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Properties

Label 893.2.a.d
Level $893$
Weight $2$
Character orbit 893.a
Self dual yes
Analytic conductor $7.131$
Analytic rank $0$
Dimension $23$
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] = [893,2,Mod(1,893)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(893, 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("893.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 893 = 19 \cdot 47 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 893.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: \(7.13064090050\)
Analytic rank: \(0\)
Dimension: \(23\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 23 q + q^{2} + 13 q^{3} + 31 q^{4} + q^{5} + 2 q^{6} + 15 q^{7} + 34 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 23 q + q^{2} + 13 q^{3} + 31 q^{4} + q^{5} + 2 q^{6} + 15 q^{7} + 34 q^{9} + 5 q^{10} + 2 q^{11} + 13 q^{12} + 13 q^{13} + 6 q^{14} + q^{15} + 35 q^{16} + 12 q^{17} + 16 q^{18} + 23 q^{19} + 3 q^{20} + q^{21} - 4 q^{22} + 13 q^{23} + 5 q^{24} + 46 q^{25} - 7 q^{26} + 55 q^{27} + 11 q^{28} - 18 q^{29} + 17 q^{30} + 22 q^{31} - 4 q^{32} + 3 q^{33} - 20 q^{34} + 25 q^{35} + 17 q^{36} + 8 q^{37} + q^{38} - 19 q^{39} - 16 q^{40} - 16 q^{41} + 26 q^{42} + 68 q^{43} - 18 q^{44} - 12 q^{45} + 13 q^{46} - 23 q^{47} + 5 q^{48} + 52 q^{49} - 21 q^{50} + 22 q^{51} + 54 q^{52} - 7 q^{53} + 16 q^{54} + 32 q^{55} + 33 q^{56} + 13 q^{57} + 6 q^{58} + 10 q^{59} - 128 q^{60} + 28 q^{61} - 24 q^{62} + 3 q^{63} + 40 q^{64} - 18 q^{65} - 80 q^{66} + 55 q^{67} + 41 q^{68} - 17 q^{69} - 40 q^{70} - 3 q^{71} - 20 q^{72} + 48 q^{73} - 55 q^{74} + 82 q^{75} + 31 q^{76} - 14 q^{77} - 62 q^{78} - 31 q^{79} - 3 q^{80} + 55 q^{81} + 48 q^{82} + 47 q^{83} - 23 q^{84} - 5 q^{85} - 71 q^{86} + 35 q^{87} + 9 q^{88} - 6 q^{89} + 58 q^{90} + 40 q^{91} + 35 q^{92} - 9 q^{93} - q^{94} + q^{95} - 25 q^{96} - 18 q^{97} - 68 q^{98} - 42 q^{99}+O(q^{100}) \) 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 −2.80052 −1.27216 5.84290 2.27082 3.56271 2.12395 −10.7621 −1.38160 −6.35948
1.2 −2.42555 3.29285 3.88328 −4.06628 −7.98697 −3.08813 −4.56798 7.84288 9.86296
1.3 −2.36692 −1.25105 3.60230 −2.10346 2.96113 −2.22210 −3.79250 −1.43488 4.97872
1.4 −2.31786 1.19559 3.37246 4.06165 −2.77120 −2.19787 −3.18116 −1.57057 −9.41433
1.5 −2.30976 2.19978 3.33497 −0.940736 −5.08096 4.70927 −3.08346 1.83904 2.17287
1.6 −1.55024 −0.0231152 0.403250 −0.718559 0.0358342 −2.40005 2.47535 −2.99947 1.11394
1.7 −1.45599 −2.79210 0.119916 1.65894 4.06528 2.91693 2.73739 4.79582 −2.41540
1.8 −1.23080 −0.711364 −0.485141 −3.43966 0.875545 5.19980 3.05870 −2.49396 4.23352
1.9 −1.00631 1.75660 −0.987335 4.09447 −1.76768 3.87614 3.00619 0.0856307 −4.12032
1.10 −0.581855 1.84991 −1.66145 −2.54642 −1.07638 −4.55068 2.13043 0.422168 1.48165
1.11 −0.154056 2.58450 −1.97627 1.39588 −0.398159 −0.0231293 0.612568 3.67966 −0.215045
1.12 −0.102666 3.45862 −1.98946 0.421030 −0.355082 4.07188 0.409581 8.96206 −0.0432253
1.13 0.512932 −2.70160 −1.73690 −0.842347 −1.38574 −1.17187 −1.91678 4.29866 −0.432067
1.14 0.772110 0.0389298 −1.40385 −2.30868 0.0300581 3.13314 −2.62814 −2.99848 −1.78256
1.15 1.15471 0.480065 −0.666651 2.72924 0.554335 1.99299 −3.07920 −2.76954 3.15148
1.16 1.28005 −2.04631 −0.361479 −4.05982 −2.61937 −2.17032 −3.02280 1.18739 −5.19677
1.17 1.67375 3.29139 0.801455 3.83185 5.50899 −3.94220 −2.00607 7.83327 6.41357
1.18 1.73522 1.97404 1.01098 2.41866 3.42540 1.62998 −1.71616 0.896853 4.19690
1.19 2.06457 −2.37898 2.26244 3.06045 −4.91156 3.81585 0.541831 2.65952 6.31850
1.20 2.37437 2.49960 3.63763 −1.61117 5.93498 0.108357 3.88834 3.24801 −3.82552
See all 23 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.23
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(19\) \( -1 \)
\(47\) \( +1 \)

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 893.2.a.d ✓ 23
3.b odd 2 1 8037.2.a.r 23
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
893.2.a.d ✓ 23 1.a even 1 1 trivial
8037.2.a.r 23 3.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{23} - T_{2}^{22} - 38 T_{2}^{21} + 37 T_{2}^{20} + 622 T_{2}^{19} - 586 T_{2}^{18} - 5746 T_{2}^{17} + \cdots - 315 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(893))\). Copy content Toggle raw display