Properties

Label 20.9.d.c
Level $20$
Weight $9$
Character orbit 20.d
Analytic conductor $8.148$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [20,9,Mod(19,20)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(20, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("20.19");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 20.d (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: \(8.14757220122\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} + 94 x^{18} + 5343 x^{16} + 172772 x^{14} + 36131456 x^{12} + 3044563968 x^{10} + 147994443776 x^{8} + 2898633162752 x^{6} + \cdots + 11\!\cdots\!76 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{74}\cdot 3^{4}\cdot 5^{12} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 

Coefficients of the \(q\)-expansion are expressed in terms of a basis \(1,\beta_1,\ldots,\beta_{19}\) for the coefficient ring described below. We also show the integral \(q\)-expansion of the trace form.

\(f(q)\) \(=\) \( q + \beta_1 q^{2} + (\beta_{6} + \beta_1) q^{3} + (\beta_{2} - 38) q^{4} + (\beta_{7} + \beta_1 - 71) q^{5} + (\beta_{8} + \beta_{2} + 170) q^{6} + ( - \beta_{13} + 3 \beta_{6} + 3 \beta_1) q^{7} + (\beta_{3} - 38 \beta_1) q^{8} + (\beta_{11} - \beta_{9} + 2 \beta_{8} - 3 \beta_{7} - 5 \beta_{2} - \beta_1 + 130) q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + \beta_1 q^{2} + (\beta_{6} + \beta_1) q^{3} + (\beta_{2} - 38) q^{4} + (\beta_{7} + \beta_1 - 71) q^{5} + (\beta_{8} + \beta_{2} + 170) q^{6} + ( - \beta_{13} + 3 \beta_{6} + 3 \beta_1) q^{7} + (\beta_{3} - 38 \beta_1) q^{8} + (\beta_{11} - \beta_{9} + 2 \beta_{8} - 3 \beta_{7} - 5 \beta_{2} - \beta_1 + 130) q^{9} + (\beta_{15} + \beta_{9} - \beta_{7} + 7 \beta_{6} - \beta_{4} - 68 \beta_1 - 208) q^{10} + (\beta_{12} - \beta_{8} - 2 \beta_{2} + 1) q^{11} + ( - \beta_{19} - \beta_{18} - \beta_{13} + 2 \beta_{7} - 96 \beta_{6} + \beta_{5} + \beta_{3} + \cdots + 139 \beta_1) q^{12}+ \cdots + ( - 138 \beta_{19} - 66 \beta_{18} - 138 \beta_{17} - 342 \beta_{16} + \cdots + 25209) q^{99}+O(q^{100}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 752 q^{4} - 1420 q^{5} + 3408 q^{6} + 2556 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 752 q^{4} - 1420 q^{5} + 3408 q^{6} + 2556 q^{9} - 4160 q^{10} + 8848 q^{14} - 59200 q^{16} - 4240 q^{20} + 410256 q^{21} - 156672 q^{24} - 657260 q^{25} - 440448 q^{26} + 660136 q^{29} + 667920 q^{30} + 4342528 q^{34} - 7191312 q^{36} - 945280 q^{40} + 7068520 q^{41} + 2666880 q^{44} - 18729060 q^{45} + 561168 q^{46} + 11719036 q^{49} + 3914880 q^{50} + 37110816 q^{54} - 35044352 q^{56} - 22734720 q^{60} - 17660440 q^{61} + 