Properties

Label 483.2.i.h
Level $483$
Weight $2$
Character orbit 483.i
Analytic conductor $3.857$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 483.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.85677441763\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Defining polynomial: \( x^{20} - 3 x^{19} + 22 x^{18} - 43 x^{17} + 245 x^{16} - 416 x^{15} + 1707 x^{14} - 2021 x^{13} + 7135 x^{12} - 6640 x^{11} + 20315 x^{10} - 10565 x^{9} + 29358 x^{8} - 9009 x^{7} + \cdots + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

$q$-expansion

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.

\(f(q)\) \(=\) \( q + (\beta_{4} + \beta_1) q^{2} - \beta_{9} q^{3} + ( - \beta_{17} + \beta_{9} - \beta_{8} - \beta_1) q^{4} + (\beta_{18} + \beta_{9} - \beta_{6} + 1) q^{5} + \beta_{4} q^{6} + ( - \beta_{16} + \beta_{14}) q^{7} + (\beta_{14} + \beta_{12} + \beta_{11} + \beta_{10} - \beta_{7} + \beta_{5} - 3 \beta_{4} + \beta_{3}) q^{8} + ( - \beta_{9} - 1) q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + (\beta_{4} + \beta_1) q^{2} - \beta_{9} q^{3} + ( - \beta_{17} + \beta_{9} - \beta_{8} - \beta_1) q^{4} + (\beta_{18} + \beta_{9} - \beta_{6} + 1) q^{5} + \beta_{4} q^{6} + ( - \beta_{16} + \beta_{14}) q^{7} + (\beta_{14} + \beta_{12} + \beta_{11} + \beta_{10} - \beta_{7} + \beta_{5} - 3 \beta_{4} + \beta_{3}) q^{8} + ( - \beta_{9} - 1) q^{9} + (\beta_{19} - \beta_{17} + \beta_{16} + \beta_{15} - 2 \beta_{14} - \beta_{13} - \beta_{12} + \beta_{9} + \beta_{7} + \beta_{6} + \beta_{5}) q^{10} + (\beta_{19} + \beta_{18} + \beta_{16} + \beta_{15} - \beta_{14} - \beta_{11} + \beta_{10} + \beta_{9} - \beta_1) q^{11} + ( - \beta_{17} + \beta_{9} - \beta_{8} + \beta_{2} - \beta_1 + 1) q^{12} + ( - \beta_{14} - \beta_{12} + \beta_{4} - \beta_{3} + \beta_{2}) q^{13} + ( - \beta_{19} - \beta_{18} + \beta_{17} + \beta_{13} + \beta_{12} + \beta_{11} - \beta_{10} + \beta_{8} - \beta_{7} + \cdots + 1) q^{14}+ \cdots + (\beta_{7} + 1) q^{99}+O(q^{100}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 3 q^{2} + 10 q^{3} - 15 q^{4} + 5 q^{5} - 6 q^{6} + 18 q^{8} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 3 q^{2} + 10 q^{3} - 15 q^{4} + 5 q^{5} - 6 q^{6} + 18 q^{8} - 10 q^{9} - 11 q^{10} - 8 q^{11} + 15 q^{12} + 11 q^{14} + 10 q^{15} - 37 q^{16} + 11 q^{17} - 3 q^{18} - q^{19} - 30 q^{20} + 12 q^{22} - 10 q^{23} + 9 q^{24} - 21 q^{25} - q^{26} - 20 q^{27} + 44 q^{28} + 44 q^{29} + 11 q^{30} + 3 q^{31} - 11 q^{32} + 8 q^{33} - 6 q^{34} - 9 q^{35} + 30 q^{36} + 3 q^{37} - 16 q^{38} - 39 q^{40} - 52 q^{41} + 7 q^{42} + 54 q^{43} - 16 q^{44} + 5 q^{45} - 3 q^{46} - 11 q^{47} - 74 q^{48} + 22 q^{49} + 4 q^{50} - 11 q^{51} - 29 q^{52} - 