Properties

Label 2700.3.p.d
Level $2700$
Weight $3$
Character orbit 2700.p
Analytic conductor $73.570$
Analytic rank $0$
Dimension $16$
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] = [2700,3,Mod(1601,2700)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2700, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2700.1601");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2700 = 2^{2} \cdot 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2700.p (of order \(6\), degree \(2\), not 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: \(73.5696713773\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 2 x^{15} + 10 x^{14} - 12 x^{13} + 6 x^{12} - 27 x^{11} - 585 x^{10} + 3618 x^{9} - 12150 x^{8} + 32562 x^{7} - 47385 x^{6} - 19683 x^{5} + 39366 x^{4} + \cdots + 43046721 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{41}]\)
Coefficient ring index: \( 3^{14} \)
Twist minimal: no (minimal twist has level 900)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

$q$-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 \(1,\beta_1,\ldots,\beta_{15}\) for the coefficient ring described below. We also show the integral \(q\)-expansion of the trace form.

\(f(q)\) \(=\) \( q - \beta_{7} q^{7}+O(q^{10}) \) Copy content Toggle raw display \( q - \beta_{7} q^{7} + \beta_{10} q^{11} + ( - \beta_{2} + \beta_1) q^{13} + (\beta_{14} - \beta_{13} + \beta_{10} - \beta_{9} - \beta_{7} + \beta_{6} + \beta_{3} - \beta_{2} + \beta_1 + 1) q^{17} + (\beta_{15} + \beta_{13} - \beta_{12} - \beta_{10} - \beta_{9} - \beta_{5} - \beta_1) q^{19} + ( - \beta_{15} + \beta_{14} - \beta_{13} + \beta_{9} - \beta_{7} + \beta_{5} + \beta_{2} - 2) q^{23} + (\beta_{14} + \beta_{11} - \beta_{10} + \beta_{7} - 2 \beta_{5} - \beta_{4} - \beta_{2} - 2 \beta_1 - 1) q^{29} + ( - \beta_{15} + \beta_{14} - 2 \beta_{13} + \beta_{12} + \beta_{11} - \beta_{9} + \beta_{6} + \beta_{3} + \cdots + 2 \beta_1) q^{31}+ \cdots + (2 \beta_{15} + 2 \beta_{13} + 2 \beta_{12} + 2 \beta_{11} + 4 \beta_{10} - 6 \beta_{8} + \cdots + 2) q^{97}+O(q^{100}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - q^{7} - 10 q^{13} + 2 q^{19} - 27 q^{23} - 9 q^{29} + 8 q^{31} - 22 q^{37} - 54 q^{41} + 44 q^{43} + 108 q^{47} - 45 q^{49} - 9 q^{59} - 55 q^{61} - 28 q^{67} + 86 q^{73} - 342 q^{77} + 11 q^{79} + 306 q^{83} - 134 q^{91} + 41 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Basis of coefficient ring in terms of a root \(\nu\) of \( x^{16} - 2 x^{15} + 10 x^{14} - 12 x^{13} + 6 x^{12} - 27 x^{11} - 585 x^{10} + 3618 x^{9} - 12150 x^{8} + 32562 x^{7} - 47385 x^{6} - 19683 x^{5} + 39366 x^{4} + \cdots + 43046721 \) : Copy content Toggle raw display

\(\beta_{1}\)\(=\) \( ( - 175 \nu^{15} - 955 \nu^{14} + 450005 \nu^{13} - 19617 \nu^{12} - 1162401 \nu^{11} - 167130 \nu^{10} + 5457609 \nu^{9} - 146668455 \nu^{8} + \cdots + 1222799505633 ) / 36541883160 \) Copy content Toggle raw display
