Newspace parameters
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.m (of order \(4\), degree \(2\), minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
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Defining polynomial: | \( x^{20} + 108x^{16} + 1318x^{12} + 4652x^{8} + 5057x^{4} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
$q$-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 \( x^{20} + 108x^{16} + 1318x^{12} + 4652x^{8} + 5057x^{4} + 256 \) :
\(\beta_{1}\) | \(=\) | \( ( -1233\nu^{19} - 120336\nu^{15} - 289166\nu^{11} + 6031344\nu^{7} + 9961151\nu^{3} ) / 5112544 \) |
\(\beta_{2}\) | \(=\) | \( ( 1843\nu^{18} + 199306\nu^{14} + 2457754\nu^{10} + 8963426\nu^{6} + 11554103\nu^{2} ) / 2556272 \) |
\(\beta_{3}\) | \(=\) | \( ( 2595\nu^{18} + 273087\nu^{14} + 2661844\nu^{10} + 4366379\nu^{6} - 932561\nu^{2} ) / 1278136 \) |
\(\beta_{4}\) | \(=\) | \( ( 4296 \nu^{18} - 7207 \nu^{16} + 477582 \nu^{14} - 770625 \nu^{12} + 7084096 \nu^{10} - 8670841 \nu^{8} + 32921622 \nu^{6} - 24076543 \nu^{4} + 42067188 \nu^{2} + \cdots - 13013696 ) / 5112544 \) |
\(\beta_{5}\) | \(=\) | \( ( - 3686 \nu^{19} + 4131 \nu^{17} - 398612 \nu^{15} + 450983 \nu^{13} - 4915508 \nu^{11} + 5923921 \nu^{9} - 17926852 \nu^{7} + 21144461 \nu^{5} + \cdots + 8864472 \nu ) / 5112544 \) |
\(\beta_{6}\) | \(=\) | \( ( - 4296 \nu^{18} - 7207 \nu^{16} - 477582 \nu^{14} - 770625 \nu^{12} - 7084096 \nu^{10} - 8670841 \nu^{8} - 32921622 \nu^{6} - 24076543 \nu^{4} + \cdots - 13013696 ) / 5112544 \) |
\(\beta_{7}\) | \(=\) | \( ( -10283\nu^{17} - 1090267\nu^{13} - 11417761\nu^{9} - 27008625\nu^{5} - 12050376\nu ) / 5112544 \) |
\(\beta_{8}\) | \(=\) | \( ( - 14579 \nu^{18} - 5890 \nu^{16} - 1567849 \nu^{14} - 610604 \nu^{12} - 18501857 \nu^{10} - 5104050 \nu^{8} - 59930247 \nu^{6} - 3630112 \nu^{4} + \cdots + 9123648 ) / 5112544 \) |
\(\beta_{9}\) | \(=\) | \( ( 14579 \nu^{18} - 5890 \nu^{16} + 1567849 \nu^{14} - 610604 \nu^{12} + 18501857 \nu^{10} - 5104050 \nu^{8} + 59930247 \nu^{6} - 3630112 \nu^{4} + 54117564 \nu^{2} + \cdots + 9123648 ) / 5112544 \) |
\(\beta_{10}\) | \(=\) | \( ( 30391\nu^{19} + 3256034\nu^{15} + 37292880\nu^{11} + 113829150\nu^{7} + 98273977\nu^{3} ) / 10225088 \) |
\(\beta_{11}\) | \(=\) | \( ( - 14918 \nu^{19} + 1504 \nu^{17} - 1619593 \nu^{15} + 147562 \nu^{13} - 20551431 \nu^{11} + 408180 \nu^{9} - 78087767 \nu^{7} - 9194094 \nu^{5} + \cdots - 24973328 \nu ) / 5112544 \) |
\(\beta_{12}\) | \(=\) | \( ( 14918 \nu^{19} + 1504 \nu^{17} + 1619593 \nu^{15} + 147562 \nu^{13} + 20551431 \nu^{11} + 408180 \nu^{9} + 78087767 \nu^{7} - 9194094 \nu^{5} + \cdots - 24973328 \nu ) / 5112544 \) |
\(\beta_{13}\) | \(=\) | \( ( 18604 \nu^{19} - 1504 \nu^{17} + 2018205 \nu^{15} - 147562 \nu^{13} + 25466939 \nu^{11} - 408180 \nu^{9} + 96014619 \nu^{7} + 9194094 \nu^{5} + \cdots + 19860784 \nu ) / 5112544 \) |
\(\beta_{14}\) | \(=\) | \( ( - 18604 \nu^{19} - 1504 \nu^{17} - 2018205 \nu^{15} - 147562 \nu^{13} - 25466939 \nu^{11} - 408180 \nu^{9} - 96014619 \nu^{7} + 9194094 \nu^{5} + \cdots + 19860784 \nu ) / 5112544 \) |
\(\beta_{15}\) | \(=\) | \( ( 10893 \nu^{19} + 3076 \nu^{17} + 13621 \nu^{16} + 1169237 \nu^{15} + 319642 \nu^{13} + 1438589 \nu^{12} + 13586349 \nu^{11} + 2746920 \nu^{9} + 14554471 \nu^{8} + \cdots + 18284064 ) / 5112544 \) |
\(\beta_{16}\) | \(=\) | \( ( - 14579 \nu^{18} + 23836 \nu^{16} - 1567849 \nu^{14} + 2504338 \nu^{12} - 18501857 \nu^{10} + 24041672 \nu^{8} - 59930247 \nu^{6} + 37863114 \nu^{4} + \cdots - 8423808 ) / 5112544 \) |