20201728 q^{64} - 44202240 q^{65} + 31902720 q^{66} + 111747216 q^{69} - 47166000 q^{70} + 19114368 q^{74} - 54998400 q^{76} + 7968320 q^{80} - 154212444 q^{81} + 101289216 q^{84} + 68800000 q^{85} + 94429648 q^{86} + 105006376 q^{89} - 230808000 q^{90} - 192757872 q^{94} + 28850688 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Basis of coefficient ring in terms of a root \(\nu\) of \( x^{20} + 94 x^{18} + 5343 x^{16} + 172772 x^{14} + 36131456 x^{12} + 3044563968 x^{10} + 147994443776 x^{8} + 2898633162752 x^{6} + \cdots + 11\!\cdots\!76 \) : Copy content Toggle raw display

\(\beta_{1}\)\(=\) \( 2\nu \) Copy content Toggle raw display
\(\beta_{2}\)\(=\) \( 4\nu^{2} + 38 \) Copy content Toggle raw display
\(\beta_{3}\)\(=\) \( 8\nu^{3} + 76\nu \) Copy content Toggle raw display
\(\beta_{4}\)\(=\) \( ( - 3302597 \nu^{18} - 1391343702 \nu^{16} - 29876009883 \nu^{14} + 1448679820940 \nu^{12} - 186292651580544 \nu^{10} + \cdots - 37\!\cdots\!28 ) / 12\!\cdots\!32 \) Copy content Toggle raw display
\(\beta_{5}\)\(=\) \( ( 10120793 \nu^{19} - 1538239314 \nu^{17} - 72882621561 \nu^{15} + 834264549700 \nu^{13} + 124572188012160 \nu^{11} + \cdots - 47\!\cdots\!48 \nu ) / 16\!\cdots\!96 \) Copy content Toggle raw display
\(\beta_{6}\)\(=\) \( ( - 21623225 \nu^{19} + 457010706 \nu^{17} + 11425127385 \nu^{15} - 2821562731204 \nu^{13} - 540171803713152 \nu^{11} + \cdots + 20\!\cdots\!28 \nu ) / 32\!\cdots\!92 \) Copy content Toggle raw display
\(\beta_{7}\)\(=\) \( ( 11547117 \nu^{19} - 488855936 \nu^{18} + 1694508294 \nu^{17} - 65873566976 \nu^{16} + 36909113715 \nu^{15} - 1089638299264 \nu^{14} + \cdots - 16\!\cdots\!80 ) / 17\!\cdots\!40 \) Copy content Toggle raw display
\(\beta_{8}\)\(=\) \( ( 607811 \nu^{18} + 30995610 \nu^{16} + 223223901 \nu^{14} + 58863964588 \nu^{12} + 18819124901760 \nu^{10} + 857972427985920 \nu^{8} + \cdots + 60\!\cdots\!92 ) / 39\!\cdots\!76 \) Copy content Toggle raw display
\(\beta_{9}\)\(=\) \( ( 103924053 \nu^{19} + 6141831296 \nu^{18} + 15250574646 \nu^{17} - 1454773281024 \nu^{16} + 332182023435 \nu^{15} + \cdots - 41\!\cdots\!40 ) / 80\!\cdots\!80 \) Copy content Toggle raw display
\(\beta_{10}\)\(=\) \( ( - 103924053 \nu^{19} - 9822609536 \nu^{18} - 15250574646 \nu^{17} + 1108780126464 \nu^{16} - 332182023435 \nu^{15} + \cdots + 32\!\cdots\!60 ) / 80\!\cdots\!80 \) Copy content Toggle raw display
\(\beta_{11}\)\(=\) \( ( 11547117 \nu^{19} + 488855936 \nu^{18} + 1694508294 \nu^{17} + 65873566976 \nu^{16} + 36909113715 \nu^{15} + 1089638299264 \nu^{14} + \cdots + 16\!\cdots\!80 ) / 35\!\cdots\!88 \) Copy content Toggle raw display
