Newspace parameters
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.bd (of order \(6\), degree \(2\), minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(2.17991597518\) |
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
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Defining polynomial: |
\( x^{16} - 4 x^{15} + 10 x^{14} - 8 x^{13} - 3 x^{12} + 32 x^{11} - 5 x^{10} - 44 x^{9} + 214 x^{8} - 132 x^{7} - 45 x^{6} + 864 x^{5} - 243 x^{4} - 1944 x^{3} + 7290 x^{2} - 8748 x + 6561 \)
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Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
$q$-expansion
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.
Basis of coefficient ring in terms of a root \(\nu\) of
\( x^{16} - 4 x^{15} + 10 x^{14} - 8 x^{13} - 3 x^{12} + 32 x^{11} - 5 x^{10} - 44 x^{9} + 214 x^{8} - 132 x^{7} - 45 x^{6} + 864 x^{5} - 243 x^{4} - 1944 x^{3} + 7290 x^{2} - 8748 x + 6561 \)
:
\(\beta_{1}\) | \(=\) |
\( \nu \)
|
\(\beta_{2}\) | \(=\) |
\( ( \nu^{15} - 4 \nu^{14} + 10 \nu^{13} - 8 \nu^{12} - 3 \nu^{11} + 32 \nu^{10} - 5 \nu^{9} - 44 \nu^{8} + 214 \nu^{7} - 132 \nu^{6} - 45 \nu^{5} + 864 \nu^{4} - 243 \nu^{3} - 1944 \nu^{2} + 7290 \nu - 8748 ) / 2187 \)
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\(\beta_{3}\) | \(=\) |
\( ( 57 \nu^{15} - 5518 \nu^{14} + 7381 \nu^{13} - 18694 \nu^{12} - 28900 \nu^{11} - 3540 \nu^{10} - 97601 \nu^{9} - 227974 \nu^{8} - 68965 \nu^{7} - 678274 \nu^{6} + \cdots - 11910402 ) / 64152 \)
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\(\beta_{4}\) | \(=\) |
\( ( - 2194 \nu^{15} + 19537 \nu^{14} - 30118 \nu^{13} + 44909 \nu^{12} + 84636 \nu^{11} - 34820 \nu^{10} + 195806 \nu^{9} + 639719 \nu^{8} - 100294 \nu^{7} + \cdots + 35549685 ) / 192456 \)
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\(\beta_{5}\) | \(=\) |
\( ( 686 \nu^{15} - 4953 \nu^{14} + 7898 \nu^{13} - 10141 \nu^{12} - 20180 \nu^{11} + 11796 \nu^{10} - 40674 \nu^{9} - 152359 \nu^{8} + 47706 \nu^{7} - 369947 \nu^{6} + \cdots - 8790525 ) / 42768 \)
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\(\beta_{6}\) | \(=\) |
\( ( - 2551 \nu^{15} - 30666 \nu^{14} + 35541 \nu^{13} - 130226 \nu^{12} - 178900 \nu^{11} - 67220 \nu^{10} - 709257 \nu^{9} - 1424186 \nu^{8} - 727301 \nu^{7} + \cdots - 73435086 ) / 128304 \)
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\(\beta_{7}\) | \(=\) |
\( ( 515 \nu^{15} - 348 \nu^{14} + 1311 \nu^{13} + 3844 \nu^{12} + 2060 \nu^{11} + 9484 \nu^{10} + 27621 \nu^{9} + 20896 \nu^{8} + 68905 \nu^{7} + 127508 \nu^{6} + 67356 \nu^{5} + \cdots + 769824 ) / 11664 \)
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\(\beta_{8}\) | \(=\) |
