↑

Properties

Label 1849.4.a.g
Level $1849$
Weight $4$
Character orbit 1849.a
Self dual yes
Analytic conductor $109.095$
Analytic rank $1$
Dimension $30$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

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: \(30\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 30 q - 6 q^{2} - 2 q^{3} + 114 q^{4} - 27 q^{5} + 8 q^{6} - 48 q^{7} - 90 q^{8} + 216 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 30 q - 6 q^{2} - 2 q^{3} + 114 q^{4} - 27 q^{5} + 8 q^{6} - 48 q^{7} - 90 q^{8} + 216 q^{9} - 27 q^{10} + 80 q^{11} + 36 q^{12} - 13 q^{13} + 36 q^{14} + 16 q^{15} + 318 q^{16} + 66 q^{17} - 80 q^{18} - 254 q^{19} - 312 q^{20} - 548 q^{21} - 305 q^{22} - 105 q^{23} + 123 q^{24} + 523 q^{25} - 549 q^{26} + 10 q^{27} - 578 q^{28} - 793 q^{29} - 1560 q^{30} - 359 q^{31} - 676 q^{32} - 208 q^{33} - 1007 q^{34} - 514 q^{35} + 776 q^{36} - 510 q^{37} - 2066 q^{38} - 898 q^{39} - 1248 q^{40} - 270 q^{41} + 915 q^{42} + 3256 q^{44} - 807 q^{45} - 1960 q^{46} + 1421 q^{47} + 632 q^{48} + 386 q^{49} + 141 q^{50} - 209 q^{51} + 2825 q^{52} - 21 q^{53} + 2368 q^{54} - 2258 q^{55} + 2521 q^{56} - 1723 q^{57} - 347 q^{58} + 1752 q^{59} + 2711 q^{60} - 1759 q^{61} - 395 q^{62} - 2204 q^{63} + 222 q^{64} - 1151 q^{65} + 160 q^{66} - 3001 q^{67} + 1921 q^{68} - 1660 q^{69} - 1597 q^{70} - 727 q^{71} - 9100 q^{72} - 4623 q^{73} - 2649 q^{74} - 1027 q^{75} - 874 q^{76} - 3556 q^{77} - 4979 q^{78} + 546 q^{79} - 5809 q^{80} - 410 q^{81} + 4397 q^{82} - 492 q^{83} - 10611 q^{84} + 1723 q^{85} + 5937 q^{87} - 3974 q^{88} - 5218 q^{89} + 10492 q^{90} - 1104 q^{91} + 1060 q^{92} - 1997 q^{93} + 2134 q^{94} + 6346 q^{95} - 11984 q^{96} + 2590 q^{97} - 6270 q^{98} - 2693 q^{99}+O(q^{100}) \) 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 −5.55308 6.73841 22.8367 8.33670 −37.4189 −27.2593 −82.3895 18.4062 −46.2944
1.2 −5.07016 5.26544 17.7066 3.42027 −26.6966 −25.1802 −49.2138 0.724844 −17.3413
1.3 −5.00294 −7.79914 17.0294 −17.6229 39.0186 25.3356 −45.1735 33.8266 88.1665
1.4 −4.74823 −6.58177 14.5457 −7.24018 31.2517 −6.49418 −31.0804 16.3197 34.3780
1.5 −4.39566 −7.85436 11.3218 −5.85216 34.5251 −12.3980 −14.6016 34.6910 25.7241
1.6 −4.36589 4.55814 11.0610 9.21441 −19.9004 12.2688 −13.3641 −6.22333 −40.2291
1.7 −3.60614 0.812227 5.00427 −5.99647 −2.92901 26.3629 10.8030 −26.3403 21.6241
1.8 −3.54418 −3.02897 4.56122 20.5936 10.7352 15.8438 12.1877 −17.8253 −72.9874
1.9 −2.89826 6.20542 0.399940 −21.5042 −17.9850 −25.5918 22.0270 11.5073 62.3249
1.10 −2.28876 6.58088 −2.76159 −7.90295 −15.0620 15.8319 24.6307 16.3080 18.0879
1.11 −1.94581 −1.92433 −4.21381 20.3652 3.74438 −13.1013 23.7658 −23.2970 −39.6269
1.12 −1.92929 −5.16200 −4.27784 3.37495 9.95900 15.9770 23.6875 −0.353756 −6.51127
1.13 −1.77522 −4.21024 −4.84859 −5.54921 7.47410 −24.8990 22.8091 −9.27388 9.85108
1.14 −1.36355 9.26361 −6.14074 1.21569 −12.6314 10.5300 19.2815 58.8145 −1.65764
1.15 −0.335126 1.29157 −7.88769 9.09411 −0.432838 −17.7083 5.32438 −25.3319 −3.04767
1.16 0.188737 1.07307 −7.96438 −16.0623 0.202528 −29.7402 −3.01306 −25.8485 −3.03154
1.17 0.830523 −7.00735 −7.31023 −4.56308 −5.81976 20.3840 −12.7155 22.1029 −3.78975
1.18 1.32038 4.35495 −6.25659 15.6111 5.75020 −4.97789 −18.8242 −8.03441 20.6126
1.19 1.40131 −7.71122 −6.03633 −16.2919 −10.8058 −16.8292 −19.6692 32.4629 −22.8300
1.20 1.56619 5.42418 −5.54704 −8.12470 8.49531 30.7370 −21.2173 2.42171 −12.7249
See all 30 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.30
Significant digits:
Format:

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.g 30
43.b odd 2 1 1849.4.a.h 30
43.f odd 14 2 43.4.e.a ✓ 60
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
43.4.e.a ✓ 60 43.f odd 14 2
1849.4.a.g 30 1.a even 1 1 trivial
1849.4.a.h 30 43.b odd 2 1

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