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Properties

Label 2033.2.a.b
Level $2033$
Weight $2$
Character orbit 2033.a
Self dual yes
Analytic conductor $16.234$
Analytic rank $1$
Dimension $37$
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: \(1\)
Dimension: \(37\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 37 q - 5 q^{2} - 3 q^{3} + 31 q^{4} - 9 q^{5} - 11 q^{6} - 39 q^{7} - 15 q^{8} + 30 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 37 q - 5 q^{2} - 3 q^{3} + 31 q^{4} - 9 q^{5} - 11 q^{6} - 39 q^{7} - 15 q^{8} + 30 q^{9} - 13 q^{10} - 13 q^{11} - 5 q^{12} - 2 q^{13} + 2 q^{14} - 34 q^{15} + 15 q^{16} - 14 q^{17} - 18 q^{18} - 37 q^{19} - 19 q^{20} - 11 q^{21} - 22 q^{22} - 35 q^{23} - 41 q^{24} + 18 q^{25} - 3 q^{26} - 15 q^{27} - 88 q^{28} + 4 q^{29} + 10 q^{30} - 37 q^{31} - 40 q^{32} + 2 q^{33} - 5 q^{34} + 4 q^{35} + 26 q^{36} - 19 q^{37} + 5 q^{38} - 60 q^{39} - 9 q^{40} - 3 q^{41} - 9 q^{42} - 89 q^{43} - 2 q^{44} - 54 q^{45} - 42 q^{46} - 34 q^{47} - 21 q^{48} + 34 q^{49} - 36 q^{50} - 28 q^{51} - 59 q^{52} + 25 q^{53} + 9 q^{54} - 44 q^{55} + 62 q^{56} + 3 q^{57} - 77 q^{58} + 6 q^{59} - 56 q^{60} - 26 q^{61} - 22 q^{62} - 91 q^{63} - 7 q^{64} - 37 q^{65} - 66 q^{66} - 50 q^{67} + 18 q^{68} + 4 q^{69} + 26 q^{70} - 41 q^{71} - 18 q^{72} - 69 q^{73} - 20 q^{74} + 15 q^{75} - 31 q^{76} - 21 q^{77} + 51 q^{78} - 89 q^{79} - 20 q^{80} + 37 q^{81} - 55 q^{82} - 35 q^{83} - 75 q^{84} - 76 q^{85} - 7 q^{86} - 66 q^{87} - 62 q^{88} + 15 q^{89} - 48 q^{90} - 29 q^{91} - 7 q^{92} - 41 q^{93} + 45 q^{94} + 9 q^{95} - 86 q^{96} - 22 q^{97} + 11 q^{98} - 74 q^{99}+O(q^{100}) \) 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 −2.76896 3.06154 5.66713 −2.39394 −8.47727 −3.20296 −10.1541 6.37301 6.62871
1.2 −2.70890 −1.10054 5.33815 3.72053 2.98126 −4.52889 −9.04271 −1.78881 −10.0786
1.3 −2.40731 0.418101 3.79512 1.95350 −1.00650 0.0986106 −4.32141 −2.82519 −4.70267
1.4 −2.36772 −1.41509 3.60608 −1.93284 3.35054 0.134022 −3.80274 −0.997514 4.57641
1.5 −2.36430 −2.67157 3.58993 −0.698609 6.31640 −2.32386 −3.75909 4.13729 1.65172
1.6 −2.36371 1.71665 3.58712 −2.47172 −4.05766 −3.53168 −3.75148 −0.0531062 5.84242
1.7 −1.91699 1.96309 1.67484 −0.676814 −3.76321 3.59999 0.623328 0.853705 1.29744
1.8 −1.85221 −0.156941 1.43069 −3.92203 0.290688 −2.73985 1.05449 −2.97537 7.26444
1.9 −1.75175 1.28028 1.06863 3.69445 −2.24272 −1.64635 1.63153 −1.36089 −6.47176
1.10 −1.70576 −3.08227 0.909622 0.783253 5.25761 2.46833 1.85992 6.50038 −1.33604
1.11 −1.44904 2.82899 0.0997036 1.65953 −4.09931 −4.67842 2.75360 5.00320 −2.40472
1.12 −1.31886 −0.953486 −0.260618 1.64951 1.25751 1.70265 2.98143 −2.09086 −2.17547
1.13 −1.17984 −3.18915 −0.607979 2.59200 3.76268 −3.32862 3.07700 7.17065 −3.05814
1.14 −1.08651 2.97639 −0.819487 −1.49661 −3.23389 0.590388 3.06341 5.85890 1.62608
1.15 −0.967046 0.907800 −1.06482 −3.67942 −0.877885 1.60365 2.96382 −2.17590 3.55817
1.16 −0.958711 −0.500716 −1.08087 1.46013 0.480041 1.83684 2.95367 −2.74928 −1.39985
1.17 −0.323222 1.18394 −1.89553 2.18779 −0.382677 −1.74809 1.25912 −1.59828 −0.707144
1.18 −0.275920 −1.40265 −1.92387 −1.22239 0.387020 −4.49502 1.08267 −1.03257 0.337282
1.19 −0.207299 −1.58446 −1.95703 −1.68699 0.328457 0.680724 0.820289 −0.489488 0.349711
1.20 0.120351 1.38110 −1.98552 −1.86192 0.166217 3.51074 −0.479662 −1.09257 −0.224085
See all 37 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.37
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.b ✓ 37
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2033.2.a.b ✓ 37 1.a even 1 1 trivial