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: |
\( x^{20} + 30 x^{18} + 371 x^{16} + 2460 x^{14} + 9517 x^{12} + 21870 x^{10} + 29001 x^{8} + 20400 x^{6} + 6399 x^{4} + 666 x^{2} + 9 \)
|
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.
Basis of coefficient ring in terms of a root \(\nu\) of
\( x^{20} + 30 x^{18} + 371 x^{16} + 2460 x^{14} + 9517 x^{12} + 21870 x^{10} + 29001 x^{8} + 20400 x^{6} + 6399 x^{4} + 666 x^{2} + 9 \)
:
\(\beta_{1}\) | \(=\) |
\( ( 33785 \nu^{19} + 39285 \nu^{18} + 894975 \nu^{17} + 1362663 \nu^{16} + 9328060 \nu^{15} + 19386102 \nu^{14} + 48734964 \nu^{13} + 145983780 \nu^{12} + \cdots - 30772215 ) / 13619376 \)
|
\(\beta_{2}\) | \(=\) |
\( ( 33785 \nu^{19} - 39285 \nu^{18} + 894975 \nu^{17} - 1362663 \nu^{16} + 9328060 \nu^{15} - 19386102 \nu^{14} + 48734964 \nu^{13} - 145983780 \nu^{12} + \cdots + 30772215 ) / 13619376 \)
|
\(\beta_{3}\) | \(=\) |
\( ( - 13302 \nu^{18} - 387493 \nu^{16} - 4601880 \nu^{14} - 28817129 \nu^{12} - 102464589 \nu^{10} - 206050063 \nu^{8} - 215234229 \nu^{6} - 87983292 \nu^{4} + \cdots + 1823586 ) / 1134948 \)
|
\(\beta_{4}\) | \(=\) |
\( ( 7095 \nu^{19} + 54336 \nu^{18} + 236351 \nu^{17} + 1624980 \nu^{16} + 3193514 \nu^{15} + 20020756 \nu^{14} + 22344730 \nu^{13} + 132212424 \nu^{12} + \cdots + 14385840 ) / 4539792 \)
|
\(\beta_{5}\) | \(=\) |
\( ( 15705 \nu^{19} - 7449 \nu^{18} + 402397 \nu^{17} - 223669 \nu^{16} + 3930438 \nu^{15} - 2731870 \nu^{14} + 17694998 \nu^{13} - 17453738 \nu^{12} + 30393363 \nu^{11} + \cdots - 661521 ) / 4539792 \)
|
\(\beta_{6}\) | \(=\) |
\( ( 66482 \nu^{19} + 47115 \nu^{18} + 2012742 \nu^{17} + 1207191 \nu^{16} + 25148026 \nu^{15} + 11791314 \nu^{14} + 168552744 \nu^{13} + 53084994 \nu^{12} + \cdots - 15821217 ) / 13619376 \)
|
\(\beta_{7}\) | \(=\) |
\( ( 66482 \nu^{19} - 47115 \nu^{18} + 2012742 \nu^{17} - 1207191 \nu^{16} + 25148026 \nu^{15} - 11791314 \nu^{14} + 168552744 \nu^{13} - 53084994 \nu^{12} + \cdots + 15821217 ) / 13619376 \)
|
\(\beta_{8}\) | \(=\) |
\( ( 65481 \nu^{19} + 34053 \nu^{18} + 1937459 \nu^{17} + 998655 \nu^{16} + 23623520 \nu^{15} + 11935630 \nu^{14} + 154800052 \nu^{13} + 75087996 \nu^{12} + \cdots - 715755 ) / 4539792 \)
|
\(\beta_{9}\) | \(=\) |
\( ( - 201140 \nu^{19} + 14217 \nu^{18} - 5787312 \nu^{17} + 295401 \nu^{16} - 67780378 \nu^{15} + 1818438 \nu^{14} - 418783860 \nu^{13} - 808986 \nu^{12} + \cdots - 9990927 ) / 13619376 \)
|
\(\beta_{10}\) | \(=\) |
\( ( 65481 \nu^{19} - 34053 \nu^{18} + 1937459 \nu^{17} - 998655 \nu^{16} + 23623520 \nu^{15} - 11935630 \nu^{14} + 154800052 \nu^{13} - 75087996 \nu^{12} + \cdots + 715755 ) / 4539792 \)
|
\(\beta_{11}\) | \(=\) |
\( ( 72585 \nu^{19} - 59235 \nu^{18} + 2051657 \nu^{17} - 1779699 \nu^{16} + 23339538 \nu^{15} - 22025558 \nu^{14} + 137072830 \nu^{13} - 145835154 \nu^{12} + \cdots + 8463585 ) / 4539792 \)
