Properties

Label 882.2.u.g
Level $882$
Weight $2$
Character orbit 882.u
Analytic conductor $7.043$
Analytic rank $0$
Dimension $18$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [882,2,Mod(127,882)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(882, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([0, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("882.127");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.u (of order \(7\), degree \(6\), 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: \(7.04280545828\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(3\) over \(\Q(\zeta_{7})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{18} + 37 x^{16} + 557 x^{14} + 4495 x^{12} + 21331 x^{10} + 60904 x^{8} + 101893 x^{6} + 91665 x^{4} + 36855 x^{2} + 5103 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 98)
Sato-Tate group: $\mathrm{SU}(2)[C_{7}]$

$q$-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 \(1,\beta_1,\ldots,\beta_{17}\) for the coefficient ring described below. We also show the integral \(q\)-expansion of the trace form.

\(f(q)\) \(=\) \( q + \beta_{9} q^{2} + ( - \beta_{13} + \beta_{10} - \beta_{9} + \beta_{6} - \beta_{5} - 1) q^{4} + (\beta_{16} - \beta_{14}) q^{5} + (\beta_{9} + \beta_{5} - \beta_{4} - \beta_1) q^{7} + \beta_{5} q^{8}+O(q^{10}) \) Copy content Toggle raw display \( q + \beta_{9} q^{2} + ( - \beta_{13} + \beta_{10} - \beta_{9} + \beta_{6} - \beta_{5} - 1) q^{4} + (\beta_{16} - \beta_{14}) q^{5} + (\beta_{9} + \beta_{5} - \beta_{4} - \beta_1) q^{7} + \beta_{5} q^{8} + (2 \beta_{17} - \beta_{16} - \beta_{14} + 2 \beta_{10} + \beta_{8} + \beta_{7} + \beta_1) q^{10} + (\beta_{17} - \beta_{16} - \beta_{14} + \beta_{10} + 2 \beta_{8} + \beta_{7} + \beta_1) q^{11} + (\beta_{16} - \beta_{15} + 2 \beta_{13} - \beta_{10} + \beta_{9} + \beta_{7} - 2 \beta_{6} + \beta_{5} - \beta_{2}) q^{13} + (\beta_{14} - \beta_{13} + \beta_{10} - \beta_{9} - \beta_{5} + \beta_{3} - 1) q^{14} - \beta_{6} q^{16} + ( - \beta_{17} + \beta_{16} + \beta_{14} + 3 \beta_{13} - \beta_{12} - 2 \beta_{10} - \beta_{8} - 2 \beta_{7} + \cdots + 1) q^{17}+ \cdots + ( - 2 \beta_{17} - \beta_{15} + 2 \beta_{14} + \beta_{13} + \beta_{12} - 2 \beta_{10} - 2 \beta_{9} + \cdots + 3) q^{98}+O(q^{100}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q - 3 q^{2} - 3 q^{4} - q^{7} - 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 18 q - 3 q^{2} - 3 q^{4} - q^{7} - 3 q^{8} - 7 q^{11} - 10 q^{13} - q^{14} - 3 q^{16} - q^{17} - 44 q^{19} - 7 q^{20} + 7 q^{22} - 21 q^{23} + q^{25} - 3 q^{26} - 8 q^{28} - 11 q^{29} - 24 q^{31} - 3 q^{32} - q^{34} + 21 q^{35} - 13 q^{37} + 19 q^{38} + 7 q^{40} - 8 q^{41} - 24 q^{43} + 21 q^{46} - 40 q^{47} - 43 q^{49} + 50 q^{50} + 18 q^{52} - 10 q^{53} + 49 q^{55} - q^{56} + 24 q^{58} - 13 q^{59} + 27 q^{61} + 11 q^{62} - 3 q^{64} - 86 q^{67} + 34 q^{68} - 14 q^{70} + 5 q^{73} - 13 q^{74} - 2 q^{76} + 14 q^{77} - 66 q^{79} - 8 q^{82} - 55 q^{83} - 49 q^{85} + 18 q^{86} - 62 q^{89} + 39 q^{91} + 21 q^{92} + 23 q^{94} + 7 q^{95} - 32 q^{97} + 48 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Basis of coefficient ring in terms of a root \(\nu\) of \( x^{18} + 37 x^{16} + 557 x^{14} + 4495 x^{12} + 21331 x^{10} + 60904 x^{8} + 101893 x^{6} + 91665 x^{4} + 36855 x^{2} + 5103 \) : Copy content Toggle raw display

