Properties

Label 260.2.bk.c
Level $260$
Weight $2$
Character orbit 260.bk
Analytic conductor $2.076$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 260.bk (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.07611045255\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(5\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
Defining polynomial: \( x^{20} + 30 x^{18} + 371 x^{16} + 2460 x^{14} + 9517 x^{12} + 21870 x^{10} + 29001 x^{8} + 20400 x^{6} + 6399 x^{4} + 666 x^{2} + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

$q$-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.

\(f(q)\) \(=\) \( q + ( - \beta_{19} - \beta_{17} + \beta_{16} - \beta_{15} - \beta_{12} + \beta_{11} + \beta_{10} - \beta_{9} - \beta_{8} + 2 \beta_{7} + \cdots + \beta_{2}) q^{3}+ \cdots + ( - \beta_{14} + \beta_{9} - \beta_{7} + \beta_{6} - \beta_{4} + \beta_{3} - 1) q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + ( - \beta_{19} - \beta_{17} + \beta_{16} - \beta_{15} - \beta_{12} + \beta_{11} + \beta_{10} - \beta_{9} - \beta_{8} + 2 \beta_{7} + \cdots + \beta_{2}) q^{3}+ \cdots + (2 \beta_{19} + 4 \beta_{18} + 3 \beta_{17} - 2 \beta_{16} - \beta_{14} + 2 \beta_{13} + 7 \beta_{12} + \cdots - 3) q^{99}+O(q^{100}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 2 q^{3} + 12 q^{5} + 6 q^{7} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 2 q^{3} + 12 q^{5} + 6 q^{7} - 12 q^{9} + 8 q^{13} - 20 q^{15} + 20 q^{19} - 12 q^{21} + 6 q^{23} + 2 q^{25} - 20 q^{27} + 24 q^{29} + 8 q^{31} - 10 q^{33} - 36 q^{35} + 4 q^{39} + 6 q^{41} + 38 q^{43} - 16 q^{45} + 14 q^{49} + 30 q^{53} + 2 q^{55} - 76 q^{57} - 24 q^{59} - 32 q^{61} - 24 q^{63} - 30 q^{65} + 22 q^{67} - 16 q^{69} - 44 q^{73} - 2 q^{75} - 12 q^{77} + 2 q^{81} + 50 q^{85} + 38 q^{87} - 30 q^{89} - 72 q^{91} - 48 q^{93} - 30 q^{95} + 46 q^{97} + 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Basis of coefficient ring in terms of a root \(\nu\) of \( x^{20} + 30 x^{18} + 371 x^{16} + 2460 x^{14} + 9517 x^{12} + 21870 x^{10} + 29001 x^{8} + 20400 x^{6} + 6399 x^{4} + 666 x^{2} + 9 \) : Copy content Toggle raw display

\(\beta_{1}\)\(=\) \( ( 33785 \nu^{19} + 39285 \nu^{18} + 894975 \nu^{17} + 1362663 \nu^{16} + 9328060 \nu^{15} + 19386102 \nu^{14} + 48734964 \nu^{13} + 145983780 \nu^{12} + \cdots - 30772215 ) / 13619376 \) Copy content Toggle raw display
\(\beta_{2}\)\(=\) \( ( 33785 \nu^{19} - 39285 \nu^{18} + 894975 \nu^{17} - 1362663 \nu^{16} + 9328060 \nu^{15} - 19386102 \nu^{14} + 48734964 \nu^{13} - 145983780 \nu^{12} + \cdots + 30772215 ) / 13619376 \) Copy content Toggle raw display
\(\beta_{3}\)\(=\) \( ( - 13302 \nu^{18} - 387493 \nu^{16} - 4601880 \nu^{14} - 28817129 \nu^{12} - 102464589 \nu^{10} - 206050063 \nu^{8} - 215234229 \nu^{6} - 87983292 \nu^{4} + \cdots + 1823586 ) / 1134948 \) Copy content Toggle raw display
\(\beta_{4}\)\(=\) \( ( 7095 \nu^{19} + 54336 \nu^{18} + 236351 \nu^{17} + 1624980 \nu^{16} + 3193514 \nu^{15} + 20020756 \nu^{14} + 22344730 \nu^{13} + 132212424 \nu^{12} + \cdots + 14385840 ) / 4539792 \) Copy content Toggle raw display