\(\beta_{12}\)\(=\) \( ( 11250533 \nu^{18} + 356503830 \nu^{16} + 6095187195 \nu^{14} + 1380868386292 \nu^{12} + 320541156988032 \nu^{10} + \cdots + 16\!\cdots\!96 ) / 15\!\cdots\!04 \) Copy content Toggle raw display
\(\beta_{13}\)\(=\) \( ( 32459431 \nu^{19} - 1527461550 \nu^{17} - 42771655815 \nu^{15} + 3554605976252 \nu^{13} + 745081528209792 \nu^{11} + \cdots - 61\!\cdots\!48 \nu ) / 26\!\cdots\!16 \) Copy content Toggle raw display
\(\beta_{14}\)\(=\) \( ( - 4397900707 \nu^{19} - 16920576256 \nu^{18} - 1027539355098 \nu^{17} - 1855269723648 \nu^{16} - 17641443616509 \nu^{15} + \cdots - 15\!\cdots\!32 ) / 16\!\cdots\!60 \) Copy content Toggle raw display
\(\beta_{15}\)\(=\) \( ( - 4073259013 \nu^{19} - 4973631424 \nu^{18} - 608485077462 \nu^{17} + 44798068608 \nu^{16} - 10172775434331 \nu^{15} + \cdots - 24\!\cdots\!28 ) / 80\!\cdots\!80 \) Copy content Toggle raw display
\(\beta_{16}\)\(=\) \( ( 875056263 \nu^{19} + 41392821248 \nu^{18} - 13654586990 \nu^{17} + 570874583040 \nu^{16} - 635936680551 \nu^{15} + \cdots - 42\!\cdots\!28 ) / 17\!\cdots\!40 \) Copy content Toggle raw display
\(\beta_{17}\)\(=\) \( ( 14557212835 \nu^{19} + 3251847424 \nu^{18} + 1888412158938 \nu^{17} + 1868182445568 \nu^{16} + 18352861149693 \nu^{15} + \cdots + 39\!\cdots\!04 ) / 16\!\cdots\!60 \) Copy content Toggle raw display
\(\beta_{18}\)\(=\) \( ( - 8062974223 \nu^{19} - 9608144128 \nu^{18} - 554664723330 \nu^{17} + 347685480960 \nu^{16} - 7477151383569 \nu^{15} + \cdots + 17\!\cdots\!68 ) / 80\!\cdots\!80 \) Copy content Toggle raw display
\(\beta_{19}\)\(=\) \( ( - 12462645249 \nu^{19} + 5208440704 \nu^{18} - 771214807134 \nu^{17} - 940547583744 \nu^{16} - 3157211583711 \nu^{15} + \cdots - 31\!\cdots\!88 ) / 80\!\cdots\!80 \) Copy content Toggle raw display
\(\nu\)\(=\) \( ( \beta_1 ) / 2 \) Copy content Toggle raw display
\(\nu^{2}\)\(=\) \( ( \beta_{2} - 38 ) / 4 \) Copy content Toggle raw display
\(\nu^{3}\)\(=\) \( ( \beta_{3} - 38\beta_1 ) / 8 \) Copy content Toggle raw display
\(\nu^{4}\)\(=\) \( ( - \beta_{19} + \beta_{18} - \beta_{17} - \beta_{16} - 2 \beta_{15} + \beta_{14} + \beta_{13} + 3 \beta_{12} - \beta_{11} + 3 \beta_{9} + \beta_{8} - \beta_{7} + \beta_{6} - \beta_{5} - 3 \beta_{4} - \beta_{3} - 40 \beta_{2} + \beta _1 - 2943 ) / 16 \) Copy content Toggle raw display
\(\nu^{5}\)\(=\) \( ( - 7 \beta_{19} - \beta_{18} - 10 \beta_{17} - 2 \beta_{15} - 6 \beta_{14} - 27 \beta_{13} - 28 \beta_{11} - 132 \beta_{7} + 70 \beta_{6} + 7 \beta_{5} - 6 \beta_{3} - 729 \beta_1 ) / 8 \) Copy content Toggle raw display
