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Properties

Label 2033.2.a.c
Level $2033$
Weight $2$
Character orbit 2033.a
Self dual yes
Analytic conductor $16.234$
Analytic rank $0$
Dimension $42$
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: \(42\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 42 q + 7 q^{2} + 11 q^{3} + 47 q^{4} + 2 q^{5} + 5 q^{6} + 38 q^{7} + 15 q^{8} + 41 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 42 q + 7 q^{2} + 11 q^{3} + 47 q^{4} + 2 q^{5} + 5 q^{6} + 38 q^{7} + 15 q^{8} + 41 q^{9} + 17 q^{10} + 4 q^{11} + 3 q^{12} + 38 q^{13} - 4 q^{14} + 28 q^{15} + 53 q^{16} + 5 q^{17} + 12 q^{18} + 42 q^{19} - 3 q^{20} + 21 q^{21} + 30 q^{22} + 17 q^{23} + 7 q^{24} + 40 q^{25} - 9 q^{26} + 23 q^{27} + 56 q^{28} + 4 q^{29} - 14 q^{30} + 47 q^{31} + 32 q^{32} + 18 q^{33} + 9 q^{34} - q^{35} + 64 q^{36} + 69 q^{37} + 7 q^{38} + 12 q^{39} + 29 q^{40} + 7 q^{41} - 57 q^{42} + 66 q^{43} + 28 q^{44} + q^{45} + 28 q^{46} + 13 q^{47} + q^{48} + 48 q^{49} - 2 q^{50} + 32 q^{51} + 49 q^{52} + 9 q^{53} - 7 q^{54} + 27 q^{55} + 28 q^{56} + 11 q^{57} + 17 q^{58} + 18 q^{59} + 20 q^{60} - 11 q^{61} + 14 q^{62} + 62 q^{63} + 27 q^{64} - q^{65} - 54 q^{66} + 70 q^{67} - 16 q^{68} + 4 q^{69} + 28 q^{70} + 7 q^{71} + 72 q^{72} + 54 q^{73} + 30 q^{74} + 21 q^{75} + 47 q^{76} - 14 q^{77} + 25 q^{78} + 107 q^{79} - 102 q^{80} + 50 q^{81} + 29 q^{82} - 23 q^{83} + 21 q^{84} + q^{85} - 43 q^{86} + 42 q^{87} + 52 q^{88} - 5 q^{89} + 18 q^{90} + 65 q^{91} + 29 q^{92} + 39 q^{93} + 25 q^{94} + 2 q^{95} - 62 q^{96} + 80 q^{97} + 41 q^{98} - 9 q^{99}+O(q^{100}) \) 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 −2.64120 1.66201 4.97596 −3.33711 −4.38970 2.89636 −7.86012 −0.237731 8.81398
1.2 −2.59726 −1.84242 4.74577 0.237751 4.78525 1.33371 −7.13149 0.394517 −0.617501
1.3 −2.52196 0.289639 4.36026 −0.264203 −0.730458 −4.03112 −5.95248 −2.91611 0.666309
1.4 −2.45880 3.12953 4.04568 0.112214 −7.69488 4.45079 −5.02992 6.79395 −0.275911
1.5 −2.37029 −2.28498 3.61828 −4.08277 5.41607 2.26145 −3.83580 2.22113 9.67734
1.6 −2.14141 −1.77114 2.58563 2.58124 3.79273 −0.601109 −1.25408 0.136930 −5.52748
1.7 −2.12388 0.358400 2.51088 3.44559 −0.761200 1.03648 −1.08504 −2.87155 −7.31802
1.8 −1.78018 −3.08567 1.16904 −2.84892 5.49304 −0.802318 1.47927 6.52136 5.07158
1.9 −1.77864 2.08380 1.16356 3.16200 −3.70633 4.42383 1.48773 1.34222 −5.62407
1.10 −1.39834 −0.124226 −0.0446574 −2.18372 0.173710 2.48251 2.85912 −2.98457 3.05358
1.11 −1.37809 1.75989 −0.100879 −1.28957 −2.42527 −1.08798 2.89519 0.0971997 1.77714
1.12 −1.34291 3.27228 −0.196591 2.54242 −4.39439 −0.0514702 2.94983 7.70784 −3.41425
1.13 −1.21885 −1.26874 −0.514414 2.04978 1.54640 3.25896 3.06468 −1.39030 −2.49837
1.14 −1.19764 0.302116 −0.565653 −2.87007 −0.361827 −0.115654 3.07273 −2.90873 3.43732
1.15 −0.798695 2.64069 −1.36209 −0.891790 −2.10910 4.30477 2.68528 3.97322 0.712268
1.16 −0.607699 0.536106 −1.63070 1.67279 −0.325791 −3.35632 2.20637 −2.71259 −1.01655
1.17 −0.420142 −2.36986 −1.82348 1.11809 0.995678 1.03980 1.60640 2.61625 −0.469757
1.18 −0.285972 −0.600959 −1.91822 −1.96801 0.171857 4.96950 1.12050 −2.63885 0.562795
1.19 −0.189826 2.48920 −1.96397 3.06877 −0.472516 −1.48849 0.752466 3.19610 −0.582534
1.20 0.0678497 −3.31177 −1.99540 −0.611206 −0.224703 1.19786 −0.271087 7.96782 −0.0414702
See all 42 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.42
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.c ✓ 42
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2033.2.a.c ✓ 42 1.a even 1 1 trivial