5 q^{53} + 3 q^{54} - 36 q^{55} + 43 q^{56} - 2 q^{57} - 16 q^{58} + 10 q^{59} - 15 q^{60} - 22 q^{61} - 64 q^{62} + 138 q^{64} + 11 q^{65} + 6 q^{66} + 2 q^{67} + 21 q^{68} - 20 q^{69} + 84 q^{70} + 54 q^{71} - 9 q^{72} + 8 q^{73} - 14 q^{74} + 21 q^{75} - 44 q^{76} + 8 q^{77} - 2 q^{78} - 21 q^{79} + 53 q^{80} - 10 q^{81} - 36 q^{82} - 24 q^{83} + 25 q^{84} + 46 q^{85} - 18 q^{86} + 22 q^{87} + 10 q^{88} - 6 q^{89} + 22 q^{90} - 62 q^{91} + 30 q^{92} - 3 q^{93} - 35 q^{94} - 44 q^{95} + 11 q^{96} + 12 q^{97} + 2 q^{98} + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Basis of coefficient ring in terms of a root \(\nu\) of \( x^{20} - 3 x^{19} + 22 x^{18} - 43 x^{17} + 245 x^{16} - 416 x^{15} + 1707 x^{14} - 2021 x^{13} + 7135 x^{12} - 6640 x^{11} + 20315 x^{10} - 10565 x^{9} + 29358 x^{8} - 9009 x^{7} + \cdots + 4 \) : Copy content Toggle raw display

\(\beta_{1}\)\(=\) \( \nu \) Copy content Toggle raw display
\(\beta_{2}\)\(=\) \( ( - 22\!\cdots\!01 \nu^{19} + \cdots - 20\!\cdots\!14 ) / 69\!\cdots\!38 \) Copy content Toggle raw display
\(\beta_{3}\)\(=\) \( ( 22\!\cdots\!60 \nu^{19} + \cdots - 13\!\cdots\!22 ) / 36\!\cdots\!14 \) Copy content Toggle raw display
\(\beta_{4}\)\(=\) \( ( - 62\!\cdots\!25 \nu^{19} + \cdots + 18\!\cdots\!90 ) / 69\!\cdots\!38 \) Copy content Toggle raw display
\(\beta_{5}\)\(=\) \( ( - 18\!\cdots\!73 \nu^{19} + \cdots - 89\!\cdots\!04 ) / 36\!\cdots\!14 \) Copy content Toggle raw display
\(\beta_{6}\)\(=\) \( ( 20\!\cdots\!92 \nu^{19} + \cdots + 13\!\cdots\!44 ) / 36\!\cdots\!14 \) Copy content Toggle raw display
\(\beta_{7}\)\(=\) \( ( - 51\!\cdots\!36 \nu^{19} + \cdots - 12\!\cdots\!86 ) / 36\!\cdots\!14 \) Copy content Toggle raw display
\(\beta_{8}\)\(=\) \( ( - 14\!\cdots\!44 \nu^{19} + \cdots + 92\!\cdots\!32 ) / 36\!\cdots\!14 \) Copy content Toggle raw display
\(\beta_{9}\)\(=\) \( ( 90\!\cdots\!45 \nu^{19} + \cdots - 45\!\cdots\!36 ) / 13\!\cdots\!76 \) Copy content Toggle raw display
\(\beta_{10}\)\(=\) \( ( 74\!\cdots\!85 \nu^{19} + \cdots + 40\!\cdots\!04 ) / 73\!\cdots\!28 \) Copy content Toggle raw display
\(\beta_{11}\)\(=\) \( ( - 77\!\cdots\!09 \nu^{19} + \cdots + 28\!\cdots\!96 ) / 73\!\cdots\!28 \) Copy content Toggle raw display
\(\beta_{12}\)\(=\) \( ( 10\!\cdots\!99 \nu^{19} + \cdots - 47\!\cdots\!12 ) / 73\!\cdots\!28 \) Copy content Toggle raw display
\(\beta_{13}\)\(=\) \( ( - 55\!\cdots\!40 \nu^{19} + \cdots + 11\!\cdots\!72 ) / 36\!\cdots\!14 \) Copy content Toggle raw display
\(\beta_{14}\)\(=\) \( ( - 11\!\cdots\!71 \nu^{19} + \cdots - 21\!\cdots\!28 ) / 73\!\cdots\!28 \) Copy content Toggle raw display