\(\nu^{6}\)\(=\) \( ( - 9 \beta_{19} + 31 \beta_{18} - 9 \beta_{17} + 13 \beta_{16} - 40 \beta_{15} + 9 \beta_{14} + 9 \beta_{13} + 9 \beta_{12} - 51 \beta_{11} - 208 \beta_{10} - 379 \beta_{9} - 21 \beta_{8} + 619 \beta_{7} + 9 \beta_{6} - 9 \beta_{5} + 111 \beta_{4} + \cdots + 126275 ) / 8 \) Copy content Toggle raw display
\(\nu^{7}\)\(=\) \( ( - 274 \beta_{19} + 406 \beta_{18} + 108 \beta_{17} + 344 \beta_{15} - 76 \beta_{14} + 2082 \beta_{13} + 512 \beta_{11} - 302 \beta_{10} + 302 \beta_{9} + 1924 \beta_{7} + 24356 \beta_{6} - 13828 \beta_{5} + \cdots + 75386 \beta_1 ) / 8 \) Copy content Toggle raw display
\(\nu^{8}\)\(=\) \( ( 139 \beta_{19} - 2451 \beta_{18} + 139 \beta_{17} - 2173 \beta_{16} + 2590 \beta_{15} - 139 \beta_{14} - 139 \beta_{13} - 8073 \beta_{12} - 1869 \beta_{11} - 5952 \beta_{10} + 9703 \beta_{9} + 56461 \beta_{8} + \cdots - 213160723 ) / 16 \) Copy content Toggle raw display
\(\nu^{9}\)\(=\) \( ( 3349 \beta_{19} + 9643 \beta_{18} + 16430 \beta_{17} + 11374 \beta_{15} + 7170 \beta_{14} - 183799 \beta_{13} - 7196 \beta_{11} - 6732 \beta_{10} + 6732 \beta_{9} - 62460 \beta_{7} - 4571346 \beta_{6} + \cdots - 54768093 \beta_1 ) / 8 \) Copy content Toggle raw display
\(\nu^{10}\)\(=\) \( ( - 10014 \beta_{19} + 63685 \beta_{18} - 10014 \beta_{17} + 43657 \beta_{16} - 73699 \beta_{15} + 10014 \beta_{14} + 10014 \beta_{13} + 19965 \beta_{12} + 180161 \beta_{11} + 90488 \beta_{10} + \cdots + 75246103 ) / 4 \) Copy content Toggle raw display
\(\nu^{11}\)\(=\) \( ( 1140020 \beta_{19} + 97392 \beta_{18} + 497136 \beta_{17} - 1893956 \beta_{15} - 118064 \beta_{14} + 10633504 \beta_{13} - 4176584 \beta_{11} + 580346 \beta_{10} - 580346 \beta_{9} + \cdots + 97932580 \beta_1 ) / 8 \) Copy content Toggle raw display
\(\nu^{12}\)\(=\) \( ( 14017923 \beta_{19} - 21976067 \beta_{18} + 14017923 \beta_{17} + 6059779 \beta_{16} + 35993990 \beta_{15} - 14017923 \beta_{14} - 14017923 \beta_{13} - 36358857 \beta_{12} + \cdots + 213177952749 ) / 16 \) Copy content Toggle raw display
\(\nu^{13}\)\(=\) \( ( 66676517 \beta_{19} + 105062355 \beta_{18} + 125825694 \beta_{17} + 44106694 \beta_{15} + 43848850 \beta_{14} + 109690273 \beta_{13} + 798523348 \beta_{11} + \cdots + 50771922467 \beta_1 ) / 8 \) Copy content Toggle raw display
\(\nu^{14}\)\(=\) \( ( 344100561 \beta_{19} - 769664947 \beta_{18} + 344100561 \beta_{17} - 81463825 \beta_{16} + 1113765508 \beta_{15} - 344100561 \beta_{14} - 344100561 \beta_{13} + \cdots + 2477743922529 ) / 8 \) Copy content Toggle raw display
\(\nu^{15}\)\(=\) \( ( 9684699242 \beta_{19} - 12949656150 \beta_{18} - 2590174476 \beta_{17} - 9848016752 \beta_{15} + 3398721388 \beta_{14} - 28392840962 \beta_{13} + \cdots + 985218925214 \beta_1 ) / 8 \) Copy content Toggle raw display