\(\beta_{1}\)\(=\) \( \nu \) Copy content Toggle raw display
\(\beta_{2}\)\(=\) \( ( - 22156 \nu^{16} - 820870 \nu^{14} - 12157877 \nu^{12} - 93603061 \nu^{10} - 405113974 \nu^{8} - 989329516 \nu^{6} - 1285555636 \nu^{4} + \cdots - 147853404 ) / 5434425 \) Copy content Toggle raw display
\(\beta_{3}\)\(=\) \( ( 11931 \nu^{17} + 205546 \nu^{16} + 724590 \nu^{15} + 7124305 \nu^{14} + 15461412 \nu^{13} + 97547162 \nu^{12} + 158083131 \nu^{11} + 687936661 \nu^{10} + \cdots + 414342459 ) / 32606550 \) Copy content Toggle raw display
\(\beta_{4}\)\(=\) \( ( 11931 \nu^{17} - 205546 \nu^{16} + 724590 \nu^{15} - 7124305 \nu^{14} + 15461412 \nu^{13} - 97547162 \nu^{12} + 158083131 \nu^{11} - 687936661 \nu^{10} + \cdots - 414342459 ) / 32606550 \) Copy content Toggle raw display
\(\beta_{5}\)\(=\) \( ( 84541 \nu^{17} - 139078 \nu^{16} + 2923675 \nu^{15} - 4661695 \nu^{14} + 40061312 \nu^{13} - 61073531 \nu^{12} + 284401426 \nu^{11} - 407127478 \nu^{10} + \cdots - 35995347 ) / 32606550 \) Copy content Toggle raw display
\(\beta_{6}\)\(=\) \( ( 84541 \nu^{17} + 139078 \nu^{16} + 2923675 \nu^{15} + 4661695 \nu^{14} + 40061312 \nu^{13} + 61073531 \nu^{12} + 284401426 \nu^{11} + 407127478 \nu^{10} + \cdots + 35995347 ) / 32606550 \) Copy content Toggle raw display
\(\beta_{7}\)\(=\) \( ( - 139078 \nu^{17} + 204342 \nu^{16} - 4661695 \nu^{15} + 7028025 \nu^{14} - 61073531 \nu^{13} + 95610369 \nu^{12} - 407127478 \nu^{11} + \cdots + 431412723 ) / 32606550 \) Copy content Toggle raw display
\(\beta_{8}\)\(=\) \( ( - 139078 \nu^{17} - 204342 \nu^{16} - 4661695 \nu^{15} - 7028025 \nu^{14} - 61073531 \nu^{13} - 95610369 \nu^{12} - 407127478 \nu^{11} + \cdots - 431412723 ) / 32606550 \) Copy content Toggle raw display
\(\beta_{9}\)\(=\) \( ( - 392750 \nu^{17} + 982311 \nu^{16} - 13284980 \nu^{15} + 33199170 \nu^{14} - 177374215 \nu^{13} + 440161887 \nu^{12} - 1228211330 \nu^{11} + \cdots + 1243654074 ) / 97819650 \) Copy content Toggle raw display
\(\beta_{10}\)\(=\) \( ( - 392750 \nu^{17} - 982311 \nu^{16} - 13284980 \nu^{15} - 33199170 \nu^{14} - 177374215 \nu^{13} - 440161887 \nu^{12} - 1228211330 \nu^{11} + \cdots - 1243654074 ) / 97819650 \) Copy content Toggle raw display
\(\beta_{11}\)\(=\) \( ( 758423 \nu^{17} - 983778 \nu^{16} + 25111235 \nu^{15} - 33034830 \nu^{14} + 324894616 \nu^{13} - 435163611 \nu^{12} + 2149982738 \nu^{11} + \cdots - 1620340767 ) / 97819650 \) Copy content Toggle raw display
\(\beta_{12}\)\(=\) \( ( 758423 \nu^{17} + 983778 \nu^{16} + 25111235 \nu^{15} + 33034830 \nu^{14} + 324894616 \nu^{13} + 435163611 \nu^{12} + 2149982738 \nu^{11} + \cdots + 1620340767 ) / 97819650 \) Copy content Toggle raw display
