Properties

Label 1007.2.a.e
Level $1007$
Weight $2$
Character orbit 1007.a
Self dual yes
Analytic conductor $8.041$
Analytic rank $0$
Dimension $28$
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] = [1007,2,Mod(1,1007)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1007, 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("1007.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1007 = 19 \cdot 53 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1007.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: \(8.04093548354\)
Analytic rank: \(0\)
Dimension: \(28\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 28 q + 3 q^{2} - q^{3} + 37 q^{4} + 5 q^{5} + q^{6} + 15 q^{7} + 9 q^{8} + 45 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 28 q + 3 q^{2} - q^{3} + 37 q^{4} + 5 q^{5} + q^{6} + 15 q^{7} + 9 q^{8} + 45 q^{9} + 11 q^{11} + 8 q^{12} + 11 q^{13} + q^{14} + 14 q^{15} + 47 q^{16} + 21 q^{17} + 12 q^{18} - 28 q^{19} - 12 q^{20} - 6 q^{21} + 17 q^{22} + 10 q^{23} + 16 q^{24} + 89 q^{25} - 14 q^{26} - 10 q^{27} + 37 q^{28} + 16 q^{29} - 29 q^{30} + 6 q^{31} - 4 q^{32} + 25 q^{33} + 11 q^{34} + 11 q^{35} + 44 q^{36} + 47 q^{37} - 3 q^{38} - 27 q^{39} - 35 q^{40} + 2 q^{41} + 45 q^{42} + 49 q^{43} + 29 q^{44} + 4 q^{45} + 29 q^{46} + 29 q^{47} - 4 q^{48} + 65 q^{49} - 20 q^{50} - 30 q^{51} - 14 q^{52} + 28 q^{53} + 8 q^{54} + 25 q^{55} - 12 q^{56} + q^{57} + 27 q^{58} - 12 q^{59} + 53 q^{60} + 26 q^{61} + 25 q^{62} + 53 q^{63} + 45 q^{64} + 6 q^{65} - 62 q^{66} + 34 q^{67} - 13 q^{68} - 13 q^{69} - 17 q^{71} + 56 q^{72} + 73 q^{73} - 87 q^{74} - 50 q^{75} - 37 q^{76} + 10 q^{77} - 26 q^{78} + 19 q^{79} + 25 q^{80} + 104 q^{81} + 56 q^{82} + 7 q^{84} + 13 q^{85} - 11 q^{86} + 34 q^{88} + 25 q^{89} - 171 q^{90} - 25 q^{91} + 33 q^{92} + 6 q^{93} - 56 q^{94} - 5 q^{95} + 8 q^{96} + 75 q^{97} + 44 q^{98} + 13 q^{99}+O(q^{100}) \) 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 −2.79936 −0.556375 5.83643 3.29617 1.55750 1.71230 −10.7396 −2.69045 −9.22719
1.2 −2.53366 −2.25575 4.41941 −2.33573 5.71528 4.14311 −6.12995 2.08839 5.91795
1.3 −2.38950 1.62577 3.70970 −3.78025 −3.88478 0.614408 −4.08532 −0.356869 9.03289
1.4 −2.38706 0.0564175 3.69805 −1.85429 −0.134672 −3.74665 −4.05333 −2.99682 4.42631
1.5 −2.34547 2.87039 3.50124 4.42818 −6.73242 −0.392048 −3.52111 5.23914 −10.3862
1.6 −1.68252 −3.19593 0.830859 −3.54229 5.37720 2.49260 1.96710 7.21397 5.95996
1.7 −1.51529 −3.16005 0.296109 2.95244 4.78840 0.224928 2.58189 6.98592 −4.47381
1.8 −1.43121 2.80880 0.0483583 −0.613402 −4.01997 5.06624 2.79321 4.88934 0.877906
1.9 −1.24731 2.80833 −0.444220 3.12412 −3.50286 −0.445019 3.04870 4.88673 −3.89675
1.10 −1.00515 −0.139424 −0.989678 2.93604 0.140142 2.04416 3.00507 −2.98056 −2.95115
1.11 −0.948115 −1.20576 −1.10108 0.444866 1.14320 −2.45657 2.94018 −1.54613 −0.421784
1.12 −0.791316 1.08394 −1.37382 −3.99094 −0.857740 −4.54351 2.66976 −1.82507 3.15810
1.13 −0.319045 −0.935679 −1.89821 −2.32921 0.298524 0.376334 1.24371 −2.12451 0.743125
1.14 0.180018 1.16800 −1.96759 0.0855821 0.210261 3.31494 −0.714240 −1.63579 0.0154064
1.15 0.541632 2.77685 −1.70664 2.24627 1.50403 −2.00794 −2.00763 4.71088 1.21665
1.16 0.570474 −3.28720 −1.67456 2.69142 −1.87526 5.04218 −2.09624 7.80570 1.53539
1.17 0.758750 −2.46973 −1.42430 3.84414 −1.87391 −4.23932 −2.59819 3.09957 2.91675
1.18 0.896802 −1.02005 −1.19575 −1.65827 −0.914780 −3.83554 −2.86595 −1.95950 −1.48714
1.19 1.26121 1.79187 −0.409342 2.69609 2.25993 2.95821 −3.03869 0.210786 3.40035
1.20 1.28042 −1.37836 −0.360526 −3.13293 −1.76487 4.02144 −3.02246 −1.10014 −4.01147
See all 28 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.28
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(19\) \(1\)
\(53\) \(-1\)

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 1007.2.a.e 28
3.b odd 2 1 9063.2.a.r 28
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1007.2.a.e 28 1.a even 1 1 trivial
9063.2.a.r 28 3.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{28} - 3 T_{2}^{27} - 42 T_{2}^{26} + 128 T_{2}^{25} + 773 T_{2}^{24} - 2398 T_{2}^{23} - 8210 T_{2}^{22} + 25984 T_{2}^{21} + 55795 T_{2}^{20} - 180640 T_{2}^{19} - 254355 T_{2}^{18} + 845427 T_{2}^{17} + 792781 T_{2}^{16} + \cdots - 5878 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1007))\). Copy content Toggle raw display