0 16.3241
1.16 −1.09413 0 −6.80288 10.8819 0 4.64141 16.1963 0 −11.9062
1.17 −0.918355 0 −7.15662 −19.7054 0 10.7153 13.9192 0 18.0965
1.18 −0.412743 0 −7.82964 15.2997 0 4.25811 6.53358 0 −6.31484
1.19 −0.271729 0 −7.92616 11.3325 0 −27.2237 4.32760 0 −3.07937
1.20 −0.123948 0 −7.98464 −3.85596 0 −18.4037 1.98126 0 0.477937
See all 37 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.37
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \(-1\)
\(239\) \(-1\)

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 2151.4.a.f 37
3.b odd 2 1 239.4.a.b ✓ 37
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
239.4.a.b ✓ 37 3.b odd 2 1
2151.4.a.f 37 1.a even 1 1 trivial