\(\beta_{2}\)\(=\) \( ( - 4099 \nu^{15} + 12833 \nu^{14} - 9679 \nu^{13} - 10653 \nu^{12} + 361803 \nu^{11} - 1741122 \nu^{10} + 5995773 \nu^{9} - 18242955 \nu^{8} + \cdots + 54664552701 ) / 36541883160 \) Copy content Toggle raw display
\(\beta_{3}\)\(=\) \( ( - 6637 \nu^{15} + 6839 \nu^{14} - 62977 \nu^{13} - 1044915 \nu^{12} + 6273021 \nu^{11} - 22610286 \nu^{10} + 56594691 \nu^{9} - 133510005 \nu^{8} + \cdots - 5151257613 ) / 36541883160 \) Copy content Toggle raw display
\(\beta_{4}\)\(=\) \( ( 3005 \nu^{15} - 46591 \nu^{14} + 136241 \nu^{13} - 478077 \nu^{12} + 1897635 \nu^{11} - 3804138 \nu^{10} - 1056627 \nu^{9} + 29472525 \nu^{8} + \cdots - 249532275699 ) / 12180627720 \) Copy content Toggle raw display
\(\beta_{5}\)\(=\) \( ( 655 \nu^{15} - 1301 \nu^{14} + 10591 \nu^{13} - 9867 \nu^{12} - 49035 \nu^{11} + 109782 \nu^{10} - 306657 \nu^{9} + 1430595 \nu^{8} - 5501925 \nu^{7} + \cdots + 4565609631 ) / 2030104620 \) Copy content Toggle raw display
\(\beta_{6}\)\(=\) \( ( - 6673 \nu^{15} + 17243 \nu^{14} - 56893 \nu^{13} + 261417 \nu^{12} + 546105 \nu^{11} - 47142 \nu^{10} + 4232079 \nu^{9} - 15060465 \nu^{8} + \cdots - 67374495657 ) / 12180627720 \) Copy content Toggle raw display
\(\beta_{7}\)\(=\) \( ( - 10129 \nu^{15} - 32833 \nu^{14} + 98447 \nu^{13} + 6897 \nu^{12} + 298569 \nu^{11} + 2217510 \nu^{10} + 3017727 \nu^{9} - 22298625 \nu^{8} + \cdots - 70544009781 ) / 18270941580 \) Copy content Toggle raw display
\(\beta_{8}\)\(=\) \( ( - 3397 \nu^{15} + 8639 \nu^{14} - 29317 \nu^{13} + 218217 \nu^{12} - 1008123 \nu^{11} + 3581334 \nu^{10} - 6198453 \nu^{9} + 5390415 \nu^{8} + \cdots + 40420871019 ) / 6090313860 \) Copy content Toggle raw display
\(\beta_{9}\)\(=\) \( ( 6937 \nu^{15} - 27959 \nu^{14} + 120625 \nu^{13} - 571827 \nu^{12} + 1574601 \nu^{11} - 1945350 \nu^{10} - 799029 \nu^{9} + 34100325 \nu^{8} + \cdots - 66660238953 ) / 9135470790 \) Copy content Toggle raw display
\(\beta_{10}\)\(=\) \( ( - 27817 \nu^{15} + 106331 \nu^{14} - 379645 \nu^{13} + 604497 \nu^{12} + 150969 \nu^{11} - 1825038 \nu^{10} + 10942983 \nu^{9} - 86884785 \nu^{8} + \cdots - 71366680449 ) / 36541883160 \) Copy content Toggle raw display
\(\beta_{11}\)\(=\) \( ( 7547 \nu^{15} + 13733 \nu^{14} - 3325 \nu^{13} - 40191 \nu^{12} + 213789 \nu^{11} - 3108888 \nu^{10} + 8237043 \nu^{9} - 14019615 \nu^{8} + \cdots + 94506684471 ) / 9135470790 \) Copy content Toggle raw display
\(\beta_{12}\)\(=\) \( ( 1997 \nu^{15} - 7639 \nu^{14} + 27881 \nu^{13} - 125889 \nu^{12} + 309711 \nu^{11} - 238842 \nu^{10} - 843759 \nu^{9} + 9604845 \nu^{8} - 30765015 \nu^{7} + \cdots - 24947434863 ) / 2030104620 \) Copy content Toggle raw display
\(\beta_{13}\)\(=\) \( ( 9625 \nu^{15} + 955 \nu^{14} - 17303 \nu^{13} + 222873 \nu^{12} - 25059 \nu^{11} - 2163564 \nu^{10} + 7178391 \nu^{9} - 20700225 \nu^{8} + \cdots + 154839055437 ) / 9135470790 \) Copy content Toggle raw display
\(\beta_{14}\)\(=\) \( ( 15275 \nu^{15} - 21505 \nu^{14} + 271415 \nu^{13} - 461859 \nu^{12} - 46347 \nu^{11} + 458730 \nu^{10} - 11790477 \nu^{9} + 39045915 \nu^{8} + \cdots + 280436632731 ) / 12180627720 \) Copy content Toggle raw display