\(\beta_{15}\)\(=\) \( ( - 71\!\cdots\!56 \nu^{19} + \cdots - 83\!\cdots\!36 ) / 36\!\cdots\!14 \) Copy content Toggle raw display
\(\beta_{16}\)\(=\) \( ( - 73\!\cdots\!06 \nu^{19} + \cdots - 22\!\cdots\!76 ) / 36\!\cdots\!14 \) Copy content Toggle raw display
\(\beta_{17}\)\(=\) \( ( 17\!\cdots\!37 \nu^{19} + \cdots - 93\!\cdots\!88 ) / 73\!\cdots\!28 \) Copy content Toggle raw display
\(\beta_{18}\)\(=\) \( ( - 18\!\cdots\!67 \nu^{19} + \cdots + 14\!\cdots\!12 ) / 73\!\cdots\!28 \) Copy content Toggle raw display
\(\beta_{19}\)\(=\) \( ( 18\!\cdots\!75 \nu^{19} + \cdots - 11\!\cdots\!52 ) / 73\!\cdots\!28 \) Copy content Toggle raw display
\(\nu\)\(=\) \( \beta_1 \) Copy content Toggle raw display
\(\nu^{2}\)\(=\) \( \beta_{17} - 3\beta_{9} + \beta_{8} - \beta_{2} + \beta _1 - 3 \) Copy content Toggle raw display
\(\nu^{3}\)\(=\) \( -\beta_{14} - \beta_{12} - \beta_{11} - \beta_{10} + \beta_{7} - \beta_{5} + 7\beta_{4} - \beta_{3} \) Copy content Toggle raw display
\(\nu^{4}\)\(=\) \( \beta_{19} - 8 \beta_{17} - \beta_{16} - \beta_{14} - \beta_{10} + 17 \beta_{9} - 7 \beta_{8} + \beta_{7} + \beta_{6} + \beta_{4} - 7 \beta_1 \) Copy content Toggle raw display
\(\nu^{5}\)\(=\) \( - 3 \beta_{19} - 10 \beta_{18} + 2 \beta_{17} - \beta_{16} - 2 \beta_{15} + 11 \beta_{14} + 10 \beta_{13} + 11 \beta_{12} + 11 \beta_{11} - 2 \beta_{10} - 12 \beta_{7} - 2 \beta_{6} - 41 \beta_{4} + 8 \beta_{3} - 29 \beta_1 \) Copy content Toggle raw display
\(\nu^{6}\)\(=\) \( 13 \beta_{16} - 13 \beta_{15} + \beta_{14} + \beta_{12} + 12 \beta_{11} + 12 \beta_{10} - 14 \beta_{7} - 14 \beta_{6} + \beta_{5} - 15 \beta_{4} + 15 \beta_{3} + 46 \beta_{2} + 112 \) Copy content Toggle raw display
\(\nu^{7}\)\(=\) \( 40 \beta_{19} + 83 \beta_{18} - 28 \beta_{17} + 28 \beta_{16} + 12 \beta_{15} - 26 \beta_{14} - 87 \beta_{13} - 30 \beta_{12} - 26 \beta_{11} + 99 \beta_{10} - 2 \beta_{8} + 14 \beta_{7} + 14 \beta_{6} + 87 \beta_{5} - 73 \beta_{4} + 179 \beta_1 \) Copy content Toggle raw display
\(\nu^{8}\)\(=\) \( - 65 \beta_{19} + 444 \beta_{17} + 2 \beta_{16} + 131 \beta_{15} + 81 \beta_{14} - 20 \beta_{13} - 46 \beta_{12} - 141 \beta_{11} + 28 \beta_{10} - 779 \beta_{9} + 311 \beta_{8} + 48 \beta_{7} + 48 \beta_{6} + 40 \beta_{4} - 153 \beta_{3} + \cdots - 779 \) Copy content Toggle raw display
\(\nu^{9}\)\(=\) \( - 177 \beta_{16} + 177 \beta_{15} - 539 \beta_{14} - 539 \beta_{12} - 581 \beta_{11} - 581 \beta_{10} + 831 \beta_{7} + 179 \beta_{6} - 724 \beta_{5} + 2738 \beta_{4} - 474 \beta_{3} + 30 \beta_{2} + 4 \) Copy content Toggle raw display
\(\nu^{10}\)\(=\) \( 433 \beta_{19} + 4 \beta_{18} - 3278 \beta_{17} - 1195 \beta_{16} - 44 \beta_{15} - 673 \beta_{14} + 261 \beta_{13} + 434 \beta_{12} + 284 \beta_{11} - 1262 \beta_{10} + 5582 \beta_{9} - 2176 \beta_{8} + 717 \beta_{7} + \cdots - 2026 \beta_1 \) Copy content Toggle raw display