\(\nu^{16}\)\(=\) \( ( - 3613266745 \beta_{19} + 38623462337 \beta_{18} - 3613266745 \beta_{17} + 31396928847 \beta_{16} - 42236729082 \beta_{15} + 3613266745 \beta_{14} + \cdots + 14\!\cdots\!21 ) / 16 \) Copy content Toggle raw display
\(\nu^{17}\)\(=\) \( ( - 264166320887 \beta_{19} - 247665438841 \beta_{18} - 506965570042 \beta_{17} - 145026223306 \beta_{15} - 222830891798 \beta_{14} + \cdots + 402665339208175 \beta_1 ) / 8 \) Copy content Toggle raw display
\(\nu^{18}\)\(=\) \( ( 206826061833 \beta_{19} - 1356326570262 \beta_{18} + 206826061833 \beta_{17} - 942674446596 \beta_{16} + 1563152632095 \beta_{15} - 206826061833 \beta_{14} + \cdots + 21\!\cdots\!92 ) / 4 \) Copy content Toggle raw display
\(\nu^{19}\)\(=\) \( ( - 28979466545816 \beta_{19} - 15746025254036 \beta_{18} - 15226592799096 \beta_{17} + 47319711735396 \beta_{15} + 6286559214840 \beta_{14} + \cdots + 20\!\cdots\!24 \beta_1 ) / 8 \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/20\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(17\)
\(\chi(n)\) \(-1\) \(-1\)

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   \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
19.1
−7.46306 2.88145i
−7.46306 + 2.88145i
−7.15078 3.58697i
−7.15078 + 3.58697i
−3.61621 7.13604i
−3.61621 + 7.13604i
−3.53165 7.17826i
−3.53165 + 7.17826i
−2.02968 7.73824i
−2.02968 + 7.73824i
2.02968 7.73824i
2.02968 + 7.73824i
3.53165 7.17826i
3.53165 + 7.17826i
3.61621 7.13604i
3.61621 + 7.13604i
7.15078 3.58697i
7.15078 + 3.58697i
7.46306 2.88145i
7.46306 + 2.88145i
−14.9261 5.76290i −76.0331 189.578 + 172.035i 291.455 + 552.882i 1134.88 + 438.171i −269.408 −1838.24 3660.34i −779.974 −1164.08 9932.01i
19.2 −14.9261 + 5.76290i −76.0331 189.578 172.035i 291.455 552.882i 1134.88 438.171i −269.408 −1838.24 + 3660.34i −779.974 −1164.08 + 9932.01i
19.3 −14.3016 7.17394i 42.6663 153.069 + 205.197i −560.298 276.932i −610.194 306.085i 869.685 −717.054 4032.75i −4740.59 6026.43 + 7980.11i
19.4 −14.3016 + 7.17394i 42.6663 153.069 205.197i −560.298 + 276.932i −610.194 + 306.085i 869.685 −717.054 + 4032.75i −4740.59 6026.43 7980.11i
19.5 −7.23243 14.2721i 44.3270 −151.384 + 206.443i 530.961 329.705i −320.592 632.638i 2826.75 4041.25 + 667.476i −4596.11 −8545.71 5193.35i
19.6 −7.23243 + 14.2721i 44.3270 −151.384 206.443i 530.961 + 329.705i −320.592 + 632.638i 2826.75 4041.25 667.476i −4596.11 −8545.71 + 5193.35i
19.7 −7.06329 14.3565i −134.970 −156.220 + 202.809i −416.235 466.234i 953.329 + 1937.69i −1863.96 4015.06 + 810.276i 11655.8 −3753.51 + 9268.83i