\( ( 533 \nu^{15} - 2036 \nu^{14} + 3545 \nu^{13} - 1876 \nu^{12} - 6828 \nu^{11} + 8356 \nu^{10} - 2509 \nu^{9} - 49216 \nu^{8} + 47039 \nu^{7} - 80580 \nu^{6} - 210588 \nu^{5} + \cdots - 2881008 ) / 11664 \)
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\(\beta_{9}\) | \(=\) |
\( ( 2209 \nu^{15} - 1038 \nu^{14} + 4653 \nu^{13} + 18122 \nu^{12} + 10156 \nu^{11} + 37244 \nu^{10} + 122175 \nu^{9} + 99098 \nu^{8} + 279395 \nu^{7} + 580462 \nu^{6} + \cdots + 4543614 ) / 42768 \)
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\(\beta_{10}\) | \(=\) |
\( ( 25793 \nu^{15} - 43421 \nu^{14} + 101321 \nu^{13} + 100655 \nu^{12} - 37320 \nu^{11} + 444640 \nu^{10} + 869603 \nu^{9} - 115039 \nu^{8} + 2984339 \nu^{7} + \cdots - 21167973 ) / 384912 \)
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\(\beta_{11}\) | \(=\) |
\( ( - 35555 \nu^{15} + 209918 \nu^{14} - 340439 \nu^{13} + 377302 \nu^{12} + 822876 \nu^{11} - 555316 \nu^{10} + 1446739 \nu^{9} + 6248686 \nu^{8} + \cdots + 358488666 ) / 384912 \)
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\(\beta_{12}\) | \(=\) |
\( ( 36175 \nu^{15} - 126178 \nu^{14} + 228019 \nu^{13} - 76154 \nu^{12} - 382332 \nu^{11} + 612740 \nu^{10} + 137617 \nu^{9} - 2689898 \nu^{8} + 3627757 \nu^{7} + \cdots - 166373838 ) / 384912 \)
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\(\beta_{13}\) | \(=\) |
\( ( 13197 \nu^{15} - 41905 \nu^{14} + 78133 \nu^{13} - 14485 \nu^{12} - 117448 \nu^{11} + 226080 \nu^{10} + 116311 \nu^{9} - 824875 \nu^{8} + 1357079 \nu^{7} + \cdots - 53118585 ) / 128304 \)
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\(\beta_{14}\) | \(=\) |
\( ( - 47866 \nu^{15} + 127777 \nu^{14} - 247654 \nu^{13} - 30859 \nu^{12} + 311940 \nu^{11} - 813620 \nu^{10} - 843826 \nu^{9} + 2022815 \nu^{8} - 5148238 \nu^{7} + \cdots + 134472069 ) / 384912 \)
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\(\beta_{15}\) | \(=\) |
\( ( - 5481 \nu^{15} + 12006 \nu^{14} - 25157 \nu^{13} - 12274 \nu^{12} + 21460 \nu^{11} - 95516 \nu^{10} - 141111 \nu^{9} + 126350 \nu^{8} - 619643 \nu^{7} + \cdots + 10314378 ) / 42768 \)
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\(\nu\) | \(=\) |
\( \beta_1 \)
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\(\nu^{2}\) | \(=\) |
\( \beta_{14} + \beta_{9} + \beta_{8} + \beta_{5} - \beta_{4} - \beta_{3} + \beta_{2} + \beta_1 \)
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\(\nu^{3}\) | \(=\) |
\( -2\beta_{15} - \beta_{13} - \beta_{12} - 2\beta_{8} + \beta_{7} + \beta_{6} - \beta_{5} - 2\beta_{4} + \beta_{3} - \beta _1 - 2 \)
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\(\nu^{4}\) | \(=\) |