\(\beta_{13}\)\(=\) \( ( 1131902 \nu^{17} - 565077 \nu^{16} + 38118995 \nu^{15} - 19214085 \nu^{14} + 504286174 \nu^{13} - 256941294 \nu^{12} + 3427520567 \nu^{11} + \cdots - 1184577858 ) / 97819650 \) Copy content Toggle raw display
\(\beta_{14}\)\(=\) \( ( - 327437 \nu^{17} - 415590 \nu^{16} - 11066390 \nu^{15} - 13795845 \nu^{14} - 146720629 \nu^{13} - 179066640 \nu^{12} - 995193797 \nu^{11} + \cdots - 668067750 ) / 32606550 \) Copy content Toggle raw display
\(\beta_{15}\)\(=\) \( ( 1348265 \nu^{17} + 566544 \nu^{16} + 44880590 \nu^{15} + 19049745 \nu^{14} + 583084150 \nu^{13} + 251943018 \nu^{12} + 3852875780 \nu^{11} + \cdots + 1707994026 ) / 97819650 \) Copy content Toggle raw display
\(\beta_{16}\)\(=\) \( ( 188359 \nu^{17} + 1253793 \nu^{16} + 6404695 \nu^{15} + 42061080 \nu^{14} + 85647098 \nu^{13} + 553459641 \nu^{12} + 588066319 \nu^{11} + \cdots + 1925365302 ) / 32606550 \) Copy content Toggle raw display
\(\beta_{17}\)\(=\) \( ( - 172327 \nu^{17} + 4743690 \nu^{16} - 5929105 \nu^{15} + 159382410 \nu^{14} - 79567079 \nu^{13} + 2100540810 \nu^{12} - 535987627 \nu^{11} + \cdots + 7019749980 ) / 97819650 \) Copy content Toggle raw display
\(\nu\)\(=\) \( \beta_1 \) Copy content Toggle raw display
\(\nu^{2}\)\(=\) \( \beta_{6} - \beta_{5} + \beta_{4} - \beta_{3} - \beta_{2} - 4 \) Copy content Toggle raw display
\(\nu^{3}\)\(=\) \( \beta_{17} - \beta_{16} + \beta_{12} + \beta_{11} + 2 \beta_{10} + \beta_{9} - \beta_{8} - \beta_{7} - \beta_{6} - \beta_{5} + \beta_{4} + \beta_{3} - 5 \beta_1 \) Copy content Toggle raw display
\(\nu^{4}\)\(=\) \( \beta_{17} - 3 \beta_{16} - 4 \beta_{14} - 2 \beta_{12} + 2 \beta_{11} - 4 \beta_{10} + 5 \beta_{9} + 4 \beta_{7} - 16 \beta_{6} + 16 \beta_{5} - 10 \beta_{4} + 10 \beta_{3} + 12 \beta_{2} + 2 \beta _1 + 30 \) Copy content Toggle raw display
\(\nu^{5}\)\(=\) \( - 13 \beta_{17} + 13 \beta_{16} + 8 \beta_{15} - 14 \beta_{13} - 19 \beta_{12} - 11 \beta_{11} - 27 \beta_{10} - 28 \beta_{9} + 15 \beta_{8} + 15 \beta_{7} + 27 \beta_{6} + 13 \beta_{5} - 18 \beta_{4} - 10 \beta_{3} + 4 \beta_{2} + 35 \beta _1 - 7 \) Copy content Toggle raw display
\(\nu^{6}\)\(=\) \( - 21 \beta_{17} + 57 \beta_{16} + 78 \beta_{14} + 37 \beta_{12} - 37 \beta_{11} + 55 \beta_{10} - 76 \beta_{9} - 4 \beta_{8} - 74 \beta_{7} + 194 \beta_{6} - 194 \beta_{5} + 110 \beta_{4} - 110 \beta_{3} - 138 \beta_{2} - 39 \beta _1 - 282 \) Copy content Toggle raw display
\(\nu^{7}\)\(=\) \( 149 \beta_{17} - 149 \beta_{16} - 152 \beta_{15} + 260 \beta_{13} + 278 \beta_{12} + 126 \beta_{11} + 338 \beta_{10} + 449 \beta_{9} - 183 \beta_{8} - 183 \beta_{7} - 410 \beta_{6} - 150 \beta_{5} + 251 \beta_{4} + 99 \beta_{3} + \cdots + 130 \) Copy content Toggle raw display