\(\nu^{11}\)\(=\) \( - 3452 \beta_{19} - 5001 \beta_{18} + 2464 \beta_{17} - 1026 \beta_{16} - 2722 \beta_{15} + 6345 \beta_{14} + 5889 \beta_{13} + 7015 \beta_{12} + 6741 \beta_{11} - 2152 \beta_{10} - 56 \beta_{9} + 302 \beta_{8} + \cdots - 56 \) Copy content Toggle raw display
\(\nu^{12}\)\(=\) \( 9737 \beta_{16} - 9737 \beta_{15} + 332 \beta_{14} + 332 \beta_{12} + 8135 \beta_{11} + 8135 \beta_{10} - 10683 \beta_{7} - 10763 \beta_{6} + 2842 \beta_{5} - 11681 \beta_{4} + 11423 \beta_{3} + 15653 \beta_{2} + \cdots + 40791 \) Copy content Toggle raw display
\(\nu^{13}\)\(=\) \( 28749 \beta_{19} + 37910 \beta_{18} - 20356 \beta_{17} + 23956 \beta_{16} + 8829 \beta_{15} - 20000 \beta_{14} - 47244 \beta_{13} - 26298 \beta_{12} - 17578 \beta_{11} + 53651 \beta_{10} + 386 \beta_{9} + \cdots + 52927 \beta_1 \) Copy content Toggle raw display
\(\nu^{14}\)\(=\) \( - 16645 \beta_{19} - 1004 \beta_{18} + 179652 \beta_{17} + 6992 \beta_{16} + 86941 \beta_{15} + 30354 \beta_{14} - 28061 \beta_{13} - 42603 \beta_{12} - 87774 \beta_{11} + 21534 \beta_{10} + \cdots - 302152 \) Copy content Toggle raw display
\(\nu^{15}\)\(=\) \( - 129544 \beta_{16} + 129544 \beta_{15} - 218511 \beta_{14} - 218511 \beta_{12} - 282629 \beta_{11} - 282629 \beta_{10} + 422291 \beta_{7} + 136536 \beta_{6} - 375607 \beta_{5} + 1190219 \beta_{4} + \cdots + 252 \) Copy content Toggle raw display
\(\nu^{16}\)\(=\) \( 95613 \beta_{19} + 10008 \beta_{18} - 1336036 \beta_{17} - 715923 \beta_{16} - 71110 \beta_{15} - 200731 \beta_{14} + 260972 \beta_{13} + 372972 \beta_{12} + 176228 \beta_{11} - 709041 \beta_{10} + \cdots - 682063 \beta_1 \) Copy content Toggle raw display
\(\nu^{17}\)\(=\) \( - 1851193 \beta_{19} - 2149200 \beta_{18} + 1263312 \beta_{17} - 613931 \beta_{16} - 1695944 \beta_{15} + 2978621 \beta_{14} + 2967752 \beta_{13} + 3446703 \beta_{12} + 3302323 \beta_{11} + \cdots + 36976 \) Copy content Toggle raw display
\(\nu^{18}\)\(=\) \( 5142647 \beta_{16} - 5142647 \beta_{15} - 145569 \beta_{14} - 145569 \beta_{12} + 4254666 \beta_{11} + 4254666 \beta_{10} - 5671250 \beta_{7} - 5756578 \beta_{6} + 2333197 \beta_{5} + \cdots + 17011682 \) Copy content Toggle raw display
\(\nu^{19}\)\(=\) \( 14578856 \beta_{19} + 16161297 \beta_{18} - 9686600 \beta_{17} + 13906594 \beta_{16} + 5014166 \beta_{15} - 11112322 \beta_{14} - 23345353 \beta_{13} - 14990584 \beta_{12} + \cdots + 19667087 \beta_1 \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(346\) \(442\)
\(\chi(n)\) \(1\) \(-1 - \beta_{9}\) \(1\)

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.

