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Properties

Label 2151.4.a.a
Level $2151$
Weight $4$
Character orbit 2151.a
Self dual yes
Analytic conductor $126.913$
Analytic rank $1$
Dimension $22$
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: \(22\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 22 q + 4 q^{2} + 50 q^{4} + 37 q^{5} - 52 q^{7} + 69 q^{8}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 22 q + 4 q^{2} + 50 q^{4} + 37 q^{5} - 52 q^{7} + 69 q^{8} - 93 q^{10} + 77 q^{11} - 218 q^{13} + 111 q^{14} - 42 q^{16} + 219 q^{17} - 476 q^{19} + 314 q^{20} - 390 q^{22} + 202 q^{23} - 271 q^{25} + 220 q^{26} - 515 q^{28} + 307 q^{29} - 1001 q^{31} + 771 q^{32} - 1297 q^{34} + 430 q^{35} - 922 q^{37} - 49 q^{38} - 1344 q^{40} + 1188 q^{41} - 192 q^{43} + 547 q^{44} - 1178 q^{46} + 102 q^{47} - 1952 q^{49} + 471 q^{50} - 1785 q^{52} + 580 q^{53} - 1730 q^{55} + 804 q^{56} - 1156 q^{58} + 1528 q^{59} - 1631 q^{61} - 2206 q^{62} + 327 q^{64} - 44 q^{65} - 689 q^{67} - 2522 q^{68} + 1175 q^{70} - 341 q^{71} - 2260 q^{73} - 4027 q^{74} - 1855 q^{76} - 1578 q^{77} + 396 q^{79} - 6183 q^{80} + 4936 q^{82} - 1065 q^{83} + 144 q^{85} - 2915 q^{86} + 1068 q^{88} + 1984 q^{89} - 2186 q^{91} - 6720 q^{92} + 174 q^{94} - 2804 q^{95} - 4946 q^{97} - 7149 q^{98}+O(q^{100}) \) 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 −4.92623 0 16.2677 3.10245 0 −6.93638 −40.7288 0 −15.2834
1.2 −4.58869 0 13.0561 15.1251 0 −25.8403 −23.2007 0 −69.4042
1.3 −3.67099 0 5.47619 −0.939206 0 −4.16512 9.26490 0 3.44782
1.4 −3.64923 0 5.31692 17.2106 0 24.0056 9.79121 0 −62.8056
1.5 −3.32790 0 3.07490 −7.52905 0 −10.0131 16.3902 0 25.0559
1.6 −2.32829 0 −2.57908 14.1221 0 −19.8005 24.6311 0 −32.8804
1.7 −2.22859 0 −3.03338 7.56659 0 −1.62323 24.5889 0 −16.8628
1.8 −2.21535 0 −3.09221 −10.2488 0 −27.8405 24.5732 0 22.7048
1.9 −1.83829 0 −4.62067 −9.40555 0 19.7665 23.2005 0 17.2902
1.10 −0.530015 0 −7.71908 0.726105 0 27.7214 8.33135 0 −0.384847
1.11 0.594431 0 −7.64665 5.61897 0 −8.56684 −9.30086 0 3.34009
1.12 0.850702 0 −7.27631 −12.0519 0 −14.5326 −12.9956 0 −10.2525
1.13 0.976149 0 −7.04713 2.51110 0 23.2375 −14.6882 0 2.45121
1.14 1.49092 0 −5.77714 −16.6313 0 −17.5795 −20.5407 0 −24.7960
1.15 1.51884 0 −5.69312 1.30911 0 −3.41938 −20.7977 0 1.98833
1.16 2.38671 0 −2.30360 5.10344 0 12.4633 −24.5917 0 12.1804
1.17 3.24958 0 2.55975 21.6437 0 3.86879 −17.6785 0 70.3329
1.18 3.42794 0 3.75080 7.18364 0 −16.4073 −14.5660 0 24.6251
1.19 4.40109 0 11.3696 3.94300 0 −14.1222 14.8300 0 17.3535
1.20 4.43192 0 11.6419 11.7413 0 6.42321 16.1407 0 52.0364
See all 22 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.22
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.a 22
3.b odd 2 1 239.4.a.a ✓ 22
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
239.4.a.a ✓ 22 3.b odd 2 1
2151.4.a.a 22 1.a even 1 1 trivial