\(\beta_{15}\)\(=\) \( ( 2066 \nu^{15} - 8128 \nu^{14} + 32378 \nu^{13} - 61512 \nu^{12} + 125553 \nu^{11} - 189837 \nu^{10} + 542691 \nu^{9} + 2641275 \nu^{8} - 11815875 \nu^{7} + \cdots + 17432327682 ) / 1522578465 \) Copy content Toggle raw display
\(\nu\)\(=\) \( ( -\beta_{11} - 2\beta_{8} - \beta_{4} - \beta_{3} + 2\beta_{2} ) / 9 \) Copy content Toggle raw display
\(\nu^{2}\)\(=\) \( ( -3\beta_{12} - \beta_{11} + 3\beta_{9} - 2\beta_{8} - \beta_{4} - \beta_{3} - 4\beta_{2} - 6 ) / 9 \) Copy content Toggle raw display
\(\nu^{3}\)\(=\) \( ( 9 \beta_{15} + 9 \beta_{14} - 3 \beta_{12} - 7 \beta_{11} + 18 \beta_{10} - 6 \beta_{9} + \beta_{8} + 9 \beta_{5} - \beta_{4} + 8 \beta_{3} - 25 \beta_{2} - 9 \beta _1 + 9 ) / 9 \) Copy content Toggle raw display
\(\nu^{4}\)\(=\) \( ( 18 \beta_{15} - 27 \beta_{14} - 9 \beta_{13} + 6 \beta_{12} - 16 \beta_{11} + 18 \beta_{10} - 6 \beta_{9} + 16 \beta_{8} - 54 \beta_{7} + 18 \beta_{6} + 90 \beta_{5} + 14 \beta_{4} + 14 \beta_{3} - 31 \beta_{2} + 18 \beta _1 + 114 ) / 9 \) Copy content Toggle raw display
\(\nu^{5}\)\(=\) \( ( - 72 \beta_{15} - 45 \beta_{14} + 81 \beta_{13} + 24 \beta_{12} - 31 \beta_{11} - 9 \beta_{10} + 66 \beta_{9} + 19 \beta_{8} + 27 \beta_{7} - 54 \beta_{6} + 144 \beta_{5} + 14 \beta_{4} - 31 \beta_{3} + 407 \beta_{2} + 18 \beta _1 - 6 ) / 9 \) Copy content Toggle raw display
\(\nu^{6}\)\(=\) \( ( 27 \beta_{15} - 306 \beta_{14} + 36 \beta_{13} + 105 \beta_{12} + 164 \beta_{11} + 234 \beta_{10} + 129 \beta_{9} - 53 \beta_{8} - 54 \beta_{7} - 180 \beta_{6} + 9 \beta_{5} + 161 \beta_{4} - 442 \beta_{3} + 1154 \beta_{2} + 207 \beta _1 + 828 ) / 9 \) Copy content Toggle raw display
\(\nu^{7}\)\(=\) \( ( 612 \beta_{15} - 135 \beta_{14} + 207 \beta_{13} + 60 \beta_{12} - 826 \beta_{11} + 342 \beta_{10} - 33 \beta_{9} + 178 \beta_{8} - 945 \beta_{7} - 171 \beta_{6} - 234 \beta_{5} - 67 \beta_{4} - 67 \beta_{3} + 3641 \beta_{2} + \cdots - 13089 ) / 9 \) Copy content Toggle raw display
\(\nu^{8}\)\(=\) \( ( 1197 \beta_{15} + 954 \beta_{14} + 837 \beta_{13} - 1542 \beta_{12} - 724 \beta_{11} - 1386 \beta_{10} + 822 \beta_{9} + 3709 \beta_{8} - 1431 \beta_{7} - 270 \beta_{6} + 144 \beta_{5} + 1346 \beta_{4} + 1004 \beta_{3} + \cdots - 2031 ) / 9 \) Copy content Toggle raw display
\(\nu^{9}\)\(=\) \( ( 3510 \beta_{15} + 18 \beta_{14} + 2223 \beta_{13} + 3777 \beta_{12} + 2225 \beta_{11} - 333 \beta_{10} - 1923 \beta_{9} + 748 \beta_{8} + 8694 \beta_{7} - 3825 \beta_{6} + 2277 \beta_{5} - 5230 \beta_{4} - 3241 \beta_{3} + \cdots - 14670 ) / 9 \) Copy content Toggle raw display
\(\nu^{10}\)\(=\) \( ( - 10809 \beta_{15} - 32616 \beta_{14} - 2547 \beta_{13} + 21309 \beta_{12} + 22484 \beta_{11} - 10512 \beta_{10} + 25698 \beta_{9} - 2828 \beta_{8} + 13878 \beta_{7} + 9711 \beta_{6} + 171 \beta_{5} + \cdots + 21822 ) / 9 \) Copy content Toggle raw display