\(\beta_{5}\)\(=\) \( ( 15705 \nu^{19} - 7449 \nu^{18} + 402397 \nu^{17} - 223669 \nu^{16} + 3930438 \nu^{15} - 2731870 \nu^{14} + 17694998 \nu^{13} - 17453738 \nu^{12} + 30393363 \nu^{11} + \cdots - 661521 ) / 4539792 \) Copy content Toggle raw display
\(\beta_{6}\)\(=\) \( ( 66482 \nu^{19} + 47115 \nu^{18} + 2012742 \nu^{17} + 1207191 \nu^{16} + 25148026 \nu^{15} + 11791314 \nu^{14} + 168552744 \nu^{13} + 53084994 \nu^{12} + \cdots - 15821217 ) / 13619376 \) Copy content Toggle raw display
\(\beta_{7}\)\(=\) \( ( 66482 \nu^{19} - 47115 \nu^{18} + 2012742 \nu^{17} - 1207191 \nu^{16} + 25148026 \nu^{15} - 11791314 \nu^{14} + 168552744 \nu^{13} - 53084994 \nu^{12} + \cdots + 15821217 ) / 13619376 \) Copy content Toggle raw display
\(\beta_{8}\)\(=\) \( ( 65481 \nu^{19} + 34053 \nu^{18} + 1937459 \nu^{17} + 998655 \nu^{16} + 23623520 \nu^{15} + 11935630 \nu^{14} + 154800052 \nu^{13} + 75087996 \nu^{12} + \cdots - 715755 ) / 4539792 \) Copy content Toggle raw display
\(\beta_{9}\)\(=\) \( ( - 201140 \nu^{19} + 14217 \nu^{18} - 5787312 \nu^{17} + 295401 \nu^{16} - 67780378 \nu^{15} + 1818438 \nu^{14} - 418783860 \nu^{13} - 808986 \nu^{12} + \cdots - 9990927 ) / 13619376 \) Copy content Toggle raw display
\(\beta_{10}\)\(=\) \( ( 65481 \nu^{19} - 34053 \nu^{18} + 1937459 \nu^{17} - 998655 \nu^{16} + 23623520 \nu^{15} - 11935630 \nu^{14} + 154800052 \nu^{13} - 75087996 \nu^{12} + \cdots + 715755 ) / 4539792 \) Copy content Toggle raw display
\(\beta_{11}\)\(=\) \( ( 72585 \nu^{19} - 59235 \nu^{18} + 2051657 \nu^{17} - 1779699 \nu^{16} + 23339538 \nu^{15} - 22025558 \nu^{14} + 137072830 \nu^{13} - 145835154 \nu^{12} + \cdots + 8463585 ) / 4539792 \) Copy content Toggle raw display
\(\beta_{12}\)\(=\) \( ( - 72576 \nu^{19} + 88389 \nu^{18} - 2173810 \nu^{17} + 2623635 \nu^{16} - 26817034 \nu^{15} + 31956386 \nu^{14} - 177144782 \nu^{13} + 207300420 \nu^{12} + \cdots + 13670085 ) / 4539792 \) Copy content Toggle raw display
\(\beta_{13}\)\(=\) \( ( 89663 \nu^{19} - 8196 \nu^{18} + 2650665 \nu^{17} - 299502 \nu^{16} + 32159852 \nu^{15} - 4457232 \nu^{14} + 207951588 \nu^{13} - 35038530 \nu^{12} + \cdots - 12592020 ) / 4539792 \) Copy content Toggle raw display
\(\beta_{14}\)\(=\) \( ( - 353 \nu^{19} - 10585 \nu^{17} - 130732 \nu^{15} - 864458 \nu^{13} - 3326801 \nu^{11} - 7574149 \nu^{9} - 9886332 \nu^{7} - 6763380 \nu^{5} - 1984833 \nu^{3} + \cdots - 8376 ) / 16752 \) Copy content Toggle raw display
\(\beta_{15}\)\(=\) \( ( 210017 \nu^{19} + 54111 \nu^{18} + 6333330 \nu^{17} + 1652277 \nu^{16} + 78814861 \nu^{15} + 20796687 \nu^{14} + 526330083 \nu^{13} + 139985934 \nu^{12} + \cdots + 22008474 ) / 6809688 \) Copy content Toggle raw display
\(\beta_{16}\)\(=\) \( ( 430079 \nu^{19} + 137379 \nu^{18} + 12923433 \nu^{17} + 4170825 \nu^{16} + 160317994 \nu^{15} + 52004406 \nu^{14} + 1068925596 \nu^{13} + 344662668 \nu^{12} + \cdots - 21883005 ) / 13619376 \) Copy content Toggle raw display
