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Properties

Label 2299.4.a.q
Level $2299$
Weight $4$
Character orbit 2299.a
Self dual yes
Analytic conductor $135.645$
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] = [2299,4,Mod(1,2299)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2299, 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("2299.1"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Level: \( N \) \(=\) \( 2299 = 11^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2299.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [23,-4,2,96,10] 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: \(135.645391103\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 23 q - 4 q^{2} + 2 q^{3} + 96 q^{4} + 10 q^{5} - 50 q^{6} - 14 q^{7} - 84 q^{8} + 243 q^{9} - 90 q^{10} + 107 q^{12} - 108 q^{13} + 71 q^{14} - 78 q^{15} + 444 q^{16} - 114 q^{17} - 95 q^{18} - 437 q^{19}+ \cdots + 1805 q^{98}+O(q^{100}) \) 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 −5.59894 4.60715 23.3481 −21.7970 −25.7952 15.1782 −85.9333 −5.77415 122.040
1.2 −5.24317 0.806023 19.4908 12.7289 −4.22611 −32.1563 −60.2483 −26.3503 −66.7395
1.3 −4.95551 9.06572 16.5570 6.78573 −44.9252 −11.6525 −42.4044 55.1874 −33.6267
1.4 −4.61880 −9.46467 13.3333 18.4669 43.7154 −4.58458 −24.6333 62.5800 −85.2947
1.5 −3.94724 −1.05358 7.58071 −5.61616 4.15875 0.473893 1.65503 −25.8900 22.1683
1.6 −3.47804 4.97020 4.09674 20.7728 −17.2865 23.1463 13.5757 −2.29715 −72.2487
1.7 −2.67006 2.93373 −0.870788 −10.9614 −7.83324 24.9567 23.6855 −18.3932 29.2676
1.8 −2.30369 −6.51039 −2.69303 5.22437 14.9979 −13.0769 24.6334 15.3852 −12.0353
1.9 −2.00635 −9.56228 −3.97456 −14.2161 19.1853 3.56262 24.0252 64.4372 28.5225
1.10 −1.74000 8.16182 −4.97239 3.80187 −14.2016 −18.3188 22.5720 39.6152 −6.61526
1.11 −0.378194 −2.13508 −7.85697 −5.50898 0.807476 −34.8263 5.99702 −22.4414 2.08347
1.12 −0.333066 1.04625 −7.88907 8.85459 −0.348470 17.6665 5.29211 −25.9054 −2.94916
1.13 0.402382 7.31917 −7.83809 −20.5888 2.94510 −9.12001 −6.37296 26.5703 −8.28457
1.14 0.803160 −5.08445 −7.35493 18.4937 −4.08363 −2.52408 −12.3325 −1.14838 14.8534
1.15 1.63331 −4.73033 −5.33231 −15.2610 −7.72608 17.6528 −21.7758 −4.62400 −24.9259
1.16 1.82498 4.31730 −4.66946 1.44786 7.87896 24.9887 −23.1215 −8.36096 2.64231
1.17 2.97006 6.79483 0.821235 18.7928 20.1810 −30.3657 −21.3213 19.1698 55.8157
1.18 3.35946 8.15108 3.28594 −6.77198 27.3832 14.0876 −15.8367 39.4401 −22.7502
1.19 3.74962 −10.0768 6.05964 12.5413 −37.7841 35.1414 −7.27560 74.5416 47.0253
1.20 4.05595 −8.67747 8.45072 −15.6701 −35.1954 −19.5063 1.82811 48.2985 −63.5573
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
\(11\) \( -1 \)
\(19\) \( +1 \)

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 2299.4.a.q ✓ 23
11.b odd 2 1 2299.4.a.r yes 23
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2299.4.a.q ✓ 23 1.a even 1 1 trivial
2299.4.a.r yes 23 11.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 \(S_{4}^{\mathrm{new}}(\Gamma_0(2299))\):

\( T_{2}^{23} + 4 T_{2}^{22} - 132 T_{2}^{21} - 500 T_{2}^{20} + 7465 T_{2}^{19} + 26554 T_{2}^{18} + \cdots - 404467200 \) Copy content Toggle raw display
\( T_{5}^{23} - 10 T_{5}^{22} - 1906 T_{5}^{21} + 18988 T_{5}^{20} + 1520556 T_{5}^{19} + \cdots - 24\!\cdots\!00 \) Copy content Toggle raw display