\( \beta_{15} - 3 \beta_{14} + 5 \beta_{13} - 4 \beta_{12} + 2 \beta_{11} - \beta_{10} - \beta_{9} + \beta_{8} - 3 \beta_{7} + \beta_{5} + \beta_{4} + \beta_{3} + 3 \beta_{2} - \beta_1 \)
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\(\nu^{5}\) | \(=\) |
\( 7 \beta_{15} - 2 \beta_{14} + \beta_{12} - 5 \beta_{11} - 5 \beta_{10} + 5 \beta_{9} + \beta_{8} - 6 \beta_{6} + 3 \beta_{5} + 4 \beta_{4} + 4 \beta_{2} - 2 \beta_1 \)
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\(\nu^{6}\) | \(=\) |
\( 10 \beta_{15} - 5 \beta_{14} - 9 \beta_{13} + 13 \beta_{12} - 6 \beta_{11} + 12 \beta_{10} - 10 \beta_{9} - 5 \beta_{8} + 3 \beta_{7} - 20 \beta_{5} + 4 \beta_{4} - 12 \beta_{3} - 11 \beta_{2} - 11 \beta _1 - 16 \)
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\(\nu^{7}\) | \(=\) |
\( - 15 \beta_{15} - 2 \beta_{14} - 8 \beta_{13} - 2 \beta_{12} + 9 \beta_{11} + 9 \beta_{10} - 6 \beta_{9} - 5 \beta_{8} - 8 \beta_{7} + 10 \beta_{6} + 21 \beta_{5} + 16 \beta_{4} + 4 \beta_{3} + \beta_{2} + 2 \beta _1 + 14 \)
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\(\nu^{8}\) | \(=\) |
\( - 37 \beta_{15} + 22 \beta_{14} - 10 \beta_{13} + 26 \beta_{12} + 18 \beta_{11} - 12 \beta_{10} - 18 \beta_{9} + 6 \beta_{8} + \beta_{7} + 4 \beta_{6} - 18 \beta_{5} + 39 \beta_{3} - 20 \beta_{2} - 10 \)
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\(\nu^{9}\) | \(=\) |
\( 22 \beta_{15} + 40 \beta_{14} + 46 \beta_{13} - 18 \beta_{12} + 14 \beta_{11} + 2 \beta_{10} + 26 \beta_{9} + 36 \beta_{8} + 44 \beta_{7} + 2 \beta_{6} + 48 \beta_{5} - 22 \beta_{4} + 15 \beta_{3} - 26 \beta_{2} + 22 \beta _1 + 36 \)
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\(\nu^{10}\) | \(=\) |
\( - 11 \beta_{15} + 14 \beta_{14} - 24 \beta_{13} - 18 \beta_{12} - 44 \beta_{11} - 50 \beta_{10} + 34 \beta_{9} + 15 \beta_{8} + 14 \beta_{7} - 22 \beta_{6} - 22 \beta_{5} - 62 \beta_{4} - 62 \beta_{3} - 40 \beta_{2} + 4 \beta _1 + 112 \)
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\(\nu^{11}\) | \(=\) |
\( 41 \beta_{15} - 78 \beta_{14} + 89 \beta_{13} - 90 \beta_{12} + 2 \beta_{11} + 68 \beta_{10} - 42 \beta_{9} - 92 \beta_{8} - 5 \beta_{7} + 61 \beta_{6} - 117 \beta_{5} - 18 \beta_{4} - 73 \beta_{3} + 66 \beta_{2} + 59 \beta _1 + 153 \)
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\(\nu^{12}\) | \(=\) |
\( - 30 \beta_{15} + 5 \beta_{14} + 24 \beta_{13} - 78 \beta_{12} - 28 \beta_{11} - 211 \beta_{10} + 267 \beta_{9} + 101 \beta_{8} - 299 \beta_{7} - 122 \beta_{6} + 356 \beta_{5} + 19 \beta_{4} - 74 \beta_{3} + 293 \beta_{2} + 481 \beta _1 - 232 \)
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\(\nu^{13}\) | \(=\) |
