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Properties

Label 2151.4.a.c
Level $2151$
Weight $4$
Character orbit 2151.a
Self dual yes
Analytic conductor $126.913$
Analytic rank $0$
Dimension $28$
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] = [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: \(28\)
Twist minimal: no (minimal twist has level 717)
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.

\(\operatorname{Tr}(f)(q) = \) \( 28 q + 13 q^{2} + 99 q^{4} + 74 q^{5} - 82 q^{7} + 135 q^{8}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 28 q + 13 q^{2} + 99 q^{4} + 74 q^{5} - 82 q^{7} + 135 q^{8} - 68 q^{10} + 258 q^{11} - 134 q^{13} + 292 q^{14} + 327 q^{16} + 364 q^{17} - 278 q^{19} + 986 q^{20} - 179 q^{22} + 668 q^{23} + 490 q^{25} + 760 q^{26} - 802 q^{28} + 714 q^{29} - 608 q^{31} + 918 q^{32} - 228 q^{34} + 934 q^{35} - 1080 q^{37} + 1395 q^{38} - 563 q^{40} + 1796 q^{41} - 1934 q^{43} + 3157 q^{44} - 940 q^{46} + 2032 q^{47} + 762 q^{49} + 1754 q^{50} - 2328 q^{52} + 1790 q^{53} - 478 q^{55} + 3557 q^{56} - 2626 q^{58} + 3622 q^{59} + 324 q^{61} + 796 q^{62} + 2023 q^{64} + 2200 q^{65} - 2444 q^{67} - 357 q^{68} + 4305 q^{70} + 1298 q^{71} - 1368 q^{73} - 813 q^{74} + 1390 q^{76} + 1408 q^{77} - 1378 q^{79} + 7684 q^{80} + 9001 q^{82} + 3524 q^{83} + 60 q^{85} + 2543 q^{86} + 1749 q^{88} + 7854 q^{89} + 850 q^{91} + 496 q^{92} + 6634 q^{94} + 3696 q^{95} - 1746 q^{97} + 4632 q^{98}+O(q^{100}) \) 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 −5.43685 0 21.5594 21.1888 0 −20.1660 −73.7203 0 −115.201
1.2 −4.27604 0 10.2845 1.46589 0 −24.3497 −9.76851 0 −6.26822
1.3 −4.23289 0 9.91739 1.28980 0 −27.4975 −8.11611 0 −5.45960
1.4 −4.04550 0 8.36609 10.3595 0 −12.7054 −1.48103 0 −41.9093
1.5 −3.82627 0 6.64037 6.06587 0 7.45896 5.20233 0 −23.2097
1.6 −3.21293 0 2.32292 13.8674 0 29.9628 18.2401 0 −44.5549
1.7 −3.00561 0 1.03369 −10.0458 0 −17.8583 20.9380 0 30.1936
1.8 −2.23264 0 −3.01532 −1.56125 0 −14.0459 24.5932 0 3.48572
1.9 −2.01135 0 −3.95446 6.74089 0 7.15060 24.0446 0 −13.5583
1.10 −1.55579 0 −5.57952 −17.3600 0 −1.16704 21.1269 0 27.0085
1.11 −0.686651 0 −7.52851 17.8875 0 15.8088 10.6627 0 −12.2825
1.12 −0.456628 0 −7.79149 −14.2736 0 −13.0550 7.21084 0 6.51773
1.13 −0.404541 0 −7.83635 0.184451 0 12.9030 6.40644 0 −0.0746179
1.14 0.608170 0 −7.63013 1.98658 0 −5.67520 −9.50578 0 1.20818
1.15 0.797577 0 −7.36387 7.16277 0 0.569206 −12.2539 0 5.71286
1.16 1.27488 0 −6.37468 17.5425 0 −26.4099 −18.3260 0 22.3646
1.17 1.64745 0 −5.28592 −5.57976 0 35.6078 −21.8878 0 −9.19235
1.18 2.03138 0 −3.87348 −11.5727 0 −13.0852 −24.1196 0 −23.5086
1.19 2.60026 0 −1.23865 11.0636 0 −16.8612 −24.0229 0 28.7682
1.20 3.06927 0 1.42044 −10.0975 0 1.48241 −20.1945 0 −30.9919
See all 28 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.28
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.c 28
3.b odd 2 1 717.4.a.a ✓ 28
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
717.4.a.a ✓ 28 3.b odd 2 1
2151.4.a.c 28 1.a even 1 1 trivial