\(\beta_{17}\)\(=\) \( ( 191039 \nu^{19} - 26604 \nu^{18} + 5681093 \nu^{17} - 774986 \nu^{16} + 69369358 \nu^{15} - 9203760 \nu^{14} + 451452628 \nu^{13} - 57634258 \nu^{12} + \cdots + 3647172 ) / 4539792 \) Copy content Toggle raw display
\(\beta_{18}\)\(=\) \( ( - 600719 \nu^{19} + 267846 \nu^{18} - 17871213 \nu^{17} + 7954470 \nu^{16} - 218545294 \nu^{15} + 96815934 \nu^{14} - 1427059092 \nu^{13} + \cdots + 28943604 ) / 13619376 \) Copy content Toggle raw display
\(\beta_{19}\)\(=\) \( ( 870232 \nu^{19} - 57567 \nu^{18} + 25941228 \nu^{17} - 1845867 \nu^{16} + 318130016 \nu^{15} - 24393126 \nu^{14} + 2086177992 \nu^{13} - 171759894 \nu^{12} + \cdots + 10941489 ) / 13619376 \) Copy content Toggle raw display
\(\nu\)\(=\) \( ( \beta_{17} + \beta_{14} + \beta_{12} + \beta_{10} - \beta_{8} - \beta_{5} - \beta_{4} - \beta_{3} + 1 ) / 2 \) Copy content Toggle raw display
\(\nu^{2}\)\(=\) \( ( - 2 \beta_{19} + \beta_{17} + 2 \beta_{16} + \beta_{14} - \beta_{12} + \beta_{10} - 2 \beta_{9} - \beta_{8} - \beta_{5} + \beta_{4} - \beta_{3} + 2 \beta_{2} - 2 \beta _1 - 5 ) / 2 \) Copy content Toggle raw display
\(\nu^{3}\)\(=\) \( - \beta_{19} - \beta_{18} - \beta_{17} - \beta_{16} + \beta_{15} - 3 \beta_{14} - \beta_{13} - 2 \beta_{12} - \beta_{11} - 3 \beta_{10} + 3 \beta_{8} - \beta_{7} - \beta_{6} + 4 \beta_{5} + \beta_{4} + \beta_{3} - \beta _1 - 3 \) Copy content Toggle raw display
\(\nu^{4}\)\(=\) \( ( 12 \beta_{19} - 5 \beta_{17} - 12 \beta_{16} - 11 \beta_{14} - 2 \beta_{13} + 7 \beta_{12} + 2 \beta_{11} - 7 \beta_{10} + 18 \beta_{9} + 7 \beta_{8} - 8 \beta_{6} + 7 \beta_{5} - 9 \beta_{4} + \beta_{3} - 10 \beta_{2} + 12 \beta _1 + 23 ) / 2 \) Copy content Toggle raw display
\(\nu^{5}\)\(=\) \( ( 18 \beta_{19} + 18 \beta_{18} + 7 \beta_{17} + 18 \beta_{16} - 18 \beta_{15} + 47 \beta_{14} + 18 \beta_{13} + 19 \beta_{12} + 18 \beta_{11} + 43 \beta_{10} - 37 \beta_{8} + 8 \beta_{7} + 8 \beta_{6} - 61 \beta_{5} - \beta_{4} - 7 \beta_{3} - 2 \beta_{2} + 16 \beta _1 + 45 ) / 2 \) Copy content Toggle raw display
\(\nu^{6}\)\(=\) \( - 39 \beta_{19} - 2 \beta_{18} + 6 \beta_{17} + 39 \beta_{16} - 2 \beta_{15} + 49 \beta_{14} + 9 \beta_{13} - 30 \beta_{12} - 9 \beta_{11} + 31 \beta_{10} - 80 \beta_{9} - 28 \beta_{8} + 11 \beta_{7} + 57 \beta_{6} - 33 \beta_{5} + 45 \beta_{4} + \beta_{3} + \cdots - 63 \) Copy content Toggle raw display
\(\nu^{7}\)\(=\) \( ( - 136 \beta_{19} - 136 \beta_{18} - 37 \beta_{17} - 136 \beta_{16} + 136 \beta_{15} - 369 \beta_{14} - 142 \beta_{13} - 93 \beta_{12} - 142 \beta_{11} - 329 \beta_{10} + 245 \beta_{8} + 8 \beta_{7} + 8 \beta_{6} + 481 \beta_{5} + \cdots - 357 ) / 2 \) Copy content Toggle raw display
\(\nu^{8}\)\(=\) \( ( 554 \beta_{19} + 76 \beta_{18} + 87 \beta_{17} - 554 \beta_{16} + 76 \beta_{15} - 833 \beta_{14} - 134 \beta_{13} + 541 \beta_{12} + 134 \beta_{11} - 565 \beta_{10} + 1398 \beta_{9} + 465 \beta_{8} - 362 \beta_{7} - 1210 \beta_{6} + \cdots + 745 ) / 2 \) Copy content Toggle raw display
