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Properties

Label 1849.4.a.k
Level $1849$
Weight $4$
Character orbit 1849.a
Self dual yes
Analytic conductor $109.095$
Analytic rank $1$
Dimension $60$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1849,4,Mod(1,1849)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
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")
 
//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);
 
Level: \( N \) \(=\) \( 1849 = 43^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1849.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(109.094531601\)
Analytic rank: \(1\)
Dimension: \(60\)
Twist minimal: no (minimal twist has level 43)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 60 q - 15 q^{2} - 37 q^{3} + 213 q^{4} - 51 q^{5} + 22 q^{6} - 54 q^{7} - 204 q^{8} + 387 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 60 q - 15 q^{2} - 37 q^{3} + 213 q^{4} - 51 q^{5} + 22 q^{6} - 54 q^{7} - 204 q^{8} + 387 q^{9} + 27 q^{10} + 43 q^{11} - 432 q^{12} + 13 q^{13} + 96 q^{14} + 65 q^{15} + 717 q^{16} - 138 q^{17} - 625 q^{18} - 610 q^{19} - 345 q^{20} + 611 q^{21} - 118 q^{22} - 243 q^{23} + 258 q^{24} + 899 q^{25} - 1071 q^{26} - 1609 q^{27} - 46 q^{28} - 773 q^{29} - 375 q^{30} - 97 q^{31} - 1967 q^{32} - 500 q^{33} - 217 q^{34} + 247 q^{35} + 175 q^{36} - 228 q^{37} + 1253 q^{38} - 1493 q^{39} + 2220 q^{40} - 951 q^{41} - 2643 q^{42} - 1378 q^{44} - 1086 q^{45} + 565 q^{46} - 2 q^{47} - 2303 q^{48} + 1264 q^{49} - 3273 q^{50} - 3076 q^{51} - 2825 q^{52} - 39 q^{53} + 5201 q^{54} - 1306 q^{55} + 3683 q^{56} + 1342 q^{57} + 2588 q^{58} - 1065 q^{59} + 2803 q^{60} - 2999 q^{61} - 5569 q^{62} - 2377 q^{63} + 2082 q^{64} - 5578 q^{65} + 3338 q^{66} + 961 q^{67} - 3754 q^{68} - 1817 q^{69} - 2738 q^{70} - 8003 q^{71} - 1412 q^{72} + 1011 q^{73} - 1413 q^{74} - 7457 q^{75} - 5516 q^{76} - 4052 q^{77} + 1091 q^{78} - 4422 q^{79} - 1610 q^{80} + 2108 q^{81} - 4676 q^{82} - 297 q^{83} - 54 q^{84} - 4333 q^{85} + 1377 q^{87} - 3652 q^{88} - 2480 q^{89} - 1414 q^{90} - 4551 q^{91} - 3286 q^{92} - 4 q^{93} - 4609 q^{94} - 835 q^{95} + 5864 q^{96} + 3785 q^{97} - 753 q^{98} + 5072 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

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.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −5.51648 0.947128 22.4316 −12.1331 −5.22481 14.8097 −79.6117 −26.1029 66.9318
1.2 −5.45533 −5.87893 21.7606 −15.7772 32.0715 −10.5901 −75.0688 7.56187 86.0700
1.3 −5.29884 2.87298 20.0777 −16.9175 −15.2234 −23.6451 −63.9980 −18.7460 89.6431
1.4 −5.27638 −1.62592 19.8401 9.68193 8.57899 −2.56298 −62.4730 −24.3564 −51.0855
1.5 −5.24990 −9.69865 19.5614 −5.59920 50.9169 0.820208 −60.6963 67.0638 29.3952
1.6 −4.92818 1.20886 16.2870 −11.7477 −5.95749 −36.0345 −40.8396 −25.5387 57.8946
1.7 −4.89580 −8.83989 15.9689 20.6381 43.2783 −10.5375 −39.0140 51.1436 −101.040
1.8 −4.85348 5.30735 15.5563 16.1569 −25.7591 27.9534 −36.6742 1.16797 −78.4173
1.9 −4.40707 −0.148254 11.4223 15.4121 0.653363 27.6883 −15.0821 −26.9780 −67.9222
1.10 −4.22240 5.78517 9.82864 5.96613 −24.4273 −8.16125 −7.72124 6.46824 −25.1914
1.11 −4.01034 9.44314 8.08281 −4.71622 −37.8702 23.9018 −0.332104 62.1728 18.9136
1.12 −3.61784 0.230904 5.08877 16.9044 −0.835373 −0.941277 10.5324 −26.9467 −61.1575
1.13 −3.57276 1.25498 4.76459 −8.29511 −4.48372 −13.8938 11.5593 −25.4250 29.6364
1.14 −3.46218 −10.0163 3.98667 −19.0537 34.6782 3.52814 13.8949 73.3264 65.9672
1.15 −3.42085 −8.07188 3.70224 −8.16009 27.6127 −23.9507 14.7020 38.1553 27.9145
1.16 −3.40283 5.79667 3.57928 10.2155 −19.7251 9.81633 15.0430 6.60143 −34.7615
1.17 −3.39478 −9.53108 3.52451 −2.38295 32.3559 −2.00316 15.1933 63.8414 8.08958
1.18 −3.00899 1.07669 1.05404 −2.94077 −3.23974 −27.1168 20.9004 −25.8407 8.84876
1.19 −2.74329 8.71284 −0.474355 −4.82785 −23.9019 0.994355 23.2476 48.9136 13.2442
1.20 −2.61993 −5.66517 −1.13597 −13.7987 14.8423 18.6959 23.9356 5.09416 36.1517
See all 60 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.60
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.k 60
43.b odd 2 1 1849.4.a.l 60
43.h odd 42 2 43.4.g.a ✓ 120
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
43.4.g.a ✓ 120 43.h odd 42 2
1849.4.a.k 60 1.a even 1 1 trivial
1849.4.a.l 60 43.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{60} + 15 T_{2}^{59} - 234 T_{2}^{58} - 4487 T_{2}^{57} + 22002 T_{2}^{56} + 629257 T_{2}^{55} + \cdots - 25\!\cdots\!56 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1849))\). Copy content Toggle raw display