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Properties

Label 1849.4.a.h
Level $1849$
Weight $4$
Character orbit 1849.a
Self dual yes
Analytic conductor $109.095$
Analytic rank $0$
Dimension $30$
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] = [1849,4,Mod(1,1849)] 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("1849.1"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1849, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 4, names="a")
 
Level: \( N \) \(=\) \( 1849 = 43^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1849.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [30,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(109.094531601\)
Analytic rank: \(0\)
Dimension: \(30\)
Twist minimal: no (minimal twist has level 43)
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.

\(\operatorname{Tr}(f)(q) = \) \( 30 q + 6 q^{2} + 2 q^{3} + 114 q^{4} + 27 q^{5} + 8 q^{6} + 48 q^{7} + 90 q^{8} + 216 q^{9} - 27 q^{10} + 80 q^{11} - 36 q^{12} - 13 q^{13} + 36 q^{14} + 16 q^{15} + 318 q^{16} + 66 q^{17} + 80 q^{18} + 254 q^{19}+ \cdots - 2693 q^{99}+O(q^{100}) \) 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 −5.24346 −0.263601 19.4939 17.3447 1.38218 −21.1320 −60.2678 −26.9305 −90.9462
1.2 −4.95333 −0.318435 16.5355 12.4187 1.57731 3.53619 −42.2793 −26.8986 −61.5142
1.3 −4.74854 2.44099 14.5486 −1.86645 −11.5911 5.76487 −31.0963 −21.0416 8.86289
1.4 −4.11874 6.75554 8.96404 −11.5913 −27.8243 18.3634 −3.97064 18.6373 47.7418
1.5 −4.08390 −9.96623 8.67820 12.0746 40.7010 17.5242 −2.76970 72.3258 −49.3113
1.6 −3.72135 5.79603 5.84847 −14.8139 −21.5691 −12.2090 8.00659 6.59399 55.1279
1.7 −3.68353 −8.25521 5.56841 −12.2925 30.4083 28.5576 8.95684 41.1485 45.2798
1.8 −3.12588 −4.83570 1.77114 −5.07243 15.1158 −2.39891 19.4707 −3.61601 15.8558
1.9 −1.99192 10.2076 −4.03226 −6.84373 −20.3326 −3.06785 23.9673 77.1944 13.6322
1.10 −1.84451 0.727573 −4.59779 12.1583 −1.34201 −17.8467 23.2367 −26.4706 −22.4260
1.11 −1.56619 −5.42418 −5.54704 8.12470 8.49531 −30.7370 21.2173 2.42171 −12.7249
1.12 −1.40131 7.71122 −6.03633 16.2919 −10.8058 16.8292 19.6692 32.4629 −22.8300
1.13 −1.32038 −4.35495 −6.25659 −15.6111 5.75020 4.97789 18.8242 −8.03441 20.6126
1.14 −0.830523 7.00735 −7.31023 4.56308 −5.81976 −20.3840 12.7155 22.1029 −3.78975
1.15 −0.188737 −1.07307 −7.96438 16.0623 0.202528 29.7402 3.01306 −25.8485 −3.03154
1.16 0.335126 −1.29157 −7.88769 −9.09411 −0.432838 17.7083 −5.32438 −25.3319 −3.04767
1.17 1.36355 −9.26361 −6.14074 −1.21569 −12.6314 −10.5300 −19.2815 58.8145 −1.65764
1.18 1.77522 4.21024 −4.84859 5.54921 7.47410 24.8990 −22.8091 −9.27388 9.85108
1.19 1.92929 5.16200 −4.27784 −3.37495 9.95900 −15.9770 −23.6875 −0.353756 −6.51127
1.20 1.94581 1.92433 −4.21381 −20.3652 3.74438 13.1013 −23.7658 −23.2970 −39.6269
See all 30 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.30
Significant digits:
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Atkin-Lehner signs

\( p \) Sign
\(43\) \( +1 \)

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 1849.4.a.h 30
43.b odd 2 1 1849.4.a.g 30
43.e even 7 2 43.4.e.a ✓ 60
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
43.4.e.a ✓ 60 43.e even 7 2
1849.4.a.g 30 43.b odd 2 1
1849.4.a.h 30 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{30} - 6 T_{2}^{29} - 159 T_{2}^{28} + 964 T_{2}^{27} + 11181 T_{2}^{26} - 68576 T_{2}^{25} + \cdots - 491617257984 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1849))\). Copy content Toggle raw display