\(\nu^{11}\)\(=\) \( ( - 30069 \beta_{15} + 27441 \beta_{14} + 49275 \beta_{13} + 29265 \beta_{12} + 9221 \beta_{11} + 39519 \beta_{10} + 46074 \beta_{9} - 15713 \beta_{8} + 79974 \beta_{7} + 39177 \beta_{6} + \cdots + 201549 ) / 9 \) Copy content Toggle raw display
\(\nu^{12}\)\(=\) \( ( 183249 \beta_{15} + 88875 \beta_{14} + 6111 \beta_{13} - 95340 \beta_{12} - 23092 \beta_{11} + 117846 \beta_{10} - 151476 \beta_{9} - 83663 \beta_{8} - 86319 \beta_{7} + 241119 \beta_{6} + \cdots + 686196 ) / 9 \) Copy content Toggle raw display
\(\nu^{13}\)\(=\) \( ( - 48231 \beta_{15} + 616032 \beta_{14} + 57636 \beta_{13} - 210243 \beta_{12} - 259981 \beta_{11} - 278703 \beta_{10} - 135600 \beta_{9} - 210278 \beta_{8} + 300861 \beta_{7} + \cdots - 9517305 ) / 9 \) Copy content Toggle raw display
\(\nu^{14}\)\(=\) \( ( - 1535859 \beta_{15} + 154773 \beta_{14} - 570780 \beta_{13} + 576690 \beta_{12} + 3217127 \beta_{11} + 1087659 \beta_{10} + 1088355 \beta_{9} + 498655 \beta_{8} + 1063881 \beta_{7} + \cdots - 1624407 ) / 9 \) Copy content Toggle raw display
\(\nu^{15}\)\(=\) \( ( 365661 \beta_{15} - 3964932 \beta_{14} + 1267038 \beta_{13} + 6857646 \beta_{12} + 5734181 \beta_{11} + 6430338 \beta_{10} - 1196727 \beta_{9} - 1374488 \beta_{8} - 1265355 \beta_{7} + \cdots - 18589725 ) / 9 \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2700\mathbb{Z}\right)^\times\).

\(n\) \(1001\) \(1351\) \(2377\)
\(\chi(n)\) \(\beta_{2}\) \(1\) \(1\)

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   \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1601.1
2.47109 1.70110i
1.13333 + 2.77769i
−1.82249 + 2.38297i
−1.69925 2.47235i
−2.99949 + 0.0553819i
2.94519 + 0.570848i
0.127146 + 2.99730i
0.844479 2.87869i
2.47109 + 1.70110i
1.13333 2.77769i
−1.82249 2.38297i
−1.69925 + 2.47235i
−2.99949 0.0553819i
2.94519 0.570848i
0.127146 2.99730i
0.844479 + 2.87869i
0 0 0 0 0 −5.40503 + 9.36178i 0 0 0
1601.2 0 0 0 0 0 −4.13058 + 7.15437i 0 0 0
1601.3 0 0 0 0 0 −2.32731 + 4.03103i 0 0 0
1601.4 0 0 0 0 0 −1.73252 + 3.00081i 0 0 0
1601.5 0 0 0 0 0 0.725042 1.25581i 0 0 0
1601.6 0 0 0 0 0 2.71262 4.69840i 0 0 0
1601.7 0 0 0 0 0 4.69530 8.13249i 0 0 0
1601.8 0 0 0 0 0 4.96248 8.59526i 0 0 0
2501.1 0 0 0 0 0 −5.40503 9.36178i 0 0 0
2501.2 0 0 0 0 0 −4.13058 7.15437i 0 0 0
2501.3 0 0 0 0 0 −2.32731 4.03103i 0 0 0
2501.4 0 0 0 0 0 −1.73252 3.00081i 0 0 0
2501.5 0 0 0 0 0 0.725042 + 1.25581i 0 0 0
2501.6 0 0 0 0 0 2.71262 + 4.69840i 0 0 0
2501.7 0 0 0 0 0 4.69530 + 8.13249i 0 0 0
2501.8 0 0 0 0 0 4.96248 + 8.59526i 0 0 0
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1601.8
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
9.d odd 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2700.3.p.d 16
3.b odd 2 1 900.3.p.e yes 16
5.b even 2 1 2700.3.p.e 16
5.c odd 4 2 2700.3.u.d 32
9.c even 3 1 900.3.p.e yes 16
9.d odd 6 1 inner 2700.3.p.d 16
15.d odd 2 1 900.3.p.d 16
15.e even 4 2 900.3.u.d 32
45.h odd 6 1 2700.3.p.e 16
45.j even 6 1 900.3.p.d 16