|
\(\beta_{12}\) | \(=\) |
\( ( - 72576 \nu^{19} + 88389 \nu^{18} - 2173810 \nu^{17} + 2623635 \nu^{16} - 26817034 \nu^{15} + 31956386 \nu^{14} - 177144782 \nu^{13} + 207300420 \nu^{12} + \cdots + 13670085 ) / 4539792 \)
|
\(\beta_{13}\) | \(=\) |
\( ( 89663 \nu^{19} - 8196 \nu^{18} + 2650665 \nu^{17} - 299502 \nu^{16} + 32159852 \nu^{15} - 4457232 \nu^{14} + 207951588 \nu^{13} - 35038530 \nu^{12} + \cdots - 12592020 ) / 4539792 \)
|
\(\beta_{14}\) | \(=\) |
\( ( - 353 \nu^{19} - 10585 \nu^{17} - 130732 \nu^{15} - 864458 \nu^{13} - 3326801 \nu^{11} - 7574149 \nu^{9} - 9886332 \nu^{7} - 6763380 \nu^{5} - 1984833 \nu^{3} + \cdots - 8376 ) / 16752 \)
|
\(\beta_{15}\) | \(=\) |
\( ( 210017 \nu^{19} + 54111 \nu^{18} + 6333330 \nu^{17} + 1652277 \nu^{16} + 78814861 \nu^{15} + 20796687 \nu^{14} + 526330083 \nu^{13} + 139985934 \nu^{12} + \cdots + 22008474 ) / 6809688 \)
|
\(\beta_{16}\) | \(=\) |
\( ( 430079 \nu^{19} + 137379 \nu^{18} + 12923433 \nu^{17} + 4170825 \nu^{16} + 160317994 \nu^{15} + 52004406 \nu^{14} + 1068925596 \nu^{13} + 344662668 \nu^{12} + \cdots - 21883005 ) / 13619376 \)
|
\(\beta_{17}\) | \(=\) |
\( ( 191039 \nu^{19} - 26604 \nu^{18} + 5681093 \nu^{17} - 774986 \nu^{16} + 69369358 \nu^{15} - 9203760 \nu^{14} + 451452628 \nu^{13} - 57634258 \nu^{12} + \cdots + 3647172 ) / 4539792 \)
|
\(\beta_{18}\) | \(=\) |
\( ( - 600719 \nu^{19} + 267846 \nu^{18} - 17871213 \nu^{17} + 7954470 \nu^{16} - 218545294 \nu^{15} + 96815934 \nu^{14} - 1427059092 \nu^{13} + \cdots + 28943604 ) / 13619376 \)
|
\(\beta_{19}\) | \(=\) |
\( ( 870232 \nu^{19} - 57567 \nu^{18} + 25941228 \nu^{17} - 1845867 \nu^{16} + 318130016 \nu^{15} - 24393126 \nu^{14} + 2086177992 \nu^{13} - 171759894 \nu^{12} + \cdots + 10941489 ) / 13619376 \)
|
\(\nu\) | \(=\) |
\( ( \beta_{17} + \beta_{14} + \beta_{12} + \beta_{10} - \beta_{8} - \beta_{5} - \beta_{4} - \beta_{3} + 1 ) / 2 \)
|
\(\nu^{2}\) | \(=\) |
\( ( - 2 \beta_{19} + \beta_{17} + 2 \beta_{16} + \beta_{14} - \beta_{12} + \beta_{10} - 2 \beta_{9} - \beta_{8} - \beta_{5} + \beta_{4} - \beta_{3} + 2 \beta_{2} - 2 \beta _1 - 5 ) / 2 \)
|
\(\nu^{3}\) | \(=\) |
\( - \beta_{19} - \beta_{18} - \beta_{17} - \beta_{16} + \beta_{15} - 3 \beta_{14} - \beta_{13} - 2 \beta_{12} - \beta_{11} - 3 \beta_{10} + 3 \beta_{8} - \beta_{7} - \beta_{6} + 4 \beta_{5} + \beta_{4} + \beta_{3} - \beta _1 - 3 \)
|
\(\nu^{4}\) | \(=\) |
\( ( 12 \beta_{19} - 5 \beta_{17} - 12 \beta_{16} - 11 \beta_{14} - 2 \beta_{13} + 7 \beta_{12} + 2 \beta_{11} - 7 \beta_{10} + 18 \beta_{9} + 7 \beta_{8} - 8 \beta_{6} + 7 \beta_{5} - 9 \beta_{4} + \beta_{3} - 10 \beta_{2} + 12 \beta _1 + 23 ) / 2 \)
|
\(\nu^{5}\) | \(=\) |
