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Properties

Label 3022.2.a.c
Level $3022$
Weight $2$
Character orbit 3022.a
Self dual yes
Analytic conductor $24.131$
Analytic rank $0$
Dimension $34$
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] = [3022,2,Mod(1,3022)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3022, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3022.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3022 = 2 \cdot 1511 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3022.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: \(24.1307914908\)
Analytic rank: \(0\)
Dimension: \(34\)
Twist minimal: yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 34 q + 34 q^{2} + 7 q^{3} + 34 q^{4} + 12 q^{5} + 7 q^{6} + 15 q^{7} + 34 q^{8} + 37 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 34 q + 34 q^{2} + 7 q^{3} + 34 q^{4} + 12 q^{5} + 7 q^{6} + 15 q^{7} + 34 q^{8} + 37 q^{9} + 12 q^{10} + 24 q^{11} + 7 q^{12} + 11 q^{13} + 15 q^{14} + 26 q^{15} + 34 q^{16} + 17 q^{17} + 37 q^{18} + 26 q^{19} + 12 q^{20} + 10 q^{21} + 24 q^{22} + 38 q^{23} + 7 q^{24} + 34 q^{25} + 11 q^{26} + 19 q^{27} + 15 q^{28} + 25 q^{29} + 26 q^{30} + 19 q^{31} + 34 q^{32} + 10 q^{33} + 17 q^{34} + 24 q^{35} + 37 q^{36} + 26 q^{37} + 26 q^{38} + 22 q^{39} + 12 q^{40} + 13 q^{41} + 10 q^{42} + 35 q^{43} + 24 q^{44} + 8 q^{45} + 38 q^{46} + 47 q^{47} + 7 q^{48} + 15 q^{49} + 34 q^{50} + 21 q^{51} + 11 q^{52} + 62 q^{53} + 19 q^{54} + 18 q^{55} + 15 q^{56} + q^{57} + 25 q^{58} + 31 q^{59} + 26 q^{60} + 18 q^{61} + 19 q^{62} + 16 q^{63} + 34 q^{64} + 6 q^{65} + 10 q^{66} + 56 q^{67} + 17 q^{68} + 5 q^{69} + 24 q^{70} + 58 q^{71} + 37 q^{72} - 9 q^{73} + 26 q^{74} + 12 q^{75} + 26 q^{76} + 26 q^{77} + 22 q^{78} + 47 q^{79} + 12 q^{80} + 22 q^{81} + 13 q^{82} + 43 q^{83} + 10 q^{84} + 13 q^{85} + 35 q^{86} + 15 q^{87} + 24 q^{88} + 4 q^{89} + 8 q^{90} + 15 q^{91} + 38 q^{92} + 28 q^{93} + 47 q^{94} + 30 q^{95} + 7 q^{96} - 6 q^{97} + 15 q^{98} + 46 q^{99}+O(q^{100}) \) 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 1.00000 −3.15009 1.00000 −2.14387 −3.15009 −1.77827 1.00000 6.92304 −2.14387
1.2 1.00000 −3.05307 1.00000 −2.30491 −3.05307 0.885670 1.00000 6.32123 −2.30491
1.3 1.00000 −2.95468 1.00000 0.754735 −2.95468 2.83087 1.00000 5.73014 0.754735
1.4 1.00000 −2.55334 1.00000 3.84583 −2.55334 2.46964 1.00000 3.51955 3.84583
1.5 1.00000 −2.29060 1.00000 2.42816 −2.29060 −3.40843 1.00000 2.24686 2.42816
1.6 1.00000 −2.16515 1.00000 −2.64666 −2.16515 −2.17220 1.00000 1.68787 −2.64666
1.7 1.00000 −2.03636 1.00000 −0.560697 −2.03636 3.33825 1.00000 1.14675 −0.560697
1.8 1.00000 −1.69372 1.00000 2.16357 −1.69372 2.46840 1.00000 −0.131314 2.16357
1.9 1.00000 −1.59968 1.00000 −0.657036 −1.59968 0.808921 1.00000 −0.441031 −0.657036
1.10 1.00000 −1.39059 1.00000 2.31823 −1.39059 −1.82322 1.00000 −1.06625 2.31823
1.11 1.00000 −1.27433 1.00000 −2.97987 −1.27433 4.54712 1.00000 −1.37609 −2.97987
1.12 1.00000 −1.09119 1.00000 −0.129085 −1.09119 −4.93273 1.00000 −1.80931 −0.129085
1.13 1.00000 −0.467920 1.00000 −2.76863 −0.467920 −2.94223 1.00000 −2.78105 −2.76863
1.14 1.00000 −0.412709 1.00000 1.14043 −0.412709 −1.71853 1.00000 −2.82967 1.14043
1.15 1.00000 −0.134440 1.00000 −4.30699 −0.134440 −1.21570 1.00000 −2.98193 −4.30699
1.16 1.00000 −0.0794069 1.00000 3.52629 −0.0794069 4.41840 1.00000 −2.99369 3.52629
1.17 1.00000 0.0132880 1.00000 3.53293 0.0132880 2.06696 1.00000 −2.99982 3.53293
1.18 1.00000 0.293908 1.00000 −2.36637 0.293908 3.14532 1.00000 −2.91362 −2.36637
1.19 1.00000 0.474804 1.00000 0.0324915 0.474804 3.32801 1.00000 −2.77456 0.0324915
1.20 1.00000 0.846487 1.00000 −1.19329 0.846487 −3.51350 1.00000 −2.28346 −1.19329
See all 34 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.34
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(1511\) \(1\)

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 3022.2.a.c ✓ 34
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
3022.2.a.c ✓ 34 1.a even 1 1 trivial