45.k odd 12 2 900.3.u.d 32
45.l even 12 2 2700.3.u.d 32
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
900.3.p.d 16 15.d odd 2 1
900.3.p.d 16 45.j even 6 1
900.3.p.e yes 16 3.b odd 2 1
900.3.p.e yes 16 9.c even 3 1
900.3.u.d 32 15.e even 4 2
900.3.u.d 32 45.k odd 12 2
2700.3.p.d 16 1.a even 1 1 trivial
2700.3.p.d 16 9.d odd 6 1 inner
2700.3.p.e 16 5.b even 2 1
2700.3.p.e 16 45.h odd 6 1
2700.3.u.d 32 5.c odd 4 2
2700.3.u.d 32 45.l even 12 2

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{7}^{16} + T_{7}^{15} + 219 T_{7}^{14} + 218 T_{7}^{13} + 33299 T_{7}^{12} + 36030 T_{7}^{11} + 2596750 T_{7}^{10} + 3758746 T_{7}^{9} + 147133197 T_{7}^{8} + 209228176 T_{7}^{7} + \cdots + 1115296517776 \) acting on \(S_{3}^{\mathrm{new}}(2700, [\chi])\). Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T^{16} \) Copy content Toggle raw display
$3$ \( T^{16} \) Copy content Toggle raw display
$5$ \( T^{16} \) Copy content Toggle raw display
$7$ \( T^{16} + T^{15} + \cdots + 1115296517776 \) Copy content Toggle raw display
$11$ \( T^{16} + \cdots + 318893306317056 \) Copy content Toggle raw display
$13$ \( T^{16} + \cdots + 206194665870400 \) Copy content Toggle raw display
$17$ \( T^{16} + 2586 T^{14} + \cdots + 47\!\cdots\!16 \) Copy content Toggle raw display
$19$ \( (T^{8} - T^{7} - 1478 T^{6} + \cdots + 261665566)^{2} \) Copy content Toggle raw display
$23$ \( T^{16} + 27 T^{15} + \cdots + 74\!\cdots\!16 \) Copy content Toggle raw display
$29$ \( T^{16} + 9 T^{15} + \cdots + 38\!\cdots\!00 \) Copy content Toggle raw display
$31$ \( T^{16} - 8 T^{15} + \cdots + 39\!\cdots\!16 \) Copy content Toggle raw display
$37$ \( (T^{8} + 11 T^{7} - 6197 T^{6} + \cdots + 38426783044)^{2} \) Copy content Toggle raw display
$41$ \( T^{16} + 54 T^{15} + \cdots + 56\!\cdots\!00 \) Copy content Toggle raw display
$43$ \( T^{16} - 44 T^{15} + \cdots + 10\!\cdots\!41 \) Copy content Toggle raw display
$47$ \( T^{16} - 108 T^{15} + \cdots + 19\!\cdots\!56 \) Copy content Toggle raw display
$53$ \( T^{16} + 32016 T^{14} + \cdots + 32\!\cdots\!76 \) Copy content Toggle raw display
$59$ \( T^{16} + 9 T^{15} + \cdots + 68\!\cdots\!01 \) Copy content Toggle raw display
$61$ \( T^{16} + 55 T^{15} + \cdots + 22\!\cdots\!16 \) Copy content Toggle raw display
$67$ \( T^{16} + 28 T^{15} + \cdots + 10\!\cdots\!76 \) Copy content Toggle raw display
$71$ \( T^{16} + 46188 T^{14} + \cdots + 41\!\cdots\!56 \) Copy content Toggle raw display
$73$ \( (T^{8} - 43 T^{7} + \cdots + 17\!\cdots\!46)^{2} \) Copy content Toggle raw display
$79$ \( T^{16} - 11 T^{15} + \cdots + 20\!\cdots\!00 \) Copy content Toggle raw display
$83$ \( T^{16} - 306 T^{15} + \cdots + 17\!\cdots\!81 \) Copy content Toggle raw display
$89$ \( T^{16} + 79173 T^{14} + \cdots + 24\!\cdots\!21 \) Copy content Toggle raw display
$97$ \( T^{16} - 41 T^{15} + \cdots + 29\!\cdots\!21 \) Copy content Toggle raw display
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