19.8 −7.06329 + 14.3565i −134.970 −156.220 202.809i −416.235 + 466.234i 953.329 1937.69i −1863.96 4015.06 810.276i 11655.8 −3753.51 9268.83i
19.9 −4.05935 15.4765i 75.2390 −223.043 + 125.649i −200.884 + 591.837i −305.422 1164.44i −4411.35 2850.02 + 2941.87i −900.091 9975.01 + 706.503i
19.10 −4.05935 + 15.4765i 75.2390 −223.043 125.649i −200.884 591.837i −305.422 + 1164.44i −4411.35 2850.02 2941.87i −900.091 9975.01 706.503i
19.11 4.05935 15.4765i −75.2390 −223.043 125.649i −200.884 + 591.837i −305.422 + 1164.44i 4411.35 −2850.02 + 2941.87i −900.091 8344.09 + 5511.45i
19.12 4.05935 + 15.4765i −75.2390 −223.043 + 125.649i −200.884 591.837i −305.422 1164.44i 4411.35 −2850.02 2941.87i −900.091 8344.09 5511.45i
19.13 7.06329 14.3565i 134.970 −156.220 202.809i −416.235 466.234i 953.329 1937.69i 1863.96 −4015.06 + 810.276i 11655.8 −9633.48 + 2682.54i
19.14 7.06329 + 14.3565i 134.970 −156.220 + 202.809i −416.235 + 466.234i 953.329 + 1937.69i 1863.96 −4015.06 810.276i 11655.8 −9633.48 2682.54i
19.15 7.23243 14.2721i −44.3270 −151.384 206.443i 530.961 329.705i −320.592 + 632.638i −2826.75 −4041.25 + 667.476i −4596.11 −865.429 9962.48i
19.16 7.23243 + 14.2721i −44.3270 −151.384 + 206.443i 530.961 + 329.705i −320.592 632.638i −2826.75 −4041.25 667.476i −4596.11 −865.429 + 9962.48i
19.17 14.3016 7.17394i −42.6663 153.069 205.197i −560.298 276.932i −610.194 + 306.085i −869.685 717.054 4032.75i −4740.59 −9999.83 + 58.9826i
19.18 14.3016 + 7.17394i −42.6663 153.069 + 205.197i −560.298 + 276.932i −610.194 306.085i −869.685 717.054 + 4032.75i −4740.59 −9999.83 58.9826i
19.19 14.9261 5.76290i 76.0331 189.578 172.035i 291.455 + 552.882i 1134.88 438.171i 269.408 1838.24 3660.34i −779.974 7536.50 + 6572.76i
19.20 14.9261 + 5.76290i 76.0331 189.578 + 172.035i 291.455 552.882i 1134.88 + 438.171i 269.408 1838.24 + 3660.34i −779.974 7536.50 6572.76i
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 19.20
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
4.b odd 2 1 inner
5.b even 2 1 inner
20.d odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 20.9.d.c 20
4.b odd 2 1 inner 20.9.d.c 20
5.b even 2 1 inner 20.9.d.c 20
5.c odd 4 2 100.9.b.g 20
8.b even 2 1 320.9.h.g 20
8.d odd 2 1 320.9.h.g 20
20.d odd 2 1 inner 20.9.d.c 20
20.e even 4 2 100.9.b.g 20
40.e odd 2 1 320.9.h.g 20
40.f even 2 1 320.9.h.g 20
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
20.9.d.c 20 1.a even 1 1 trivial
20.9.d.c 20 4.b odd 2 1 inner
20.9.d.c 20 5.b even 2 1 inner
20.9.d.c 20 20.d odd 2 1 inner
100.9.b.g 20 5.c odd 4 2
100.9.b.g 20 20.e even 4 2
320.9.h.g 20 8.b even 2 1
320.9.h.g 20 8.d odd 2 1
320.9.h.g 20 40.e odd 2 1
