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Properties

Label 141.7.b.a
Level $141$
Weight $7$
Character orbit 141.b
Analytic conductor $32.438$
Analytic rank $0$
Dimension $92$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [141,7,Mod(95,141)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(141, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("141.95");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 141 = 3 \cdot 47 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 141.b (of order \(2\), degree \(1\), minimal)

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: no
Analytic conductor: \(32.4376257904\)
Analytic rank: \(0\)
Dimension: \(92\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 92 q + 20 q^{3} - 2944 q^{4} - 160 q^{6} + 568 q^{7} - 1380 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 92 q + 20 q^{3} - 2944 q^{4} - 160 q^{6} + 568 q^{7} - 1380 q^{9} + 3840 q^{10} + 5 q^{12} - 1016 q^{13} - 3520 q^{15} + 82928 q^{16} + 1561 q^{18} + 25096 q^{19} + 19520 q^{21} - 9072 q^{22} + 24653 q^{24} - 278692 q^{25} - 5188 q^{27} + 9856 q^{28} + 5854 q^{30} - 61208 q^{31} - 5920 q^{33} - 43440 q^{34} + 736 q^{36} + 159112 q^{37} - 112096 q^{39} - 389892 q^{40} - 346075 q^{42} + 45064 q^{43} - 41856 q^{45} - 38700 q^{46} + 440172 q^{48} + 1710324 q^{49} - 19376 q^{51} + 680644 q^{52} + 379319 q^{54} + 476976 q^{55} - 856600 q^{57} - 1043664 q^{58} + 612802 q^{60} + 760360 q^{61} + 1117968 q^{63} - 2292736 q^{64} + 42700 q^{66} - 1098872 q^{67} - 221152 q^{69} - 703236 q^{70} - 1129548 q^{72} - 46568 q^{73} + 5244 q^{75} - 3467108 q^{76} + 2056972 q^{78} + 1539160 q^{79} - 1344892 q^{81} + 3875424 q^{82} - 659781 q^{84} - 3300960 q^{85} + 1203936 q^{87} + 2349492 q^{88} - 7166018 q^{90} + 520784 q^{91} + 1670368 q^{93} - 4420 q^{96} + 699352 q^{97} + 1556096 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
95.1 − 15.2935i 17.4336 + 20.6172i −169.892 − 84.2351i 315.309 − 266.621i 344.215 1619.45i −121.137 + 718.865i −1288.25
95.2 − 15.1857i 20.9176 − 17.0720i −166.605 64.5367i −259.250 − 317.649i −103.455 1558.13i 146.095 − 714.211i 980.035
95.3 − 15.1296i −26.2564 − 6.29300i −164.904 − 153.229i −95.2104 + 397.248i 33.9778 1526.64i 649.796 + 330.463i −2318.29
95.4 − 15.1161i −12.1728 − 24.1003i −164.497 182.371i −364.302 + 184.006i 522.029 1519.12i −432.646 + 586.736i 2756.74
95.5 − 15.0174i 5.10410 + 26.5132i −161.524 241.162i 398.160 − 76.6506i −563.322 1464.56i −676.896 + 270.652i 3621.64
95.6 − 14.5331i 3.50734 − 26.7712i −147.212 − 84.1280i −389.069 − 50.9725i −523.936 1209.32i −704.397 − 187.791i −1222.64
95.7 − 14.2045i −20.7266 + 17.3034i −137.769 62.4943i 245.787 + 294.411i 370.254 1047.85i 130.181 − 717.282i 887.702
95.8 − 14.0496i −10.3711 + 24.9287i −133.392 − 129.097i 350.238 + 145.710i −272.121 974.924i −513.879 − 517.078i −1813.76
95.9 − 13.9149i 26.9317 + 1.91976i −129.625 36.6200i 26.7133 − 374.752i −72.0694 913.174i 721.629 + 103.404i 509.565
95.10 − 13.2759i −22.4217 − 15.0422i −112.249 102.248i −199.698 + 297.668i −351.093 640.549i 276.466 + 674.542i 1357.43
95.11 − 12.7673i 25.9748 − 7.36960i −99.0041 − 243.243i −94.0899 − 331.628i 203.920 446.908i 620.378 − 382.847i −3105.55
95.12 − 12.5745i 15.5043 − 22.1047i −94.1175 − 47.0817i −277.955 − 194.958i 662.069 378.711i −248.235 − 685.434i −592.028
95.13 − 12.4531i −25.0848 + 9.98764i −91.0806 146.075i 124.377 + 312.384i −8.95791 337.238i 529.494 − 501.076i 1819.09
95.14 − 12.0769i −7.20338 − 26.0214i −81.8527 − 162.027i −314.259 + 86.9948i 91.4040 215.606i −625.223 + 374.883i −1956.79
95.15 − 11.5491i 20.1101 + 18.0162i −69.3807 − 108.388i 208.070 − 232.253i −565.321 62.1423i 79.8348 + 724.615i −1251.78
95.16 − 11.3204i 19.5892 + 18.5812i −64.1517 168.218i 210.347 − 221.758i 509.647 1.71770i 38.4767 + 727.984i 1904.30
95.17 − 10.9978i 26.9068 + 2.24110i −56.9516 90.3608i 24.6472 − 295.916i −113.819 − 77.5173i 718.955 + 120.602i 993.770
95.18 − 10.9500i −1.08597 + 26.9782i −55.9023 78.6049i 295.410 + 11.8913i 249.223 − 88.6702i −726.641 − 58.5947i 860.723
95.19 − 10.7796i 2.76356 − 26.8582i −52.1998 81.2288i −289.521 − 29.7900i −5.41104 − 127.201i −713.726 − 148.448i 875.614
95.20 − 10.3585i −26.3409 + 5.92935i −43.2994 32.3115i 61.4195 + 272.853i −572.775 − 214.428i 658.686 − 312.369i 334.700
See all 92 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 95.92
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 141.7.b.a ✓ 92
3.b odd 2 1 inner 141.7.b.a ✓ 92
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
141.7.b.a ✓ 92 1.a even 1 1 trivial
141.7.b.a ✓ 92 3.b odd 2 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{7}^{\mathrm{new}}(141, [\chi])\).