\( 27 \beta_{15} + 238 \beta_{14} - 349 \beta_{13} + 305 \beta_{12} - 146 \beta_{11} + 220 \beta_{10} + 121 \beta_{9} - 164 \beta_{8} + 265 \beta_{7} - 17 \beta_{6} - 271 \beta_{5} - 486 \beta_{4} - 3 \beta_{3} + 166 \beta_{2} - 384 \beta _1 - 643 \)
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\(\nu^{14}\) | \(=\) |
\( - 289 \beta_{15} - 753 \beta_{14} + 145 \beta_{13} - 851 \beta_{12} + 332 \beta_{11} + 383 \beta_{10} - 608 \beta_{9} - 481 \beta_{8} - 73 \beta_{7} + 314 \beta_{6} + 209 \beta_{5} + 146 \beta_{4} + 626 \beta_{3} - 9 \beta_{2} + \cdots - 687 \)
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\(\nu^{15}\) | \(=\) |
\( 786 \beta_{15} - 652 \beta_{14} + 1048 \beta_{13} - 316 \beta_{12} + 169 \beta_{11} - 773 \beta_{10} - 385 \beta_{9} + 1261 \beta_{8} - 590 \beta_{7} - 644 \beta_{6} + 33 \beta_{5} + 1406 \beta_{4} + 493 \beta_{3} + 1169 \beta_{2} + \cdots + 1595 \)
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Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(1\) | \(1 + \beta_{5}\) | \(1\) |
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 | \(\iota_m(\nu)\) | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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43.1 |
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−2.20165 | − | 1.27113i | 0.500000 | − | 0.866025i | 2.23152 | + | 3.86511i | − | 4.07309i | −2.20165 | + | 1.27113i | 0.866025 | − | 0.500000i | − | 6.26168i | −0.500000 | − | 0.866025i | −5.17741 | + | 8.96754i | ||||||||||||||||||||||||||||||||||||||||||||||||||
43.2 | −1.98604 | − | 1.14664i | 0.500000 | − | 0.866025i | 1.62956 | + | 2.82249i | 0.692320i | −1.98604 | + | 1.14664i | −0.866025 | + | 0.500000i | − | 2.88753i | −0.500000 | − | 0.866025i | 0.793841 | − | 1.37497i | ||||||||||||||||||||||||||||||||||||||||||||||||||||
43.3 | −1.44724 | − | 0.835563i | 0.500000 | − | 0.866025i | 0.396329 | + | 0.686463i | 2.68351i | −1.44724 | + | 0.835563i | 0.866025 | − | 0.500000i | 2.01762i | −0.500000 | − | 0.866025i | 2.24224 | − | 3.88368i | |||||||||||||||||||||||||||||||||||||||||||||||||||||
43.4 | −0.654865 | − | 0.378087i | 0.500000 | − | 0.866025i | −0.714101 | − | 1.23686i | − | 4.01537i | −0.654865 | + | 0.378087i | −0.866025 | + | 0.500000i | 2.59231i | −0.500000 | − | 0.866025i | −1.51816 | + | 2.62953i | ||||||||||||||||||||||||||||||||||||||||||||||||||||
43.5 | 0.924500 | + | 0.533760i | 0.500000 | − | 0.866025i | −0.430200 | − | 0.745128i | − | 0.994065i | 0.924500 | − | 0.533760i | 0.866025 | − | 0.500000i | − | 3.05354i | −0.500000 | − | 0.866025i | 0.530592 | − | 0.919013i | |||||||||||||||||||||||||||||||||||||||||||||||||||
