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Properties

Label 2151.4.a.d
Level $2151$
Weight $4$
Character orbit 2151.a
Self dual yes
Analytic conductor $126.913$
Analytic rank $1$
Dimension $32$
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: \(1\)
Dimension: \(32\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q - 11 q^{2} + 147 q^{4} - 66 q^{5} + 58 q^{7} - 153 q^{8}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 32 q - 11 q^{2} + 147 q^{4} - 66 q^{5} + 58 q^{7} - 153 q^{8} + 52 q^{10} - 270 q^{11} + 48 q^{13} - 184 q^{14} + 775 q^{16} - 384 q^{17} + 216 q^{19} - 534 q^{20} + 437 q^{22} - 712 q^{23} + 1190 q^{25} - 436 q^{26} + 598 q^{28} - 562 q^{29} + 384 q^{31} - 1770 q^{32} + 452 q^{34} - 1026 q^{35} + 770 q^{37} - 733 q^{38} + 877 q^{40} - 1648 q^{41} + 1592 q^{43} - 1595 q^{44} + 532 q^{46} - 1540 q^{47} + 2134 q^{49} - 1646 q^{50} - 144 q^{52} - 1708 q^{53} + 1282 q^{55} - 2155 q^{56} + 1086 q^{58} - 2396 q^{59} + 364 q^{61} - 2180 q^{62} + 1663 q^{64} - 1520 q^{65} + 2728 q^{67} - 1545 q^{68} - 4609 q^{70} - 3322 q^{71} - 188 q^{73} - 1111 q^{74} - 3134 q^{76} - 556 q^{77} - 462 q^{79} - 6076 q^{80} - 7965 q^{82} - 4604 q^{83} - 852 q^{85} - 549 q^{86} - 1127 q^{88} - 6742 q^{89} + 1390 q^{91} - 1802 q^{92} - 2796 q^{94} - 448 q^{95} - 1322 q^{97} - 1000 q^{98}+O(q^{100}) \) 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 −5.59453 0 23.2988 −16.4914 0 −10.5009 −85.5894 0 92.2616
1.2 −5.31397 0 20.2383 −1.11401 0 6.72325 −65.0342 0 5.91984
1.3 −5.23366 0 19.3912 13.4597 0 28.9382 −59.6177 0 −70.4436
1.4 −5.16397 0 18.6666 0.429463 0 −25.9056 −55.0823 0 −2.21774
1.5 −4.76460 0 14.7014 −12.2551 0 22.9067 −31.9296 0 58.3909
1.6 −4.73063 0 14.3788 −2.38638 0 21.4748 −30.1758 0 11.2891
1.7 −4.24177 0 9.99259 −19.4944 0 −4.35055 −8.45209 0 82.6908
1.8 −3.87098 0 6.98450 17.8390 0 4.77620 3.93099 0 −69.0545
1.9 −3.63855 0 5.23901 −13.7159 0 7.38539 10.0460 0 49.9058
1.10 −2.74193 0 −0.481825 19.5291 0 −9.73710 23.2566 0 −53.5474
1.11 −2.35922 0 −2.43409 −3.14815 0 −17.8040 24.6163 0 7.42716
1.12 −2.25922 0 −2.89594 −14.4181 0 23.8295 24.6163 0 32.5737
1.13 −2.06669 0 −3.72878 0.727240 0 31.6777 24.2398 0 −1.50298
1.14 −1.28682 0 −6.34409 14.8834 0 −31.0382 18.4583 0 −19.1522
1.15 −1.10380 0 −6.78162 −20.8736 0 −33.6250 16.3160 0 23.0403
1.16 −0.980358 0 −7.03890 13.2849 0 4.25684 14.7435 0 −13.0240
1.17 −0.197960 0 −7.96081 0.664309 0 12.2133 3.15960 0 −0.131506
1.18 0.323742 0 −7.89519 −13.7872 0 10.6908 −5.14594 0 −4.46348
1.19 0.560231 0 −7.68614 −18.3687 0 31.3786 −8.78786 0 −10.2907
1.20 0.752561 0 −7.43365 −3.00130 0 −33.6762 −11.6148 0 −2.25866
See all 32 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.32
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.d 32
3.b odd 2 1 717.4.a.d ✓ 32
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
717.4.a.d ✓ 32 3.b odd 2 1
2151.4.a.d 32 1.a even 1 1 trivial