\(\nu^{8}\)\(=\) \( 314 \beta_{17} - 826 \beta_{16} - 1140 \beta_{14} - 511 \beta_{12} + 511 \beta_{11} - 644 \beta_{10} + 958 \beta_{9} + 88 \beta_{8} + 1052 \beta_{7} - 2273 \beta_{6} + 2273 \beta_{5} - 1277 \beta_{4} + 1277 \beta_{3} + \cdots + 3003 \) Copy content Toggle raw display
\(\nu^{9}\)\(=\) \( - 1724 \beta_{17} + 1724 \beta_{16} + 2162 \beta_{15} - 3698 \beta_{13} - 3666 \beta_{12} - 1504 \beta_{11} - 4170 \beta_{10} - 6144 \beta_{9} + 2157 \beta_{8} + 2157 \beta_{7} + 5444 \beta_{6} + 1746 \beta_{5} + \cdots - 1849 \) Copy content Toggle raw display
\(\nu^{10}\)\(=\) \( - 4172 \beta_{17} + 10878 \beta_{16} + 15050 \beta_{14} + 6479 \beta_{12} - 6479 \beta_{11} + 7479 \beta_{10} - 11651 \beta_{9} - 1345 \beta_{8} - 13705 \beta_{7} + 26821 \beta_{6} - 26821 \beta_{5} + \cdots - 34186 \) Copy content Toggle raw display
\(\nu^{11}\)\(=\) \( 20350 \beta_{17} - 20350 \beta_{16} - 28008 \beta_{15} + 48126 \beta_{13} + 46240 \beta_{12} + 18232 \beta_{11} + 51098 \beta_{10} + 78874 \beta_{9} - 25519 \beta_{8} - 25519 \beta_{7} - 68877 \beta_{6} + \cdots + 24063 \) Copy content Toggle raw display
\(\nu^{12}\)\(=\) \( 52794 \beta_{17} - 137384 \beta_{16} - 190178 \beta_{14} - 79839 \beta_{12} + 79839 \beta_{11} - 88095 \beta_{10} + 140889 \beta_{9} + 18039 \beta_{8} + 172139 \beta_{7} - 320015 \beta_{6} + \cdots + 402428 \) Copy content Toggle raw display
\(\nu^{13}\)\(=\) \( - 243458 \beta_{17} + 243458 \beta_{16} + 349856 \beta_{15} - 603626 \beta_{13} - 571770 \beta_{12} - 221914 \beta_{11} - 623754 \beta_{10} - 983922 \beta_{9} + 304796 \beta_{8} + \cdots - 301813 \) Copy content Toggle raw display
\(\nu^{14}\)\(=\) \( - 653849 \beta_{17} + 1701303 \beta_{16} + 2355152 \beta_{14} + 974413 \beta_{12} - 974413 \beta_{11} + 1050938 \beta_{10} - 1704787 \beta_{9} - 229045 \beta_{8} - 2126107 \beta_{7} + \cdots - 4815518 \) Copy content Toggle raw display
\(\nu^{15}\)\(=\) \( 2934645 \beta_{17} - 2934645 \beta_{16} - 4303978 \beta_{15} + 7446340 \beta_{13} + 7006094 \beta_{12} + 2702116 \beta_{11} + 7598308 \beta_{10} + 12110003 \beta_{9} - 3667691 \beta_{8} + \cdots + 3723170 \) Copy content Toggle raw display
\(\nu^{16}\)\(=\) \( 8018533 \beta_{17} - 20869105 \beta_{16} - 28887638 \beta_{14} - 11855422 \beta_{12} + 11855422 \beta_{11} - 12640824 \beta_{10} + 20659357 \beta_{9} + 2839124 \beta_{8} + \cdots + 58084703 \) Copy content Toggle raw display
\(\nu^{17}\)\(=\) \( - 35516117 \beta_{17} + 35516117 \beta_{16} + 52598482 \beta_{15} - 91150198 \beta_{13} - 85485223 \beta_{12} - 32886741 \beta_{11} - 92458457 \beta_{10} - 148092538 \beta_{9} + \cdots - 45575099 \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(-\beta_{10}\) \(1\)

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   \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
127.1
1.77390i
1.45077i
2.27298i
2.03053i
0.691444i
1.85421i
2.46793i
0.545199i
3.48640i
2.46793i
0.545199i
3.48640i
2.03053i
0.691444i
1.85421i
1.77390i
1.45077i
2.27298i
−0.900969 0.433884i 0 0.623490 + 0.781831i −0.617224 2.70423i 0 −0.959796 2.46552i −0.222521 0.974928i 0 −0.617224 + 2.70423i