Label \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
277.1
1.39981 2.42454i
1.25760 2.17823i
1.13751 1.97023i
0.599601 1.03854i
0.432430 0.748990i
−0.0131282 + 0.0227388i
−0.384545 + 0.666052i
−0.526755 + 0.912367i
−1.03253 + 1.78839i
−1.37000 + 2.37290i
1.39981 + 2.42454i
1.25760 + 2.17823i
1.13751 + 1.97023i
0.599601 + 1.03854i
0.432430 + 0.748990i
−0.0131282 0.0227388i
−0.384545 0.666052i
−0.526755 0.912367i
−1.03253 1.78839i
−1.37000 2.37290i
−1.39981 2.42454i 0.500000 0.866025i −2.91893 + 5.05574i 0.973538 + 1.68622i −2.79962 −2.64333 + 0.113245i 10.7446 −0.500000 0.866025i 2.72553 4.72076i
277.2 −1.25760 2.17823i 0.500000 0.866025i −2.16313 + 3.74664i −2.15868 3.73894i −2.51520 1.42694 2.22797i 5.85100 −0.500000 0.866025i −5.42951 + 9.40419i
277.3 −1.13751 1.97023i 0.500000 0.866025i −1.58786 + 2.75026i 0.619347 + 1.07274i −2.27502 1.84753 + 1.89384i 2.67481 −0.500000 0.866025i 1.40903 2.44051i
277.4 −0.599601 1.03854i 0.500000 0.866025i 0.280958 0.486633i 0.286327 + 0.495932i −1.19920 −1.87398 1.86767i −3.07225 −0.500000 0.866025i 0.343363 0.594723i
277.5 −0.432430 0.748990i 0.500000 0.866025i 0.626009 1.08428i 1.24779 + 2.16123i −0.864859 −0.0271380 + 2.64561i −2.81254 −0.500000 0.866025i 1.07916 1.86916i
277.6 0.0131282 + 0.0227388i 0.500000 0.866025i 0.999655 1.73145i −1.38914 2.40606i 0.0262565 −2.58821 + 0.548771i 0.105008 −0.500000 0.866025i 0.0364740 0.0631748i
277.7 0.384545 + 0.666052i 0.500000 0.866025i 0.704250 1.21980i 2.01355 + 3.48756i 0.769091 2.63574 0.229917i 2.62145 −0.500000 0.866025i −1.54860 + 2.68225i
277.8 0.526755 + 0.912367i 0.500000 0.866025i 0.445058 0.770863i −1.08806 1.88457i 1.05351 1.36439 + 2.26681i 3.04477 −0.500000 0.866025i 1.14628 1.98542i
277.9 1.03253 + 1.78839i 0.500000 0.866025i −1.13223 + 1.96108i 0.304427 + 0.527282i 2.06506 2.05425 1.66735i −0.546135 −0.500000 0.866025i −0.628658 + 1.08887i
277.10 1.37000 + 2.37290i 0.500000 0.866025i −2.75378 + 4.76968i 1.69091 + 2.92874i 2.73999 −2.19620 1.47537i −9.61066 −0.500000 0.866025i −4.63307 + 8.02471i
415.1 −1.39981 + 2.42454i 0.500000 + 0.866025i −2.91893 5.05574i 0.973538 1.68622i −2.79962 −2.64333 0.113245i 10.7446 −0.500000 + 0.866025i 2.72553 + 4.72076i
415.2 −1.25760 + 2.17823i 0.500000 + 0.866025i −2.16313 3.74664i −2.15868 + 3.73894i −2.51520 1.42694 + 2.22797i 5.85100 −0.500000 + 0.866025i −5.42951 9.40419i
