Properties

Label 4017.2.a.g
Level $4017$
Weight $2$
Character orbit 4017.a
Self dual yes
Analytic conductor $32.076$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4017,2,Mod(1,4017)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4017, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("4017.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4017 = 3 \cdot 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4017.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: \(32.0759064919\)
Analytic rank: \(0\)
Dimension: \(24\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9} - 2 q^{10} + 7 q^{11} - 25 q^{12} - 24 q^{13} + 8 q^{14} - 3 q^{15} + 23 q^{16} + 4 q^{17} + 3 q^{18} - 20 q^{19} + 8 q^{20} - 11 q^{21} + 5 q^{22} + 41 q^{23} - 6 q^{24} + 23 q^{25} - 3 q^{26} - 24 q^{27} + 16 q^{28} + 12 q^{29} + 2 q^{30} + 2 q^{31} + 25 q^{32} - 7 q^{33} - 11 q^{34} + 36 q^{35} + 25 q^{36} + 18 q^{37} + 10 q^{38} + 24 q^{39} + 14 q^{40} - 9 q^{41} - 8 q^{42} + 23 q^{43} + 41 q^{44} + 3 q^{45} + 7 q^{46} + 32 q^{47} - 23 q^{48} + 11 q^{49} + 26 q^{50} - 4 q^{51} - 25 q^{52} + 46 q^{53} - 3 q^{54} + 18 q^{55} + 26 q^{56} + 20 q^{57} + 37 q^{58} - 12 q^{59} - 8 q^{60} - q^{61} + 53 q^{62} + 11 q^{63} + 26 q^{64} - 3 q^{65} - 5 q^{66} + 8 q^{67} + 6 q^{68} - 41 q^{69} + 19 q^{70} + 20 q^{71} + 6 q^{72} + 12 q^{73} + 86 q^{74} - 23 q^{75} - 28 q^{76} + 23 q^{77} + 3 q^{78} + 27 q^{79} + 6 q^{80} + 24 q^{81} - 28 q^{82} + 33 q^{83} - 16 q^{84} - 13 q^{85} + 63 q^{86} - 12 q^{87} + 11 q^{88} - 2 q^{90} - 11 q^{91} + 79 q^{92} - 2 q^{93} - 12 q^{94} + 37 q^{95} - 25 q^{96} - 14 q^{97} + 20 q^{98} + 7 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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 −2.64656 −1.00000 5.00429 2.13528 2.64656 3.46294 −7.95105 1.00000 −5.65115
1.2 −2.42509 −1.00000 3.88107 −0.736887 2.42509 −2.40625 −4.56178 1.00000 1.78702
1.3 −2.29414 −1.00000 3.26307 −3.12687 2.29414 −2.80124 −2.89765 1.00000 7.17346
1.4 −2.16909 −1.00000 2.70494 0.657691 2.16909 −0.817989 −1.52908 1.00000 −1.42659
1.5 −1.94312 −1.00000 1.77572 −0.275874 1.94312 3.15290 0.435811 1.00000 0.536057
1.6 −1.52294 −1.00000 0.319360 3.31668 1.52294 −2.60872 2.55952 1.00000 −5.05112
1.7 −1.32626 −1.00000 −0.241032 −0.192408 1.32626 3.16535 2.97219 1.00000 0.255184
1.8 −1.17908 −1.00000 −0.609765 4.22706 1.17908 3.50133 3.07713 1.00000 −4.98405
1.9 −0.607674 −1.00000 −1.63073 −3.70104 0.607674 0.175250 2.20630 1.00000 2.24902
1.10 −0.574597 −1.00000 −1.66984 −2.72483 0.574597 0.829930 2.10868 1.00000 1.56568
1.11 −0.389331 −1.00000 −1.84842 0.642702 0.389331 −1.35418 1.49831 1.00000 −0.250224
1.12 0.0298243 −1.00000 −1.99911 3.06004 −0.0298243 −1.69214 −0.119271 1.00000 0.0912635
1.13 0.543206 −1.00000 −1.70493 2.45290 −0.543206 0.874109 −2.01254 1.00000 1.33243
1.14 0.671722 −1.00000 −1.54879 −1.67775 −0.671722 5.02977 −2.38380 1.00000 −1.12698
1.15 0.794802 −1.00000 −1.36829 −2.06654 −0.794802 −0.419104 −2.67712 1.00000 −1.64249
1.16 1.05828 −1.00000 −0.880046 −0.912505 −1.05828 −3.63309 −3.04789 1.00000 −0.965685
1.17 1.57828 −1.00000 0.490964 −1.83430 −1.57828 4.32058 −2.38168 1.00000 −2.89504
1.18 1.68466 −1.00000 0.838074 0.142092 −1.68466 −0.0282508 −1.95745 1.00000 0.239376
1.19 1.73242 −1.00000 1.00128 0.756937 −1.73242 −4.14115 −1.73020 1.00000 1.31133
1.20 1.86289 −1.00000 1.47035 4.02931 −1.86289 3.22519 −0.986675 1.00000 7.50616
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.24
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \(1\)
\(13\) \(1\)
\(103\) \(-1\)

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 4017.2.a.g 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4017.2.a.g 24 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4017))\):

\( T_{2}^{24} - 3 T_{2}^{23} - 32 T_{2}^{22} + 99 T_{2}^{21} + 432 T_{2}^{20} - 1397 T_{2}^{19} - 3194 T_{2}^{18} + 11029 T_{2}^{17} + 14007 T_{2}^{16} - 53536 T_{2}^{15} - 36577 T_{2}^{14} + 165500 T_{2}^{13} + 52434 T_{2}^{12} + \cdots - 64 \) Copy content Toggle raw display
\( T_{23}^{24} - 41 T_{23}^{23} + 558 T_{23}^{22} - 493 T_{23}^{21} - 62179 T_{23}^{20} + 568371 T_{23}^{19} - 75174 T_{23}^{18} - 25272080 T_{23}^{17} + 115269488 T_{23}^{16} + 257472706 T_{23}^{15} + \cdots + 138468131840 \) Copy content Toggle raw display