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Properties

Label 2033.2.a.d
Level $2033$
Weight $2$
Character orbit 2033.a
Self dual yes
Analytic conductor $16.234$
Analytic rank $0$
Dimension $44$
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] = [2033,2,Mod(1,2033)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2033, 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("2033.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2033 = 19 \cdot 107 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2033.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: \(16.2335867309\)
Analytic rank: \(0\)
Dimension: \(44\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 44 q + 4 q^{2} + 3 q^{3} + 52 q^{4} + 3 q^{5} + 5 q^{6} + 43 q^{7} + 12 q^{8} + 51 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 44 q + 4 q^{2} + 3 q^{3} + 52 q^{4} + 3 q^{5} + 5 q^{6} + 43 q^{7} + 12 q^{8} + 51 q^{9} + q^{10} + 19 q^{11} + 5 q^{12} + 4 q^{13} + 12 q^{14} + 30 q^{15} + 64 q^{16} + 12 q^{17} + 27 q^{18} - 44 q^{19} + 17 q^{20} + q^{21} + 34 q^{22} + 37 q^{23} + 7 q^{24} + 67 q^{25} + 15 q^{26} + 9 q^{27} + 76 q^{28} + 14 q^{29} + 14 q^{30} + 39 q^{31} + 3 q^{32} + 14 q^{33} - 3 q^{34} + 28 q^{35} + 21 q^{36} + 7 q^{37} - 4 q^{38} + 44 q^{39} - 11 q^{40} + 3 q^{41} + 39 q^{42} + 55 q^{43} + 22 q^{44} + 6 q^{45} + 28 q^{46} + 42 q^{47} - 3 q^{48} + 71 q^{49} + 9 q^{50} - 26 q^{51} + 3 q^{52} + 7 q^{53} + 15 q^{54} + 62 q^{55} - 40 q^{56} - 3 q^{57} + 57 q^{58} - 18 q^{60} + 46 q^{61} - 50 q^{62} + 123 q^{63} + 98 q^{64} + 3 q^{65} - 26 q^{66} + 80 q^{67} + 8 q^{68} - 16 q^{69} - 36 q^{70} + 15 q^{71} - 33 q^{72} + 37 q^{73} - 50 q^{74} + 9 q^{75} - 52 q^{76} + 27 q^{77} - 13 q^{78} + 97 q^{79} + 64 q^{80} + 52 q^{81} - 19 q^{82} + 45 q^{83} - 19 q^{84} + 68 q^{85} + 19 q^{86} + 22 q^{87} + 106 q^{88} + 5 q^{89} - 6 q^{90} - 11 q^{91} + 37 q^{92} - 29 q^{93} - 39 q^{94} - 3 q^{95} + 26 q^{96} + 12 q^{97} - 4 q^{98} + 86 q^{99}+O(q^{100}) \) 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 −2.79664 1.75929 5.82120 2.76779 −4.92011 2.68960 −10.6865 0.0951096 −7.74050
1.2 −2.70602 −2.73518 5.32255 −0.276750 7.40145 3.64838 −8.99089 4.48119 0.748891
1.3 −2.69169 0.356927 5.24519 −2.10196 −0.960738 −1.09160 −8.73504 −2.87260 5.65781
1.4 −2.38224 0.248286 3.67506 −3.28034 −0.591476 2.13698 −3.99038 −2.93835 7.81455
1.5 −2.31795 −1.66989 3.37289 4.15671 3.87072 4.92641 −3.18230 −0.211469 −9.63505
1.6 −2.07293 −2.03236 2.29705 2.66748 4.21295 −1.82773 −0.615772 1.13049 −5.52952
1.7 −2.06020 2.82397 2.24442 2.27430 −5.81794 0.979346 −0.503550 4.97481 −4.68552
1.8 −1.99555 1.91008 1.98220 1.04388 −3.81166 −3.59673 0.0355192 0.648423 −2.08311
1.9 −1.94133 −1.80884 1.76876 −0.729145 3.51156 −2.51254 0.448918 0.271909 1.41551
1.10 −1.93674 0.582805 1.75097 −0.580214 −1.12874 4.48903 0.482307 −2.66034 1.12373
1.11 −1.79521 3.02020 1.22277 −3.80932 −5.42189 1.26317 1.39528 6.12160 6.83853
1.12 −1.27369 0.221170 −0.377716 1.83082 −0.281702 −2.74457 3.02847 −2.95108 −2.33190
1.13 −1.23343 −3.05421 −0.478649 −2.69831 3.76715 −0.473014 3.05724 6.32818 3.32818
1.14 −1.10936 −1.47116 −0.769330 −2.26963 1.63204 0.352284 3.07217 −0.835686 2.51783
1.15 −1.03273 1.63502 −0.933462 3.65892 −1.68854 3.25241 3.02948 −0.326708 −3.77869
1.16 −0.895180 1.34050 −1.19865 0.0615537 −1.19999 3.18783 2.86337 −1.20306 −0.0551016
1.17 −0.846929 −2.31388 −1.28271 −3.69673 1.95970 5.15281 2.78022 2.35406 3.13087
1.18 −0.749658 1.37204 −1.43801 −3.14619 −1.02856 −3.50949 2.57733 −1.11750 2.35857
1.19 −0.472196 −2.05925 −1.77703 1.65446 0.972369 −0.519707 1.78350 1.24050 −0.781228
1.20 −0.268790 2.38963 −1.92775 4.21657 −0.642310 0.233841 1.05574 2.71033 −1.13337
See all 44 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.44
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(19\) \( +1 \)
\(107\) \( -1 \)

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 2033.2.a.d ✓ 44
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2033.2.a.d ✓ 44 1.a even 1 1 trivial