127.2 −0.900969 0.433884i 0 0.623490 + 0.781831i 0.504793 + 2.21164i 0 −0.541999 + 2.58964i −0.222521 0.974928i 0 0.504793 2.21164i
127.3 −0.900969 0.433884i 0 0.623490 + 0.781831i 0.790878 + 3.46506i 0 −1.76964 1.96682i −0.222521 0.974928i 0 0.790878 3.46506i
253.1 0.623490 + 0.781831i 0 −0.222521 + 0.974928i −3.56715 + 1.71785i 0 1.88523 1.85632i −0.900969 + 0.433884i 0 −3.56715 1.71785i
253.2 0.623490 + 0.781831i 0 −0.222521 + 0.974928i −1.21470 + 0.584969i 0 −2.20984 + 1.45485i −0.900969 + 0.433884i 0 −1.21470 0.584969i
253.3 0.623490 + 0.781831i 0 −0.222521 + 0.974928i 3.25739 1.56868i 0 1.11567 + 2.39902i −0.900969 + 0.433884i 0 3.25739 + 1.56868i
379.1 −0.222521 0.974928i 0 −0.900969 + 0.433884i −1.33526 1.67436i 0 0.635079 + 2.56840i 0.623490 + 0.781831i 0 −1.33526 + 1.67436i
379.2 −0.222521 0.974928i 0 −0.900969 + 0.433884i 0.294977 + 0.369889i 0 −0.972480 2.46055i 0.623490 + 0.781831i 0 0.294977 0.369889i
379.3 −0.222521 0.974928i 0 −0.900969 + 0.433884i 1.88629 + 2.36534i 0 2.31779 1.27588i 0.623490 + 0.781831i 0 1.88629 2.36534i
505.1 −0.222521 + 0.974928i 0 −0.900969 0.433884i −1.33526 + 1.67436i 0 0.635079 2.56840i 0.623490 0.781831i 0 −1.33526 1.67436i
505.2 −0.222521 + 0.974928i 0 −0.900969 0.433884i 0.294977 0.369889i 0 −0.972480 + 2.46055i 0.623490 0.781831i 0 0.294977 + 0.369889i
505.3 −0.222521 + 0.974928i 0 −0.900969 0.433884i 1.88629 2.36534i 0 2.31779 + 1.27588i 0.623490 0.781831i 0 1.88629 + 2.36534i
631.1 0.623490 0.781831i 0 −0.222521 0.974928i −3.56715 1.71785i 0 1.88523 + 1.85632i −0.900969 0.433884i 0 −3.56715 + 1.71785i
631.2 0.623490 0.781831i 0 −0.222521 0.974928i −1.21470 0.584969i 0 −2.20984 1.45485i −0.900969 0.433884i 0 −1.21470 + 0.584969i
631.3 0.623490 0.781831i 0 −0.222521 0.974928i 3.25739 + 1.56868i 0 1.11567 2.39902i −0.900969 0.433884i 0 3.25739 1.56868i
757.1 −0.900969 + 0.433884i 0 0.623490 0.781831i −0.617224 + 2.70423i 0 −0.959796 + 2.46552i −0.222521 + 0.974928i 0 −0.617224 2.70423i
757.2 −0.900969 + 0.433884i 0 0.623490 0.781831i 0.504793 2.21164i 0 −0.541999 2.58964i −0.222521 + 0.974928i 0 0.504793 + 2.21164i
757.3 −0.900969 + 0.433884i 0 0.623490 0.781831i 0.790878 3.46506i 0 −1.76964 + 1.96682i −0.222521 + 0.974928i 0 0.790878 + 3.46506i
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 127.3
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
49.e even 7 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 882.2.u.g 18
3.b odd 2 1 98.2.e.b 18
12.b even 2 1 784.2.u.d 18
21.c even 2 1 686.2.e.b 18
21.g even 6 2 686.2.g.g 36
21.h odd 6 2 686.2.g.h 36
49.e even 7 1 inner 882.2.u.g 18
147.k even 14 1 686.2.e.b 18
147.k even 14 1 4802.2.a.c 9
147.l odd 14 1 98.2.e.b 18
147.l odd 14 1 4802.2.a.d 9
147.n odd 42 2 686.2.g.h 36
147.o even 42 2 686.2.g.g 36
588.u even 14 1 784.2.u.d 18
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
98.2.e.b 18 3.b odd 2 1
98.2.e.b 18 147.l odd 14 1
