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Properties

Label 1573.4.a.q
Level $1573$
Weight $4$
Character orbit 1573.a
Self dual yes
Analytic conductor $92.810$
Analytic rank $0$
Dimension $38$
CM no
Inner twists $1$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [1573,4,Mod(1,1573)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1573, 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("1573.1"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Level: \( N \) \(=\) \( 1573 = 11^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1573.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [38,-3,19,181,52] 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: \(92.8100044390\)
Analytic rank: \(0\)
Dimension: \(38\)
Twist minimal: no (minimal twist has level 143)
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.

\(\operatorname{Tr}(f)(q) = \) \( 38 q - 3 q^{2} + 19 q^{3} + 181 q^{4} + 52 q^{5} - 104 q^{6} - 12 q^{7} - 57 q^{8} + 477 q^{9} + 30 q^{10} + 122 q^{12} - 494 q^{13} + 181 q^{14} + 264 q^{15} + 961 q^{16} + 33 q^{17} - 28 q^{18} - 107 q^{19}+ \cdots - 2043 q^{98}+O(q^{100}) \) 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 −5.59756 −4.33320 23.3327 −9.25656 24.2553 −18.6611 −85.8255 −8.22341 51.8141
1.2 −5.47216 7.11294 21.9445 19.0280 −38.9231 16.5628 −76.3064 23.5940 −104.124
1.3 −5.29233 1.25757 20.0087 12.1886 −6.65547 −11.7568 −63.5540 −25.4185 −64.5059
1.4 −5.29064 8.72980 19.9909 −10.5796 −46.1862 4.89419 −63.4394 49.2095 55.9728
1.5 −4.72103 −4.72755 14.2881 0.427348 22.3189 23.9427 −29.6865 −4.65028 −2.01752
1.6 −4.32339 9.99811 10.6917 −14.1731 −43.2257 −28.4242 −11.6371 72.9622 61.2757
1.7 −4.15222 −8.58190 9.24094 6.15304 35.6340 −2.19831 −5.15264 46.6491 −25.5488
1.8 −3.98792 −2.76589 7.90349 −14.0062 11.0301 21.9303 0.384876 −19.3499 55.8554
1.9 −3.84210 3.39547 6.76175 13.7209 −13.0457 −27.2218 4.75748 −15.4708 −52.7170
1.10 −3.47600 9.47394 4.08259 19.5807 −32.9314 −25.2036 13.6169 62.7556 −68.0627
1.11 −2.93908 1.60840 0.638194 −2.87090 −4.72720 −11.4871 21.6369 −24.4131 8.43781
1.12 −2.91707 −4.12394 0.509296 8.63058 12.0298 30.5724 21.8509 −9.99308 −25.1760
1.13 −2.02267 7.14115 −3.90882 −2.71732 −14.4442 20.7420 24.0876 23.9961 5.49623
1.14 −1.94140 3.20469 −4.23098 19.8679 −6.22158 28.3912 23.7452 −16.7300 −38.5714
1.15 −1.75527 −7.13584 −4.91902 8.67981 12.5253 −22.4666 22.6764 23.9202 −15.2354
1.16 −1.59859 −8.83427 −5.44450 −15.6170 14.1224 −26.0920 21.4923 51.0443 24.9652
1.17 −1.40229 2.44516 −6.03358 −13.4517 −3.42882 −4.78543 19.6792 −21.0212 18.8632
1.18 −0.962891 7.49065 −7.07284 −17.9030 −7.21268 25.5980 14.5135 29.1098 17.2386
1.19 0.336372 −8.24445 −7.88685 −6.61521 −2.77321 10.8382 −5.34390 40.9710 −2.22517
1.20 0.453664 6.65479 −7.79419 −5.35620 3.01904 −27.7636 −7.16526 17.2862 −2.42992
See all 38 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.38
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(11\) \( +1 \)
\(13\) \( +1 \)

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 1573.4.a.q 38
11.b odd 2 1 1573.4.a.r 38
11.c even 5 2 143.4.h.b ✓ 76
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
143.4.h.b ✓ 76 11.c even 5 2
1573.4.a.q 38 1.a even 1 1 trivial
1573.4.a.r 38 11.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{38} + 3 T_{2}^{37} - 238 T_{2}^{36} - 688 T_{2}^{35} + 25878 T_{2}^{34} + 71961 T_{2}^{33} + \cdots + 34\!\cdots\!64 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1573))\). Copy content Toggle raw display