\(\nu^{9}\)\(=\) \( 499 \beta_{19} + 499 \beta_{18} + 124 \beta_{17} + 499 \beta_{16} - 499 \beta_{15} + 1460 \beta_{14} + 551 \beta_{13} + 217 \beta_{12} + 551 \beta_{11} + 1295 \beta_{10} - 857 \beta_{8} - 248 \beta_{7} - 248 \beta_{6} - 1935 \beta_{5} + \cdots + 1448 \) Copy content Toggle raw display
\(\nu^{10}\)\(=\) \( ( - 4154 \beta_{19} - 944 \beta_{18} - 1823 \beta_{17} + 4154 \beta_{16} - 944 \beta_{15} + 6965 \beta_{14} + 966 \beta_{13} - 4819 \beta_{12} - 966 \beta_{11} + 5013 \beta_{10} - 11998 \beta_{9} - 3855 \beta_{8} + \cdots - 4627 ) / 2 \) Copy content Toggle raw display
\(\nu^{11}\)\(=\) \( ( - 7394 \beta_{19} - 7374 \beta_{18} - 1867 \beta_{17} - 7394 \beta_{16} + 7374 \beta_{15} - 23407 \beta_{14} - 8596 \beta_{13} - 1739 \beta_{12} - 8596 \beta_{11} - 20673 \beta_{10} + 12507 \beta_{8} + \cdots - 23737 ) / 2 \) Copy content Toggle raw display
\(\nu^{12}\)\(=\) \( 16060 \beta_{19} + 4908 \beta_{18} + 10713 \beta_{17} - 16060 \beta_{16} + 4908 \beta_{15} - 28917 \beta_{14} - 3526 \beta_{13} + 21003 \beta_{12} + 3526 \beta_{11} - 21635 \beta_{10} + 50782 \beta_{9} + \cdots + 14982 \) Copy content Toggle raw display
\(\nu^{13}\)\(=\) \( ( 55912 \beta_{19} + 55452 \beta_{18} + 14887 \beta_{17} + 55912 \beta_{16} - 55452 \beta_{15} + 189683 \beta_{14} + 67656 \beta_{13} + 3947 \beta_{12} + 67656 \beta_{11} + 166299 \beta_{10} - 94263 \beta_{8} + \cdots + 195423 ) / 2 \) Copy content Toggle raw display
\(\nu^{14}\)\(=\) \( ( - 252878 \beta_{19} - 93112 \beta_{18} - 213107 \beta_{17} + 252878 \beta_{16} - 93112 \beta_{15} + 478593 \beta_{14} + 52860 \beta_{13} - 359545 \beta_{12} - 52860 \beta_{11} + 366229 \beta_{10} + \cdots - 201853 ) / 2 \) Copy content Toggle raw display
\(\nu^{15}\)\(=\) \( - 215855 \beta_{19} - 212533 \beta_{18} - 61098 \beta_{17} - 215855 \beta_{16} + 212533 \beta_{15} - 774158 \beta_{14} - 268575 \beta_{13} + 13355 \beta_{12} - 268575 \beta_{11} - 672284 \beta_{10} + \cdots - 805634 \) Copy content Toggle raw display
\(\nu^{16}\)\(=\) \( ( 2013708 \beta_{19} + 838112 \beta_{18} + 1962909 \beta_{17} - 2013708 \beta_{16} + 838112 \beta_{15} - 3952693 \beta_{14} - 407094 \beta_{13} + 3037049 \beta_{12} + 407094 \beta_{11} + \cdots + 1411421 ) / 2 \) Copy content Toggle raw display
\(\nu^{17}\)\(=\) \( ( 3392222 \beta_{19} + 3314446 \beta_{18} + 1016735 \beta_{17} + 3392222 \beta_{16} - 3314446 \beta_{15} + 12692143 \beta_{14} + 4296602 \beta_{13} - 559677 \beta_{12} + 4296602 \beta_{11} + \cdots + 13286633 ) / 2 \) Copy content Toggle raw display
\(\nu^{18}\)\(=\) \( - 8080497 \beta_{19} - 3654094 \beta_{18} - 8669055 \beta_{17} + 8080497 \beta_{16} - 3654094 \beta_{15} + 16301048 \beta_{14} + 1602795 \beta_{13} - 12710265 \beta_{12} + \cdots - 5104464 \) Copy content Toggle raw display
\(\nu^{19}\)\(=\) \( ( - 27013592 \beta_{19} - 26203988 \beta_{18} - 8502479 \beta_{17} - 27013592 \beta_{16} + 26203988 \beta_{15} - 104274927 \beta_{14} - 34578050 \beta_{13} + 6564189 \beta_{12} + \cdots - 109516551 ) / 2 \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).