415.3 −1.13751 + 1.97023i 0.500000 + 0.866025i −1.58786 2.75026i 0.619347 1.07274i −2.27502 1.84753 1.89384i 2.67481 −0.500000 + 0.866025i 1.40903 + 2.44051i
415.4 −0.599601 + 1.03854i 0.500000 + 0.866025i 0.280958 + 0.486633i 0.286327 0.495932i −1.19920 −1.87398 + 1.86767i −3.07225 −0.500000 + 0.866025i 0.343363 + 0.594723i
415.5 −0.432430 + 0.748990i 0.500000 + 0.866025i 0.626009 + 1.08428i 1.24779 2.16123i −0.864859 −0.0271380 2.64561i −2.81254 −0.500000 + 0.866025i 1.07916 + 1.86916i
415.6 0.0131282 0.0227388i 0.500000 + 0.866025i 0.999655 + 1.73145i −1.38914 + 2.40606i 0.0262565 −2.58821 0.548771i 0.105008 −0.500000 + 0.866025i 0.0364740 + 0.0631748i
415.7 0.384545 0.666052i 0.500000 + 0.866025i 0.704250 + 1.21980i 2.01355 3.48756i 0.769091 2.63574 + 0.229917i 2.62145 −0.500000 + 0.866025i −1.54860 2.68225i
415.8 0.526755 0.912367i 0.500000 + 0.866025i 0.445058 + 0.770863i −1.08806 + 1.88457i 1.05351 1.36439 2.26681i 3.04477 −0.500000 + 0.866025i 1.14628 + 1.98542i
415.9 1.03253 1.78839i 0.500000 + 0.866025i −1.13223 1.96108i 0.304427 0.527282i 2.06506 2.05425 + 1.66735i −0.546135 −0.500000 + 0.866025i −0.628658 1.08887i
415.10 1.37000 2.37290i 0.500000 + 0.866025i −2.75378 4.76968i 1.69091 2.92874i 2.73999 −2.19620 + 1.47537i −9.61066 −0.500000 + 0.866025i −4.63307 8.02471i
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 415.10
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.c even 3 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 483.2.i.h 20
7.c even 3 1 inner 483.2.i.h 20
7.c even 3 1 3381.2.a.bi 10
7.d odd 6 1 3381.2.a.bj 10
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
483.2.i.h 20 1.a even 1 1 trivial
483.2.i.h 20 7.c even 3 1 inner
3381.2.a.bi 10 7.c even 3 1
3381.2.a.bj 10 7.d odd 6 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(483, [\chi])\):

\( T_{2}^{20} + 3 T_{2}^{19} + 22 T_{2}^{18} + 43 T_{2}^{17} + 245 T_{2}^{16} + 416 T_{2}^{15} + 1707 T_{2}^{14} + 2021 T_{2}^{13} + 7135 T_{2}^{12} + 6640 T_{2}^{11} + 20315 T_{2}^{10} + 10565 T_{2}^{9} + 29358 T_{2}^{8} + 9009 T_{2}^{7} + \cdots + 4 \) Copy content Toggle raw display
\( T_{5}^{20} - 5 T_{5}^{19} + 48 T_{5}^{18} - 187 T_{5}^{17} + 1263 T_{5}^{16} - 4454 T_{5}^{15} + 20191 T_{5}^{14} - 56713 T_{5}^{13} + 197781 T_{5}^{12} - 485572 T_{5}^{11} + 1332915 T_{5}^{10} - 2655713 T_{5}^{9} + \cdots + 556516 \) Copy content Toggle raw display