\( ( 18 \beta_{19} + 18 \beta_{18} + 7 \beta_{17} + 18 \beta_{16} - 18 \beta_{15} + 47 \beta_{14} + 18 \beta_{13} + 19 \beta_{12} + 18 \beta_{11} + 43 \beta_{10} - 37 \beta_{8} + 8 \beta_{7} + 8 \beta_{6} - 61 \beta_{5} - \beta_{4} - 7 \beta_{3} - 2 \beta_{2} + 16 \beta _1 + 45 ) / 2 \)
|
\(\nu^{6}\) | \(=\) |
\( - 39 \beta_{19} - 2 \beta_{18} + 6 \beta_{17} + 39 \beta_{16} - 2 \beta_{15} + 49 \beta_{14} + 9 \beta_{13} - 30 \beta_{12} - 9 \beta_{11} + 31 \beta_{10} - 80 \beta_{9} - 28 \beta_{8} + 11 \beta_{7} + 57 \beta_{6} - 33 \beta_{5} + 45 \beta_{4} + \beta_{3} + \cdots - 63 \)
|
\(\nu^{7}\) | \(=\) |
\( ( - 136 \beta_{19} - 136 \beta_{18} - 37 \beta_{17} - 136 \beta_{16} + 136 \beta_{15} - 369 \beta_{14} - 142 \beta_{13} - 93 \beta_{12} - 142 \beta_{11} - 329 \beta_{10} + 245 \beta_{8} + 8 \beta_{7} + 8 \beta_{6} + 481 \beta_{5} + \cdots - 357 ) / 2 \)
|
\(\nu^{8}\) | \(=\) |
\( ( 554 \beta_{19} + 76 \beta_{18} + 87 \beta_{17} - 554 \beta_{16} + 76 \beta_{15} - 833 \beta_{14} - 134 \beta_{13} + 541 \beta_{12} + 134 \beta_{11} - 565 \beta_{10} + 1398 \beta_{9} + 465 \beta_{8} - 362 \beta_{7} - 1210 \beta_{6} + \cdots + 745 ) / 2 \)
|
\(\nu^{9}\) | \(=\) |
\( 499 \beta_{19} + 499 \beta_{18} + 124 \beta_{17} + 499 \beta_{16} - 499 \beta_{15} + 1460 \beta_{14} + 551 \beta_{13} + 217 \beta_{12} + 551 \beta_{11} + 1295 \beta_{10} - 857 \beta_{8} - 248 \beta_{7} - 248 \beta_{6} - 1935 \beta_{5} + \cdots + 1448 \)
|
\(\nu^{10}\) | \(=\) |
\( ( - 4154 \beta_{19} - 944 \beta_{18} - 1823 \beta_{17} + 4154 \beta_{16} - 944 \beta_{15} + 6965 \beta_{14} + 966 \beta_{13} - 4819 \beta_{12} - 966 \beta_{11} + 5013 \beta_{10} - 11998 \beta_{9} - 3855 \beta_{8} + \cdots - 4627 ) / 2 \)
|
\(\nu^{11}\) | \(=\) |
\( ( - 7394 \beta_{19} - 7374 \beta_{18} - 1867 \beta_{17} - 7394 \beta_{16} + 7374 \beta_{15} - 23407 \beta_{14} - 8596 \beta_{13} - 1739 \beta_{12} - 8596 \beta_{11} - 20673 \beta_{10} + 12507 \beta_{8} + \cdots - 23737 ) / 2 \)
|
\(\nu^{12}\) | \(=\) |
\( 16060 \beta_{19} + 4908 \beta_{18} + 10713 \beta_{17} - 16060 \beta_{16} + 4908 \beta_{15} - 28917 \beta_{14} - 3526 \beta_{13} + 21003 \beta_{12} + 3526 \beta_{11} - 21635 \beta_{10} + 50782 \beta_{9} + \cdots + 14982 \)
|
\(\nu^{13}\) | \(=\) |
\( ( 55912 \beta_{19} + 55452 \beta_{18} + 14887 \beta_{17} + 55912 \beta_{16} - 55452 \beta_{15} + 189683 \beta_{14} + 67656 \beta_{13} + 3947 \beta_{12} + 67656 \beta_{11} + 166299 \beta_{10} - 94263 \beta_{8} + \cdots + 195423 ) / 2 \)
|
\(\nu^{14}\) | \(=\) |
\( ( - 252878 \beta_{19} - 93112 \beta_{18} - 213107 \beta_{17} + 252878 \beta_{16} - 93112 \beta_{15} + 478593 \beta_{14} + 52860 \beta_{13} - 359545 \beta_{12} - 52860 \beta_{11} + 366229 \beta_{10} + \cdots - 201853 ) / 2 \)
|
\(\nu^{15}\) | \(=\) |