\(n\) \(41\) \(131\) \(157\)
\(\chi(n)\) \(\beta_{6}\) \(1\) \(\beta_{6} + \beta_{7}\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
33.1
1.49418i
1.86950i
2.27790i
0.676406i
0.402430i
0.125665i
1.70974i
2.86589i
1.14923i
2.44766i
0.125665i
1.70974i
2.86589i
1.14923i
2.44766i
1.49418i
1.86950i
2.27790i
0.676406i
0.402430i
0 −2.51912 + 0.674996i 0 2.14030 0.647383i 0 −1.45437 + 0.839682i 0 3.29226 1.90079i 0
33.2 0 −2.41732 + 0.647720i 0 −2.18528 0.473860i 0 3.34088 1.92886i 0 2.82584 1.63150i 0
33.3 0 0.243028 0.0651192i 0 0.356684 + 2.20744i 0 −4.30824 + 2.48736i 0 −2.54325 + 1.46835i 0
33.4 0 0.834228 0.223531i 0 2.20306 0.382788i 0 2.07295 1.19682i 0 −1.95211 + 1.12705i 0
33.5 0 2.49316 0.668040i 0 −0.380790 2.20341i 0 −0.749297 + 0.432607i 0 3.17149 1.83106i 0
97.1 0 −0.690650 2.57754i 0 −0.0143596 2.23602i 0 1.87342 1.08162i 0 −3.56864 + 2.06036i 0
97.2 0 −0.563138 2.10166i 0 1.75876 + 1.38086i 0 1.25530 0.724750i 0 −1.50178 + 0.867051i 0
97.3 0 0.355132 + 1.32537i 0 1.50965 + 1.64953i 0 −3.40883 + 1.96809i 0 0.967585 0.558635i 0
97.4 0 0.387600 + 1.44654i 0 1.95799 1.07994i 0 2.10545 1.21558i 0 0.655821 0.378639i 0
97.5 0 0.877081 + 3.27331i 0 −1.34601 + 1.78557i 0 2.27273 1.31216i 0 −7.34722 + 4.24192i 0
193.1 0 −0.690650 + 2.57754i 0 −0.0143596 + 2.23602i 0 1.87342 + 1.08162i 0 −3.56864 2.06036i 0
193.2 0 −0.563138 + 2.10166i 0 1.75876 1.38086i 0 1.25530 + 0.724750i 0 −1.50178 0.867051i 0
193.3 0 0.355132 1.32537i 0 1.50965 1.64953i 0 −3.40883 1.96809i 0 0.967585 + 0.558635i 0
193.4 0 0.387600 1.44654i 0 1.95799 + 1.07994i 0 2.10545 + 1.21558i 0 0.655821 + 0.378639i 0
193.5 0 0.877081 3.27331i 0 −1.34601 1.78557i 0 2.27273 + 1.31216i 0 −7.34722 4.24192i 0
197.1 0 −2.51912 0.674996i 0 2.14030 + 0.647383i 0 −1.45437 0.839682i 0 3.29226 + 1.90079i 0
197.2 0 −2.41732 0.647720i 0 −2.18528 + 0.473860i 0 3.34088 + 1.92886i 0 2.82584 + 1.63150i 0
197.3 0 0.243028 + 0.0651192i 0 0.356684 2.20744i 0 −4.30824 2.48736i 0 −2.54325 1.46835i 0
197.4 0 0.834228 + 0.223531i 0 2.20306 + 0.382788i 0 2.07295 + 1.19682i 0 −1.95211 1.12705i 0
197.5 0 2.49316 + 0.668040i 0 −0.380790 + 2.20341i 0 −0.749297 0.432607i 0 3.17149 + 1.83106i 0
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 197.5
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
65.o even 12 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 260.2.bk.c yes 20
5.b even 2 1 1300.2.bs.d 20
5.c odd 4 1 260.2.bf.c 20
5.c odd 4 1 1300.2.bn.d 20
13.f odd 12 1 260.2.bf.c 20
65.o even 12 1 inner 260.2.bk.c yes 20
65.s odd 12 1 1300.2.bn.d 20
65.t even 12 1 1300.2.bs.d 20
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
260.2.bf.c 20 5.c odd 4 1
260.2.bf.c 20 13.f odd 12 1
260.2.bk.c yes 20 1.a even 1 1 trivial