43.6 | 1.15033 | + | 0.664145i | 0.500000 | − | 0.866025i | −0.117823 | − | 0.204075i | − | 1.55828i | 1.15033 | − | 0.664145i | −0.866025 | + | 0.500000i | − | 2.96959i | −0.500000 | − | 0.866025i | 1.03492 | − | 1.79254i | |||||||||||||||||||||||||||||||||||||||||||||||||||
43.7 | 1.85837 | + | 1.07293i | 0.500000 | − | 0.866025i | 1.30235 | + | 2.25573i | 1.91954i | 1.85837 | − | 1.07293i | 0.866025 | − | 0.500000i | 1.29759i | −0.500000 | − | 0.866025i | −2.05953 | + | 3.56721i | |||||||||||||||||||||||||||||||||||||||||||||||||||||
43.8 | 2.35660 | + | 1.36058i | 0.500000 | − | 0.866025i | 2.70236 | + | 4.68063i | − | 1.58278i | 2.35660 | − | 1.36058i | −0.866025 | + | 0.500000i | 9.26480i | −0.500000 | − | 0.866025i | 2.15350 | − | 3.72996i | ||||||||||||||||||||||||||||||||||||||||||||||||||||
127.1 | −2.20165 | + | 1.27113i | 0.500000 | + | 0.866025i | 2.23152 | − | 3.86511i | 4.07309i | −2.20165 | − | 1.27113i | 0.866025 | + | 0.500000i | 6.26168i | −0.500000 | + | 0.866025i | −5.17741 | − | 8.96754i | |||||||||||||||||||||||||||||||||||||||||||||||||||||
127.2 | −1.98604 | + | 1.14664i | 0.500000 | + | 0.866025i | 1.62956 | − | 2.82249i | − | 0.692320i | −1.98604 | − | 1.14664i | −0.866025 | − | 0.500000i | 2.88753i | −0.500000 | + | 0.866025i | 0.793841 | + | 1.37497i | ||||||||||||||||||||||||||||||||||||||||||||||||||||
127.3 | −1.44724 | + | 0.835563i | 0.500000 | + | 0.866025i | 0.396329 | − | 0.686463i | − | 2.68351i | −1.44724 | − | 0.835563i | 0.866025 | + | 0.500000i | − | 2.01762i | −0.500000 | + | 0.866025i | 2.24224 | + | 3.88368i | |||||||||||||||||||||||||||||||||||||||||||||||||||
127.4 | −0.654865 | + | 0.378087i | 0.500000 | + | 0.866025i | −0.714101 | + | 1.23686i | 4.01537i | −0.654865 | − | 0.378087i | −0.866025 | − | 0.500000i | − | 2.59231i | −0.500000 | + | 0.866025i | −1.51816 | − | 2.62953i | ||||||||||||||||||||||||||||||||||||||||||||||||||||
127.5 | 0.924500 | − | 0.533760i | 0.500000 | + | 0.866025i | −0.430200 | + | 0.745128i | 0.994065i | 0.924500 | + | 0.533760i | 0.866025 | + | 0.500000i | 3.05354i | −0.500000 | + | 0.866025i | 0.530592 | + | 0.919013i | |||||||||||||||||||||||||||||||||||||||||||||||||||||
127.6 | 1.15033 | − | 0.664145i | 0.500000 | + | 0.866025i | −0.117823 | + | 0.204075i | 1.55828i | 1.15033 | + | 0.664145i | −0.866025 | − | 0.500000i | 2.96959i | −0.500000 | + | 0.866025i | 1.03492 | + | 1.79254i | |||||||||||||||||||||||||||||||||||||||||||||||||||||
127.7 | 1.85837 | − | 1.07293i | 0.500000 | + | 0.866025i | 1.30235 | − | 2.25573i | − | 1.91954i | 1.85837 | + | 1.07293i | 0.866025 | + | 0.500000i | − | 1.29759i | −0.500000 | + | 0.866025i | −2.05953 | − | 3.56721i | |||||||||||||||||||||||||||||||||||||||||||||||||||