686.2.e.b 18 21.c even 2 1
686.2.e.b 18 147.k even 14 1
686.2.g.g 36 21.g even 6 2
686.2.g.g 36 147.o even 42 2
686.2.g.h 36 21.h odd 6 2
686.2.g.h 36 147.n odd 42 2
784.2.u.d 18 12.b even 2 1
784.2.u.d 18 588.u even 14 1
882.2.u.g 18 1.a even 1 1 trivial
882.2.u.g 18 49.e even 7 1 inner
4802.2.a.c 9 147.k even 14 1
4802.2.a.d 9 147.l odd 14 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5}^{18} + 7 T_{5}^{16} + 28 T_{5}^{15} + 42 T_{5}^{14} - 42 T_{5}^{13} + 2415 T_{5}^{12} - 1372 T_{5}^{11} + 30331 T_{5}^{10} + 10143 T_{5}^{9} + 224861 T_{5}^{8} + 383866 T_{5}^{7} + 1522969 T_{5}^{6} + \cdots + 1750329 \) acting on \(S_{2}^{\mathrm{new}}(882, [\chi])\). Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( (T^{6} + T^{5} + T^{4} + T^{3} + T^{2} + T + 1)^{3} \) Copy content Toggle raw display
$3$ \( T^{18} \) Copy content Toggle raw display
$5$ \( T^{18} + 7 T^{16} + 28 T^{15} + \cdots + 1750329 \) Copy content Toggle raw display
$7$ \( T^{18} + T^{17} + 22 T^{16} + \cdots + 40353607 \) Copy content Toggle raw display
$11$ \( T^{18} + 7 T^{17} + 28 T^{16} + \cdots + 1750329 \) Copy content Toggle raw display
$13$ \( T^{18} + 10 T^{17} + 60 T^{16} + \cdots + 253009 \) Copy content Toggle raw display
$17$ \( T^{18} + T^{17} + 9 T^{16} + \cdots + 78428736 \) Copy content Toggle raw display
$19$ \( (T^{9} + 22 T^{8} + 189 T^{7} + 778 T^{6} + \cdots + 1597)^{2} \) Copy content Toggle raw display
$23$ \( T^{18} + 21 T^{17} + \cdots + 371981669409 \) Copy content Toggle raw display
$29$ \( T^{18} + 11 T^{17} + \cdots + 86066940809529 \) Copy content Toggle raw display
$31$ \( (T^{9} + 12 T^{8} - 56 T^{7} - 1240 T^{6} + \cdots - 24347)^{2} \) Copy content Toggle raw display
$37$ \( T^{18} + 13 T^{17} + \cdots + 1254429120169 \) Copy content Toggle raw display
$41$ \( T^{18} + 8 T^{17} - 26 T^{16} + \cdots + 463067361 \) Copy content Toggle raw display
$43$ \( T^{18} + 24 T^{17} + \cdots + 2751859630129 \) Copy content Toggle raw display
$47$ \( T^{18} + 40 T^{17} + \cdots + 13724825409 \) Copy content Toggle raw display
$53$ \( T^{18} + 10 T^{17} + \cdots + 9696939948081 \) Copy content Toggle raw display
$59$ \( T^{18} + 13 T^{17} + \cdots + 3058927542441 \) Copy content Toggle raw display
$61$ \( T^{18} - 27 T^{17} + \cdots + 18702537077449 \) Copy content Toggle raw display
$67$ \( (T^{9} + 43 T^{8} + 653 T^{7} + \cdots - 73289)^{2} \) Copy content Toggle raw display
$71$ \( T^{18} + \cdots + 700061588590329 \) Copy content Toggle raw display
$73$ \( T^{18} - 5 T^{17} + \cdots + 10720627932169 \) Copy content Toggle raw display
$79$ \( (T^{9} + 33 T^{8} + 225 T^{7} + \cdots + 10692919)^{2} \) Copy content Toggle raw display
$83$ \( T^{18} + \cdots + 115077625675776 \) Copy content Toggle raw display
$89$ \( T^{18} + 62 T^{17} + \cdots + 60940353321 \) Copy content Toggle raw display
$97$ \( (T^{9} + 16 T^{8} - 238 T^{7} + \cdots + 1259329)^{2} \) Copy content Toggle raw display
show more
show less