↑

Properties

Label 4017.2.a.j
Level $4017$
Weight $2$
Character orbit 4017.a
Self dual yes
Analytic conductor $32.076$
Analytic rank $0$
Dimension $25$
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: \(25\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9} - 6 q^{10} + 21 q^{11} - 28 q^{12} + 25 q^{13} + 10 q^{14} - 7 q^{15} + 30 q^{16} + 14 q^{17} + 6 q^{18} + 12 q^{19} + 24 q^{20} - 17 q^{21} + 3 q^{22} + 41 q^{23} - 21 q^{24} + 30 q^{25} + 6 q^{26} - 25 q^{27} + 14 q^{28} + 22 q^{29} + 6 q^{30} + 14 q^{31} + 28 q^{32} - 21 q^{33} - 11 q^{34} + 14 q^{35} + 28 q^{36} - 6 q^{37} + 16 q^{38} - 25 q^{39} - 34 q^{40} + 33 q^{41} - 10 q^{42} + 35 q^{43} + 45 q^{44} + 7 q^{45} + 3 q^{46} + 48 q^{47} - 30 q^{48} - 4 q^{49} + 7 q^{50} - 14 q^{51} + 28 q^{52} + 18 q^{53} - 6 q^{54} + 10 q^{55} + 32 q^{56} - 12 q^{57} + 33 q^{58} + 46 q^{59} - 24 q^{60} - 19 q^{61} + 5 q^{62} + 17 q^{63} + 29 q^{64} + 7 q^{65} - 3 q^{66} + 16 q^{67} + 20 q^{68} - 41 q^{69} - 43 q^{70} + 60 q^{71} + 21 q^{72} - 14 q^{73} - 50 q^{74} - 30 q^{75} + 59 q^{77} - 6 q^{78} + 7 q^{79} + 32 q^{80} + 25 q^{81} + 18 q^{82} + 23 q^{83} - 14 q^{84} - 9 q^{85} - 9 q^{86} - 22 q^{87} + 23 q^{88} + 10 q^{89} - 6 q^{90} + 17 q^{91} + 69 q^{92} - 14 q^{93} - 30 q^{94} + 81 q^{95} - 28 q^{96} - 10 q^{97} + 55 q^{98} + 21 q^{99}+O(q^{100}) \) 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 −2.65319 −1.00000 5.03939 3.62608 2.65319 −1.69720 −8.06407 1.00000 −9.62067
1.2 −2.36961 −1.00000 3.61506 −2.39998 2.36961 −0.116274 −3.82707 1.00000 5.68703
1.3 −2.18299 −1.00000 2.76546 2.14752 2.18299 0.603238 −1.67100 1.00000 −4.68803
1.4 −1.97968 −1.00000 1.91913 2.16016 1.97968 5.12656 0.160099 1.00000 −4.27642
1.5 −1.79927 −1.00000 1.23739 1.64720 1.79927 1.60963 1.37215 1.00000 −2.96376
1.6 −1.55573 −1.00000 0.420296 −1.90089 1.55573 0.0358686 2.45759 1.00000 2.95727
1.7 −1.27578 −1.00000 −0.372378 −0.506188 1.27578 −3.05259 3.02664 1.00000 0.645786
1.8 −0.925244 −1.00000 −1.14392 3.08995 0.925244 −0.0396192 2.90890 1.00000 −2.85895
1.9 −0.858580 −1.00000 −1.26284 −4.02605 0.858580 1.69085 2.80141 1.00000 3.45668
1.10 −0.491539 −1.00000 −1.75839 −1.95668 0.491539 −2.76715 1.84740 1.00000 0.961784
1.11 −0.254687 −1.00000 −1.93513 −0.644426 0.254687 3.73934 1.00223 1.00000 0.164127
1.12 −0.0371239 −1.00000 −1.99862 2.55043 0.0371239 1.94695 0.148445 1.00000 −0.0946818
1.13 0.0202075 −1.00000 −1.99959 −1.35659 −0.0202075 −0.669195 −0.0808216 1.00000 −0.0274131
1.14 0.506527 −1.00000 −1.74343 4.00697 −0.506527 4.25155 −1.89615 1.00000 2.02964
1.15 0.940078 −1.00000 −1.11625 −1.95082 −0.940078 −0.363346 −2.92952 1.00000 −1.83392
1.16 1.30548 −1.00000 −0.295718 2.71388 −1.30548 2.93494 −2.99702 1.00000 3.54292
1.17 1.39323 −1.00000 −0.0589163 0.623512 −1.39323 −3.51013 −2.86854 1.00000 0.868695
1.18 1.59660 −1.00000 0.549133 −3.22334 −1.59660 2.57812 −2.31645 1.00000 −5.14639
1.19 1.86177 −1.00000 1.46619 −1.56946 −1.86177 2.25881 −0.993826 1.00000 −2.92198
1.20 2.02058 −1.00000 2.08276 4.24376 −2.02058 −1.21618 0.167219 1.00000 8.57486
See all 25 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.25
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.j ✓ 25
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4017.2.a.j ✓ 25 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(4017))\):

\( T_{2}^{25} - 6 T_{2}^{24} - 21 T_{2}^{23} + 183 T_{2}^{22} + 103 T_{2}^{21} - 2375 T_{2}^{20} + 983 T_{2}^{19} + \cdots - 4 \) Copy content Toggle raw display
\( T_{23}^{25} - 41 T_{23}^{24} + 578 T_{23}^{23} - 1729 T_{23}^{22} - 33531 T_{23}^{21} + \cdots - 51544992512 \) Copy content Toggle raw display