260.2.bk.c yes 20 65.o even 12 1 inner
1300.2.bn.d 20 5.c odd 4 1
1300.2.bn.d 20 65.s odd 12 1
1300.2.bs.d 20 5.b even 2 1
1300.2.bs.d 20 65.t even 12 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{20} + 2 T_{3}^{19} + 8 T_{3}^{18} + 28 T_{3}^{17} - 26 T_{3}^{16} - 106 T_{3}^{15} - 500 T_{3}^{14} - 1366 T_{3}^{13} + 2867 T_{3}^{12} + 5410 T_{3}^{11} + 14776 T_{3}^{10} + 43502 T_{3}^{9} - 9730 T_{3}^{8} + 76600 T_{3}^{7} + \cdots + 21904 \) acting on \(S_{2}^{\mathrm{new}}(260, [\chi])\). Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T^{20} \) Copy content Toggle raw display
$3$ \( T^{20} + 2 T^{19} + 8 T^{18} + \cdots + 21904 \) Copy content Toggle raw display
$5$ \( T^{20} - 12 T^{19} + 71 T^{18} + \cdots + 9765625 \) Copy content Toggle raw display
$7$ \( T^{20} - 6 T^{19} - 24 T^{18} + \cdots + 27625536 \) Copy content Toggle raw display
$11$ \( T^{20} - 12 T^{18} + 128 T^{17} + \cdots + 8202496 \) Copy content Toggle raw display
$13$ \( T^{20} - 8 T^{19} + \cdots + 137858491849 \) Copy content Toggle raw display
$17$ \( T^{20} + 93 T^{18} + \cdots + 109980446689 \) Copy content Toggle raw display
$19$ \( T^{20} - 20 T^{19} + \cdots + 472279824 \) Copy content Toggle raw display
$23$ \( T^{20} - 6 T^{19} + 60 T^{18} + \cdots + 3139984 \) Copy content Toggle raw display
$29$ \( T^{20} - 24 T^{19} + \cdots + 341103961 \) Copy content Toggle raw display
$31$ \( T^{20} - 8 T^{19} + \cdots + 54838398976 \) Copy content Toggle raw display
$37$ \( T^{20} - 285 T^{18} + \cdots + 52\!\cdots\!69 \) Copy content Toggle raw display
$41$ \( T^{20} - 6 T^{19} + \cdots + 10017978284161 \) Copy content Toggle raw display
$43$ \( T^{20} - 38 T^{19} + \cdots + 319577657344 \) Copy content Toggle raw display
$47$ \( T^{20} + 224 T^{18} + \cdots + 5858983936 \) Copy content Toggle raw display
$53$ \( T^{20} - 30 T^{19} + \cdots + 90\!\cdots\!64 \) Copy content Toggle raw display
$59$ \( T^{20} + 24 T^{19} + \cdots + 26\!\cdots\!96 \) Copy content Toggle raw display
$61$ \( T^{20} + 32 T^{19} + \cdots + 43\!\cdots\!41 \) Copy content Toggle raw display
$67$ \( T^{20} - 22 T^{19} + \cdots + 11546104977936 \) Copy content Toggle raw display
$71$ \( T^{20} - 24 T^{18} + \cdots + 27\!\cdots\!76 \) Copy content Toggle raw display
$73$ \( (T^{10} + 22 T^{9} - 123 T^{8} + \cdots - 119575728)^{2} \) Copy content Toggle raw display
$79$ \( T^{20} + \cdots + 207459544743936 \) Copy content Toggle raw display
$83$ \( T^{20} + 896 T^{18} + \cdots + 10\!\cdots\!36 \) Copy content Toggle raw display
$89$ \( T^{20} + \cdots + 237919334033956 \) Copy content Toggle raw display
$97$ \( T^{20} - 46 T^{19} + \cdots + 963004643584 \) Copy content Toggle raw display
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