Properties

Label 883.2.a.b
Level $883$
Weight $2$
Character orbit 883.a
Self dual yes
Analytic conductor $7.051$
Analytic rank $0$
Dimension $39$
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] = [883,2,Mod(1,883)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("883.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(883, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 883 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 883.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [39] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(7.05079049848\)
Analytic rank: \(0\)
Dimension: \(39\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 39 q + 10 q^{2} + 7 q^{3} + 40 q^{4} + 29 q^{5} + q^{6} + 6 q^{7} + 27 q^{8} + 42 q^{9} + 10 q^{10} + 5 q^{11} + 5 q^{12} + 35 q^{13} + 13 q^{14} + 2 q^{15} + 34 q^{16} + 55 q^{17} + 16 q^{18} + 6 q^{19}+ \cdots - 35 q^{99}+O(q^{100}) \) 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 −2.54744 −0.264532 4.48947 −0.174837 0.673881 −2.95843 −6.34177 −2.93002 0.445386
1.2 −2.49979 −1.24114 4.24894 3.97791 3.10259 −1.11008 −5.62188 −1.45957 −9.94393
1.3 −2.37710 0.464970 3.65063 0.968332 −1.10528 1.59555 −3.92372 −2.78380 −2.30183
1.4 −2.33624 3.16936 3.45800 0.744169 −7.40437 1.46915 −3.40622 7.04483 −1.73855
1.5 −1.97265 1.33673 1.89133 −3.63796 −2.63689 −2.39815 0.214370 −1.21316 7.17640
1.6 −1.96706 2.38849 1.86934 3.20967 −4.69832 0.301504 0.257012 2.70489 −6.31363
1.7 −1.85490 −2.78290 1.44065 0.725683 5.16199 −4.16403 1.03753 4.74452 −1.34607
1.8 −1.83858 −2.66154 1.38039 0.125230 4.89347 2.96113 1.13921 4.08382 −0.230246
1.9 −1.35317 0.370593 −0.168938 −0.295904 −0.501474 4.07071 2.93494 −2.86266 0.400408
1.10 −1.18433 2.56331 −0.597360 −0.200015 −3.03581 0.889323 3.07613 3.57057 0.236884
1.11 −1.06077 −1.96189 −0.874759 −1.31656 2.08112 0.596497 3.04947 0.849004 1.39658
1.12 −1.03411 −0.0722685 −0.930610 2.41298 0.0747338 −3.21992 3.03058 −2.99478 −2.49529
1.13 −1.02440 1.79094 −0.950597 3.62258 −1.83464 4.92500 3.02260 0.207460 −3.71099
1.14 −0.822063 −3.04736 −1.32421 3.53262 2.50512 2.13517 2.73271 6.28641 −2.90404
1.15 −0.624896 0.326966 −1.60950 −2.78741 −0.204320 −3.57532 2.25557 −2.89309 1.74184
1.16 −0.448021 2.05294 −1.79928 4.12354 −0.919759 −1.68451 1.70216 1.21456 −1.84743
1.17 −0.146062 2.50721 −1.97867 −3.28544 −0.366209 2.04229 0.581133 3.28611 0.479879
1.18 0.273303 −1.49861 −1.92531 −2.84705 −0.409575 −4.10714 −1.07280 −0.754160 −0.778108
1.19 0.332305 3.23662 −1.88957 1.51177 1.07554 −3.89589 −1.29252 7.47573 0.502368
1.20 0.358779 −0.933971 −1.87128 2.17298 −0.335089 4.81961 −1.38893 −2.12770 0.779619
See all 39 embeddings
\(n\): e.g. 2-40 or 80-90
Embeddings: e.g. 1-3 or 1.39
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(883\) \( -1 \)

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 883.2.a.b ✓ 39
3.b odd 2 1 7947.2.a.e 39
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
883.2.a.b ✓ 39 1.a even 1 1 trivial
7947.2.a.e 39 3.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{39} - 10 T_{2}^{38} - 9 T_{2}^{37} + 401 T_{2}^{36} - 716 T_{2}^{35} - 6830 T_{2}^{34} + \cdots + 6696 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(883))\). Copy content Toggle raw display