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Properties

Label 8033.2.a.c
Level $8033$
Weight $2$
Character orbit 8033.a
Self dual yes
Analytic conductor $64.144$
Analytic rank $1$
Dimension $154$
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] = [8033,2,Mod(1,8033)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8033, 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("8033.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8033 = 29 \cdot 277 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8033.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: \(64.1438279437\)
Analytic rank: \(1\)
Dimension: \(154\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 154 q - 12 q^{2} - 36 q^{3} + 142 q^{4} - 9 q^{5} - 11 q^{6} - 68 q^{7} - 33 q^{8} + 146 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 154 q - 12 q^{2} - 36 q^{3} + 142 q^{4} - 9 q^{5} - 11 q^{6} - 68 q^{7} - 33 q^{8} + 146 q^{9} - 40 q^{10} - 36 q^{11} - 67 q^{12} - 51 q^{13} - 19 q^{14} - 48 q^{15} + 122 q^{16} - 54 q^{17} - 46 q^{18} - 73 q^{19} - 21 q^{20} - 8 q^{21} - 23 q^{22} - 38 q^{23} - 17 q^{24} + 133 q^{25} - 20 q^{26} - 129 q^{27} - 99 q^{28} + 154 q^{29} - 10 q^{30} - 91 q^{31} - 88 q^{32} - 39 q^{33} - 42 q^{34} - 36 q^{35} + 101 q^{36} - 50 q^{37} - 17 q^{38} - 33 q^{39} - 92 q^{40} - 31 q^{41} - 62 q^{42} - 154 q^{43} - 42 q^{44} - 14 q^{45} - 24 q^{46} - 140 q^{47} - 118 q^{48} + 126 q^{49} - 5 q^{50} - 16 q^{51} - 133 q^{52} - 40 q^{53} + 14 q^{54} - 203 q^{55} - 44 q^{56} - 16 q^{57} - 12 q^{58} + 5 q^{59} - 28 q^{60} - 106 q^{61} - 30 q^{62} - 145 q^{63} + 111 q^{64} - 15 q^{65} - 49 q^{66} - 78 q^{67} - 118 q^{68} - 32 q^{69} - 43 q^{70} - 4 q^{71} - 152 q^{72} - 137 q^{73} + 9 q^{74} - 129 q^{75} - 204 q^{76} - 76 q^{77} + 15 q^{78} - 141 q^{79} - 44 q^{80} + 122 q^{81} - 71 q^{82} - 90 q^{83} + 92 q^{84} - 41 q^{85} + 9 q^{86} - 36 q^{87} - 109 q^{88} - 51 q^{89} - 82 q^{90} - 22 q^{91} - 8 q^{92} - 10 q^{93} - 106 q^{94} - 55 q^{95} - 49 q^{96} - 140 q^{97} - 4 q^{98} - 101 q^{99}+O(q^{100}) \) 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 −2.82218 1.84090 5.96471 −0.0331224 −5.19535 1.38101 −11.1891 0.388906 0.0934774
1.2 −2.80099 −1.33349 5.84554 0.375260 3.73510 1.86520 −10.7713 −1.22179 −1.05110
1.3 −2.75023 2.46000 5.56375 3.61525 −6.76556 0.234720 −9.80113 3.05159 −9.94275
1.4 −2.73685 −2.64760 5.49034 −2.28975 7.24607 −2.70237 −9.55253 4.00977 6.26669
1.5 −2.71211 1.42746 5.35553 −2.33399 −3.87141 −3.68484 −9.10055 −0.962372 6.33003
1.6 −2.71067 −3.12256 5.34773 3.18562 8.46423 −1.32961 −9.07461 6.75039 −8.63517
1.7 −2.66581 −3.36665 5.10653 −1.10799 8.97484 −4.45627 −8.28140 8.33433 2.95369
1.8 −2.65912 −0.292744 5.07094 3.25351 0.778443 −0.266213 −8.16600 −2.91430 −8.65148
1.9 −2.60300 −1.50583 4.77561 −2.67375 3.91967 −1.75019 −7.22491 −0.732487 6.95977
1.10 −2.51869 0.856221 4.34380 2.85854 −2.15656 −2.09984 −5.90330 −2.26688 −7.19979
1.11 −2.50518 1.00988 4.27592 1.71073 −2.52992 5.05485 −5.70160 −1.98015 −4.28569
1.12 −2.49784 3.18584 4.23922 −0.569133 −7.95772 −1.98471 −5.59321 7.14957 1.42160
1.13 −2.47502 −2.70377 4.12575 2.22843 6.69190 4.05795 −5.26128 4.31037 −5.51542
1.14 −2.40713 −0.707338 3.79429 −1.84039 1.70266 −2.62774 −4.31910 −2.49967 4.43006
1.15 −2.38939 −1.95815 3.70919 −1.03440 4.67879 1.98730 −4.08392 0.834367 2.47157
1.16 −2.38444 0.0319476 3.68556 2.00388 −0.0761772 0.134217 −4.01912 −2.99898 −4.77812
1.17 −2.33752 2.79433 3.46401 −2.95818 −6.53182 2.23509 −3.42216 4.80831 6.91481
1.18 −2.33650 −1.34355 3.45924 −2.97087 3.13920 1.58277 −3.40951 −1.19488 6.94144
1.19 −2.30013 −2.89342 3.29061 2.38391 6.65525 −4.38144 −2.96858 5.37188 −5.48331
1.20 −2.25887 1.60047 3.10247 −3.14219 −3.61525 −0.353570 −2.49034 −0.438494 7.09779
See next 80 embeddings (of 154 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.154
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(29\) \(-1\)
\(277\) \(-1\)

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 8033.2.a.c ✓ 154
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8033.2.a.c ✓ 154 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{154} + 12 T_{2}^{153} - 153 T_{2}^{152} - 2385 T_{2}^{151} + 9749 T_{2}^{150} + 230393 T_{2}^{149} + \cdots - 66516032 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8033))\). Copy content Toggle raw display