Properties

Label 1849.4.a.i
Level $1849$
Weight $4$
Character orbit 1849.a
Self dual yes
Analytic conductor $109.095$
Analytic rank $1$
Dimension $50$
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: \(50\)
Twist minimal: yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9} - 137 q^{10} - 252 q^{11} - 48 q^{12} - 192 q^{13} - 272 q^{14} - 314 q^{15} + 542 q^{16} - 236 q^{17} - 386 q^{18} + 12 q^{19} + 108 q^{20} - 408 q^{21} + 1235 q^{22} - 630 q^{23} - 613 q^{24} + 1098 q^{25} + 1493 q^{26} + 10 q^{27} - 242 q^{28} + 208 q^{29} - 48 q^{30} - 932 q^{31} - 1124 q^{32} + 254 q^{33} + 765 q^{34} - 1452 q^{35} + 747 q^{36} - 90 q^{37} - 1213 q^{38} - 1610 q^{39} - 1693 q^{40} - 1354 q^{41} - 16 q^{42} - 2704 q^{44} + 4508 q^{45} + 233 q^{46} - 3484 q^{47} - 376 q^{48} + 1324 q^{49} - 408 q^{50} + 4054 q^{51} - 2176 q^{52} - 726 q^{53} - 6497 q^{54} - 3288 q^{55} - 7097 q^{56} - 870 q^{57} + 275 q^{58} - 4370 q^{59} - 3891 q^{60} + 1172 q^{61} - 1546 q^{62} - 3686 q^{63} + 606 q^{64} + 2610 q^{65} - 4697 q^{66} - 344 q^{67} - 3221 q^{68} + 136 q^{69} - 1310 q^{70} + 162 q^{71} - 5814 q^{72} + 746 q^{73} - 4332 q^{74} + 236 q^{75} + 1338 q^{76} + 2024 q^{77} - 2782 q^{78} - 2656 q^{79} - 5713 q^{80} - 86 q^{81} - 4168 q^{82} - 3514 q^{83} - 4269 q^{84} - 7558 q^{85} - 10278 q^{87} + 11692 q^{88} + 2640 q^{89} - 8286 q^{90} - 5946 q^{91} - 4271 q^{92} - 2 q^{93} + 9062 q^{94} - 12140 q^{95} - 700 q^{96} - 3864 q^{97} - 2826 q^{98} - 8174 q^{99}+O(q^{100}) \) 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.

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 −5.46223 9.09504 21.8360 −6.15202 −49.6792 2.59059 −75.5754 55.7197 33.6038
1.2 −5.40604 −2.51556 21.2252 −3.24888 13.5992 35.6131 −71.4960 −20.6720 17.5635
1.3 −5.33984 −6.59560 20.5139 12.0752 35.2195 18.2315 −66.8223 16.5020 −64.4799
1.4 −5.05256 9.36203 17.5283 14.1438 −47.3022 −13.7151 −48.1425 60.6475 −71.4625
1.5 −4.85844 −5.73018 15.6044 14.4569 27.8397 −13.1859 −36.9457 5.83494 −70.2380
1.6 −4.80125 −5.52870 15.0520 18.8098 26.5447 0.563586 −33.8585 3.56656 −90.3106
1.7 −4.78088 1.15757 14.8568 −21.3015 −5.53419 24.0536 −32.7814 −25.6600 101.840
1.8 −4.52050 −1.75128 12.4349 −13.0472 7.91667 4.32755 −20.0482 −23.9330 58.9799
1.9 −3.90499 3.52020 7.24897 −10.7056 −13.7464 28.1424 2.93275 −14.6082 41.8054
1.10 −3.81936 8.34786 6.58755 2.56409 −31.8835 −3.42361 5.39467 42.6867 −9.79321
1.11 −3.53489 7.81725 4.49548 1.07981 −27.6332 −33.3014 12.3881 34.1094 −3.81700
1.12 −3.52844 −3.06369 4.44988 −14.8551 10.8100 −18.1642 12.5264 −17.6138 52.4155
1.13 −3.43471 −1.13642 3.79726 −2.82850 3.90328 −33.5669 14.4352 −25.7086 9.71508
1.14 −3.22072 −8.71909 2.37305 13.5152 28.0818 −24.0687 18.1228 49.0226 −43.5288
1.15 −3.06679 −2.01332 1.40518 −11.9365 6.17442 −10.6583 20.2249 −22.9465 36.6067
1.16 −3.04766 −1.42990 1.28824 10.9474 4.35784 8.62569 20.4552 −24.9554 −33.3638
1.17 −2.53235 8.01322 −1.58719 20.7136 −20.2923 3.06093 24.2781 37.2117 −52.4541
1.18 −2.25115 4.02813 −2.93234 4.98765 −9.06790 5.25109 24.6103 −10.7742 −11.2279
1.19 −2.06784 −3.28982 −3.72402 0.905592 6.80284 0.553732 24.2434 −16.1771 −1.87262
1.20 −1.26350 −9.40007 −6.40356 −0.325119 11.8770 −8.80478 18.1989 61.3613 0.410789
See all 50 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.50
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.i 50
43.b odd 2 1 1849.4.a.j yes 50
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1849.4.a.i 50 1.a even 1 1 trivial
1849.4.a.j yes 50 43.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{50} + 10 T_{2}^{49} - 243 T_{2}^{48} - 2664 T_{2}^{47} + 26833 T_{2}^{46} + 330340 T_{2}^{45} - 1768829 T_{2}^{44} - 25331608 T_{2}^{43} + 76406200 T_{2}^{42} + 1346150396 T_{2}^{41} + \cdots + 16\!\cdots\!28 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1849))\). Copy content Toggle raw display