127.8 | 2.35660 | − | 1.36058i | 0.500000 | + | 0.866025i | 2.70236 | − | 4.68063i | 1.58278i | 2.35660 | + | 1.36058i | −0.866025 | − | 0.500000i | − | 9.26480i | −0.500000 | + | 0.866025i | 2.15350 | + | 3.72996i | ||||||||||||||||||||||||||||||||||||||||||||||||||||
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
13.e | even | 6 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 273.2.bd.b | ✓ | 16 |
3.b | odd | 2 | 1 | 819.2.ct.c | 16 | ||
13.e | even | 6 | 1 | inner | 273.2.bd.b | ✓ | 16 |
13.f | odd | 12 | 1 | 3549.2.a.ba | 8 | ||
13.f | odd | 12 | 1 | 3549.2.a.bc | 8 | ||
39.h | odd | 6 | 1 | 819.2.ct.c | 16 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
273.2.bd.b | ✓ | 16 | 1.a | even | 1 | 1 | trivial |
273.2.bd.b | ✓ | 16 | 13.e | even | 6 | 1 | inner |
819.2.ct.c | 16 | 3.b | odd | 2 | 1 | ||
819.2.ct.c | 16 | 39.h | odd | 6 | 1 | ||
3549.2.a.ba | 8 | 13.f | odd | 12 | 1 | ||
3549.2.a.bc | 8 | 13.f | odd | 12 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{16} - 15 T_{2}^{14} + 152 T_{2}^{12} + 6 T_{2}^{11} - 839 T_{2}^{10} - 24 T_{2}^{9} + 3348 T_{2}^{8} - 78 T_{2}^{7} - 7502 T_{2}^{6} + 768 T_{2}^{5} + 11883 T_{2}^{4} - 3072 T_{2}^{3} - 7616 T_{2}^{2} + 1464 T_{2} + 3721 \)
acting on \(S_{2}^{\mathrm{new}}(273, [\chi])\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T^{16} - 15 T^{14} + 152 T^{12} + \cdots + 3721 \)
$3$
\( (T^{2} - T + 1)^{8} \)
$5$
\( T^{16} + 50 T^{14} + 943 T^{12} + \cdots + 20449 \)
$7$
\( (T^{4} - T^{2} + 1)^{4} \)
$11$
\( T^{16} - 68 T^{14} + 3295 T^{12} + \cdots + 583696 \)
$13$
\( T^{16} + 12 T^{15} + \cdots + 815730721 \)
$17$
\( T^{16} + 2 T^{15} + 95 T^{14} + \cdots + 238177489 \)
$19$
\( T^{16} - 79 T^{14} + 4962 T^{12} + \cdots + 9412624 \)
$23$
\( T^{16} + 6 T^{15} + 93 T^{14} + \cdots + 22886656 \)
$29$
\( T^{16} + 12 T^{15} + \cdots + 81511963009 \)
$31$
\( T^{16} + 238 T^{14} + \cdots + 1539149824 \)
$37$
\( T^{16} + 6 T^{15} + \cdots + 223550241721 \)
$41$
\( T^{16} + 30 T^{15} + \cdots + 7256313856 \)
$43$
\( T^{16} - 14 T^{15} + \cdots + 599528101264 \)
$47$
\( T^{16} + 566 T^{14} + \cdots + 1683953296 \)
$53$
\( (T^{8} - 14 T^{7} - 124 T^{6} + 2434 T^{5} + \cdots - 8807)^{2} \)
$59$
\( T^{16} + 24 T^{15} + \cdots + 2315546542864 \)
$61$
\( T^{16} - 2 T^{15} + \cdots + 114864732889 \)
$67$
\( T^{16} - 30 T^{15} + \cdots + 119295633664 \)
$71$
\( T^{16} + 6 T^{15} - 224 T^{14} + \cdots + 672053776 \)
$73$
\( T^{16} + 550 T^{14} + \cdots + 9572078569 \)
$79$
\( (T^{8} - 46 T^{7} + 741 T^{6} - 4238 T^{5} + \cdots - 7916)^{2} \)
$83$
\( T^{16} + 572 T^{14} + 107158 T^{12} + \cdots + 1430416 \)
$89$
\( T^{16} - 18 T^{15} + \cdots + 29787842814976 \)
$97$
\( T^{16} + 6 T^{15} - 229 T^{14} + \cdots + 43264 \)
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