\( T_{11}^{20} + 8 T_{11}^{19} + 88 T_{11}^{18} + 320 T_{11}^{17} + 2504 T_{11}^{16} + 6744 T_{11}^{15} + 49792 T_{11}^{14} + 87344 T_{11}^{13} + 539456 T_{11}^{12} + 847040 T_{11}^{11} + 4167744 T_{11}^{10} + 5391104 T_{11}^{9} + \cdots + 31719424 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T^{20} + 3 T^{19} + 22 T^{18} + 43 T^{17} + \cdots + 4 \) Copy content Toggle raw display
$3$ \( (T^{2} - T + 1)^{10} \) Copy content Toggle raw display
$5$ \( T^{20} - 5 T^{19} + 48 T^{18} + \cdots + 556516 \) Copy content Toggle raw display
$7$ \( T^{20} - 11 T^{18} + \cdots + 282475249 \) Copy content Toggle raw display
$11$ \( T^{20} + 8 T^{19} + 88 T^{18} + \cdots + 31719424 \) Copy content Toggle raw display
$13$ \( (T^{10} - 57 T^{8} + 32 T^{7} + 1150 T^{6} + \cdots + 30667)^{2} \) Copy content Toggle raw display
$17$ \( T^{20} - 11 T^{19} + \cdots + 53029799524 \) Copy content Toggle raw display
$19$ \( T^{20} + T^{19} + 104 T^{18} + \cdots + 13176284944 \) Copy content Toggle raw display
$23$ \( (T^{2} + T + 1)^{10} \) Copy content Toggle raw display
$29$ \( (T^{10} - 22 T^{9} + 106 T^{8} + \cdots + 198784)^{2} \) Copy content Toggle raw display
$31$ \( T^{20} - 3 T^{19} + \cdots + 3370484748544 \) Copy content Toggle raw display
$37$ \( T^{20} + \cdots + 345393601613824 \) Copy content Toggle raw display
$41$ \( (T^{10} + 26 T^{9} + 102 T^{8} + \cdots - 30634016)^{2} \) Copy content Toggle raw display
$43$ \( (T^{10} - 27 T^{9} + 151 T^{8} + \cdots + 59884)^{2} \) Copy content Toggle raw display
$47$ \( T^{20} + 11 T^{19} + 252 T^{18} + \cdots + 5161984 \) Copy content Toggle raw display
$53$ \( T^{20} + 5 T^{19} + \cdots + 7340588259904 \) Copy content Toggle raw display
$59$ \( T^{20} - 10 T^{19} + \cdots + 119638508544 \) Copy content Toggle raw display
$61$ \( T^{20} + 22 T^{19} + \cdots + 155728101376 \) Copy content Toggle raw display
$67$ \( T^{20} - 2 T^{19} + \cdots + 3442498027609 \) Copy content Toggle raw display
$71$ \( (T^{10} - 27 T^{9} - 73 T^{8} + \cdots + 5367896)^{2} \) Copy content Toggle raw display
$73$ \( T^{20} - 8 T^{19} + \cdots + 60216094569409 \) Copy content Toggle raw display
$79$ \( T^{20} + 21 T^{19} + \cdots + 21\!\cdots\!64 \) Copy content Toggle raw display
$83$ \( (T^{10} + 12 T^{9} - 468 T^{8} + \cdots - 947876608)^{2} \) Copy content Toggle raw display
$89$ \( T^{20} + 6 T^{19} + \cdots + 175748762176 \) Copy content Toggle raw display
$97$ \( (T^{10} - 6 T^{9} - 684 T^{8} + \cdots - 21133952)^{2} \) Copy content Toggle raw display
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