320.9.h.g 20 40.f even 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{10} - 33444 T_{3}^{8} + 357004800 T_{3}^{6} - 1615110935040 T_{3}^{4} + \cdots - 21\!\cdots\!00 \) acting on \(S_{9}^{\mathrm{new}}(20, [\chi])\). Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T^{20} + 376 T^{18} + \cdots + 12\!\cdots\!76 \) Copy content Toggle raw display
$3$ \( (T^{10} - 33444 T^{8} + \cdots - 21\!\cdots\!00)^{2} \) Copy content Toggle raw display
$5$ \( (T^{10} + 710 T^{9} + \cdots + 90\!\cdots\!25)^{2} \) Copy content Toggle raw display
$7$ \( (T^{10} - 31753764 T^{8} + \cdots - 29\!\cdots\!00)^{2} \) Copy content Toggle raw display
$11$ \( (T^{10} + 999897600 T^{8} + \cdots + 15\!\cdots\!00)^{2} \) Copy content Toggle raw display
$13$ \( (T^{10} + 4307527296 T^{8} + \cdots + 15\!\cdots\!00)^{2} \) Copy content Toggle raw display
$17$ \( (T^{10} + 39851142656 T^{8} + \cdots + 57\!\cdots\!00)^{2} \) Copy content Toggle raw display
$19$ \( (T^{10} + 92184752640 T^{8} + \cdots + 54\!\cdots\!00)^{2} \) Copy content Toggle raw display
$23$ \( (T^{10} - 510426064164 T^{8} + \cdots - 72\!\cdots\!00)^{2} \) Copy content Toggle raw display
$29$ \( (T^{5} - 165034 T^{4} + \cdots - 30\!\cdots\!52)^{4} \) Copy content Toggle raw display
$31$ \( (T^{10} + 5638508605440 T^{8} + \cdots + 51\!\cdots\!00)^{2} \) Copy content Toggle raw display
$37$ \( (T^{10} + 11893689000576 T^{8} + \cdots + 30\!\cdots\!00)^{2} \) Copy content Toggle raw display
$41$ \( (T^{5} - 1767130 T^{4} + \cdots + 51\!\cdots\!28)^{4} \) Copy content Toggle raw display
$43$ \( (T^{10} - 38122870151844 T^{8} + \cdots - 13\!\cdots\!00)^{2} \) Copy content Toggle raw display
$47$ \( (T^{10} - 29539975189284 T^{8} + \cdots - 25\!\cdots\!00)^{2} \) Copy content Toggle raw display
$53$ \( (T^{10} + 171214156558976 T^{8} + \cdots + 74\!\cdots\!00)^{2} \) Copy content Toggle raw display
$59$ \( (T^{10} + \cdots + 53\!\cdots\!00)^{2} \) Copy content Toggle raw display
$61$ \( (T^{5} + 4415110 T^{4} + \cdots + 50\!\cdots\!68)^{4} \) Copy content Toggle raw display
$67$ \( (T^{10} + \cdots - 19\!\cdots\!00)^{2} \) Copy content Toggle raw display
$71$ \( (T^{10} + \cdots + 92\!\cdots\!00)^{2} \) Copy content Toggle raw display
$73$ \( (T^{10} + \cdots + 86\!\cdots\!00)^{2} \) Copy content Toggle raw display
$79$ \( (T^{10} + \cdots + 74\!\cdots\!00)^{2} \) Copy content Toggle raw display
$83$ \( (T^{10} + \cdots - 78\!\cdots\!00)^{2} \) Copy content Toggle raw display
$89$ \( (T^{5} - 26251594 T^{4} + \cdots + 38\!\cdots\!28)^{4} \) Copy content Toggle raw display
$97$ \( (T^{10} + \cdots + 34\!\cdots\!00)^{2} \) Copy content Toggle raw display
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