\( - 215855 \beta_{19} - 212533 \beta_{18} - 61098 \beta_{17} - 215855 \beta_{16} + 212533 \beta_{15} - 774158 \beta_{14} - 268575 \beta_{13} + 13355 \beta_{12} - 268575 \beta_{11} - 672284 \beta_{10} + \cdots - 805634 \)
|
\(\nu^{16}\) | \(=\) |
\( ( 2013708 \beta_{19} + 838112 \beta_{18} + 1962909 \beta_{17} - 2013708 \beta_{16} + 838112 \beta_{15} - 3952693 \beta_{14} - 407094 \beta_{13} + 3037049 \beta_{12} + 407094 \beta_{11} + \cdots + 1411421 ) / 2 \)
|
\(\nu^{17}\) | \(=\) |
\( ( 3392222 \beta_{19} + 3314446 \beta_{18} + 1016735 \beta_{17} + 3392222 \beta_{16} - 3314446 \beta_{15} + 12692143 \beta_{14} + 4296602 \beta_{13} - 559677 \beta_{12} + 4296602 \beta_{11} + \cdots + 13286633 ) / 2 \)
|
\(\nu^{18}\) | \(=\) |
\( - 8080497 \beta_{19} - 3654094 \beta_{18} - 8669055 \beta_{17} + 8080497 \beta_{16} - 3654094 \beta_{15} + 16301048 \beta_{14} + 1602795 \beta_{13} - 12710265 \beta_{12} + \cdots - 5104464 \)
|
\(\nu^{19}\) | \(=\) |
\( ( - 27013592 \beta_{19} - 26203988 \beta_{18} - 8502479 \beta_{17} - 27013592 \beta_{16} + 26203988 \beta_{15} - 104274927 \beta_{14} - 34578050 \beta_{13} + 6564189 \beta_{12} + \cdots - 109516551 ) / 2 \)
|
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 |
|
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 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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 \(S_{2}^{\mathrm{new}}(260, [\chi])\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T^{20} \)
$3$
\( T^{20} + 2 T^{19} + 8 T^{18} + \cdots + 21904 \)
$5$
\( T^{20} - 12 T^{19} + 71 T^{18} + \cdots + 9765625 \)
$7$
\( T^{20} - 6 T^{19} - 24 T^{18} + \cdots + 27625536 \)
$11$
\( T^{20} - 12 T^{18} + 128 T^{17} + \cdots + 8202496 \)
$13$
\( T^{20} - 8 T^{19} + \cdots + 137858491849 \)
$17$
\( T^{20} + 93 T^{18} + \cdots + 109980446689 \)
$19$
\( T^{20} - 20 T^{19} + \cdots + 472279824 \)
$23$
\( T^{20} - 6 T^{19} + 60 T^{18} + \cdots + 3139984 \)
$29$
\( T^{20} - 24 T^{19} + \cdots + 341103961 \)
$31$
\( T^{20} - 8 T^{19} + \cdots + 54838398976 \)
$37$
\( T^{20} - 285 T^{18} + \cdots + 52\!\cdots\!69 \)
$41$
\( T^{20} - 6 T^{19} + \cdots + 10017978284161 \)
$43$
\( T^{20} - 38 T^{19} + \cdots + 319577657344 \)
$47$
\( T^{20} + 224 T^{18} + \cdots + 5858983936 \)
$53$
\( T^{20} - 30 T^{19} + \cdots + 90\!\cdots\!64 \)
$59$
\( T^{20} + 24 T^{19} + \cdots + 26\!\cdots\!96 \)
$61$
\( T^{20} + 32 T^{19} + \cdots + 43\!\cdots\!41 \)
$67$
\( T^{20} - 22 T^{19} + \cdots + 11546104977936 \)
$71$
\( T^{20} - 24 T^{18} + \cdots + 27\!\cdots\!76 \)
$73$
\( (T^{10} + 22 T^{9} - 123 T^{8} + \cdots - 119575728)^{2} \)
$79$
\( T^{20} + \cdots + 207459544743936 \)
$83$
\( T^{20} + 896 T^{18} + \cdots + 10\!\cdots\!36 \)
$89$
\( T^{20} + \cdots + 237919334033956 \)
$97$
\( T^{20} - 46 T^{19} + \cdots + 963004643584 \)
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