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Properties

Label 1519.4.a.h
Level $1519$
Weight $4$
Character orbit 1519.a
Self dual yes
Analytic conductor $89.624$
Analytic rank $1$
Dimension $23$
CM no
Inner twists $1$

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Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [1519,4,Mod(1,1519)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1519, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1519.1"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Level: \( N \) \(=\) \( 1519 = 7^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1519.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [23,5,-6,91,-40] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(89.6239012987\)
Analytic rank: \(1\)
Dimension: \(23\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 23 q + 5 q^{2} - 6 q^{3} + 91 q^{4} - 40 q^{5} - 36 q^{6} + 39 q^{8} + 211 q^{9} - 40 q^{10} + 44 q^{11} - 414 q^{12} + 20 q^{13} + 523 q^{16} - 306 q^{17} + 51 q^{18} - 296 q^{19} - 400 q^{20} - 326 q^{22}+ \cdots - 3456 q^{99}+O(q^{100}) \) 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.

Copy content comment:embeddings in the coefficient field
 
Copy content gp:mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −5.55366 −3.48173 22.8431 −17.8646 19.3364 0 −82.4336 −14.8775 99.2138
1.2 −5.05459 −8.33158 17.5489 9.38810 42.1127 0 −48.2657 42.4152 −47.4530
1.3 −4.35366 6.31105 10.9544 4.77794 −27.4762 0 −12.8623 12.8294 −20.8015
1.4 −3.90548 −0.0954929 7.25277 −10.1187 0.372946 0 2.91827 −26.9909 39.5185
1.5 −3.43344 7.14275 3.78854 20.1541 −24.5242 0 14.4598 24.0189 −69.1980
1.6 −3.38966 5.26780 3.48978 −18.6068 −17.8561 0 15.2881 0.749758 63.0706
1.7 −2.30906 −9.33501 −2.66824 −2.50266 21.5551 0 24.6336 60.1424 5.77879
1.8 −1.88515 −5.49288 −4.44620 9.32401 10.3549 0 23.4630 3.17171 −17.5772
1.9 −1.77012 0.155254 −4.86667 8.85943 −0.274819 0 22.7756 −26.9759 −15.6823
1.10 −0.448584 5.38920 −7.79877 8.53069 −2.41751 0 7.08708 2.04348 −3.82673
1.11 0.189863 −5.02070 −7.96395 −18.3852 −0.953245 0 −3.03096 −1.79257 −3.49067
1.12 0.260561 8.04086 −7.93211 −21.9581 2.09513 0 −4.15129 37.6554 −5.72144
1.13 1.06861 −5.09781 −6.85807 1.69042 −5.44757 0 −15.8775 −1.01232 1.80640
1.14 1.20680 2.47885 −6.54363 −10.1765 2.99147 0 −17.5513 −20.8553 −12.2810
1.15 1.28627 10.2631 −6.34552 −1.02970 13.2010 0 −18.4521 78.3306 −1.32447
1.16 2.54037 −2.27926 −1.54650 10.9847 −5.79018 0 −24.2517 −21.8050 27.9054
1.17 3.43289 −7.72707 3.78474 −12.7805 −26.5262 0 −14.4705 32.7076 −43.8739
1.18 3.44360 1.20269 3.85839 17.2945 4.14160 0 −14.2621 −25.5535 59.5555
1.19 3.47766 6.93872 4.09412 −2.31439 24.1305 0 −13.5833 21.1459 −8.04868
1.20 4.77516 3.21029 14.8022 −4.53317 15.3297 0 32.4816 −16.6940 −21.6466
See all 23 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.23
Significant digits:
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Atkin-Lehner signs

\( p \) Sign
\(7\) \( -1 \)
\(31\) \( +1 \)

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 1519.4.a.h ✓ 23
7.b odd 2 1 1519.4.a.i yes 23
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1519.4.a.h ✓ 23 1.a even 1 1 trivial
1519.4.a.i yes 23 7.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1519))\):

\( T_{2}^{23} - 5 T_{2}^{22} - 125 T_{2}^{21} + 627 T_{2}^{20} + 6546 T_{2}^{19} - 33032 T_{2}^{18} + \cdots - 106186752 \) Copy content Toggle raw display
\( T_{3}^{23} + 6 T_{3}^{22} - 398 T_{3}^{21} - 2288 T_{3}^{20} + 67412 T_{3}^{19} + 364180 T_{3}^{18} + \cdots + 3359484280832 \) Copy content Toggle raw display