\(\beta_{17}\) | \(=\) | \( ( - 10893 \nu^{19} - 21341 \nu^{18} - 3076 \nu^{17} - 1169237 \nu^{15} - 2286103 \nu^{14} - 319642 \nu^{13} - 13586349 \nu^{11} - 26164285 \nu^{10} + \cdots + 963320 \nu ) / 5112544 \) |
\(\beta_{18}\) | \(=\) | \( ( - 11787 \nu^{18} - 17752 \nu^{17} - 8973 \nu^{16} - 1237829 \nu^{14} - 1889572 \nu^{13} - 946867 \nu^{12} - 11825941 \nu^{10} - 20478392 \nu^{9} - 9468811 \nu^{8} + \cdots - 349920 ) / 5112544 \) |
\(\beta_{19}\) | \(=\) | \( ( - 77979 \nu^{19} - 23574 \nu^{18} + 17946 \nu^{16} - 8384792 \nu^{15} - 2475658 \nu^{14} + 1893734 \nu^{12} - 98874134 \nu^{11} - 23651882 \nu^{10} + \cdots + 699840 ) / 10225088 \) |
\(\nu\) | \(=\) | \( ( -\beta_{14} - \beta_{13} - \beta_{12} - \beta_{11} ) / 2 \) |
\(\nu^{2}\) | \(=\) | \( ( 2 \beta_{17} + 2 \beta_{14} - \beta_{13} + 2 \beta_{12} - \beta_{11} + 2 \beta_{10} + \beta_{9} - \beta_{8} - \beta_{7} + \beta_{6} - \beta_{5} - \beta_{4} + 6 \beta_{2} + \beta_1 ) / 2 \) |
\(\nu^{3}\) | \(=\) | \( ( 4 \beta_{19} - 2 \beta_{16} - 5 \beta_{14} + 5 \beta_{13} - 5 \beta_{12} + 5 \beta_{11} + 8 \beta_{10} - 2 \beta_{8} + 2 \beta_{6} - 2 \beta_{4} + 2 \beta_{3} - 4 \beta_{2} + 2 \beta_1 ) / 2 \) |
\(\nu^{4}\) | \(=\) | \( ( 4 \beta_{16} + 18 \beta_{15} - 18 \beta_{14} + 9 \beta_{13} - 18 \beta_{12} + 9 \beta_{11} - 18 \beta_{10} + 15 \beta_{9} + 11 \beta_{8} + 9 \beta_{7} + 13 \beta_{6} + 9 \beta_{5} + 13 \beta_{4} - 9 \beta _1 - 38 ) / 2 \) |
\(\nu^{5}\) | \(=\) | \( ( - 48 \beta_{18} - 24 \beta_{16} + 59 \beta_{14} + 39 \beta_{13} + 63 \beta_{12} + 43 \beta_{11} - 48 \beta_{9} + 24 \beta_{8} + 76 \beta_{7} - 24 \beta_{6} - 20 \beta_{5} + 24 \beta_{4} - 24 \beta_{3} + 48 \beta_{2} ) / 2 \) |
\(\nu^{6}\) | \(=\) | \( ( - 166 \beta_{17} - 166 \beta_{14} + 83 \beta_{13} - 166 \beta_{12} + 83 \beta_{11} - 166 \beta_{10} - 131 \beta_{9} + 131 \beta_{8} + 83 \beta_{7} - 111 \beta_{6} + 83 \beta_{5} + 111 \beta_{4} + 52 \beta_{3} - 330 \beta_{2} - 83 \beta_1 ) / 2 \) |
\(\nu^{7}\) | \(=\) | \( ( - 492 \beta_{19} + 246 \beta_{16} + 411 \beta_{14} - 411 \beta_{13} + 359 \beta_{12} - 359 \beta_{11} - 976 \beta_{10} + 246 \beta_{8} - 246 \beta_{6} + 246 \beta_{4} - 246 \beta_{3} + 492 \beta_{2} - 186 \beta_1 ) / 2 \) |
\(\nu^{8}\) | \(=\) | \( ( - 544 \beta_{16} - 1582 \beta_{15} + 1582 \beta_{14} - 791 \beta_{13} + 1582 \beta_{12} - 791 \beta_{11} + 1582 \beta_{10} - 1637 \beta_{9} - 1093 \beta_{8} - 791 \beta_{7} - 1279 \beta_{6} - 791 \beta_{5} + \cdots + 3122 ) / 2 \) |
\(\nu^{9}\) | \(=\) | \( ( 4856 \beta_{18} + 2428 \beta_{16} - 5213 \beta_{14} - 3445 \beta_{13} - 5757 \beta_{12} - 3989 \beta_{11} + 4856 \beta_{9} - 2428 \beta_{8} - 7832 \beta_{7} + 2428 \beta_{6} + 1768 \beta_{5} - 2428 \beta_{4} + \cdots - 4856 \beta_{2} ) / 2 \) |
\(\nu^{10}\) | \(=\) | \( ( 15282 \beta_{17} + 15282 \beta_{14} - 7641 \beta_{13} + 15282 \beta_{12} - 7641 \beta_{11} + 15282 \beta_{10} + 12441 \beta_{9} - 12441 \beta_{8} - 7641 \beta_{7} + 10673 \beta_{6} - 7641 \beta_{5} + \cdots + 7641 \beta_1 ) / 2 \) |
\(\nu^{11}\) | \(=\) | \( ( 47428 \beta_{19} - 23714 \beta_{16} - 38789 \beta_{14} + 38789 \beta_{13} - 33389 \beta_{12} + 33389 \beta_{11} + 93656 \beta_{10} - 23714 \beta_{8} + 23714 \beta_{6} - 23714 \beta_{4} + 23714 \beta_{3} + \cdots + 17050 \beta_1 ) / 2 \) |
\(\nu^{12}\) | \(=\) | \( ( 52828 \beta_{16} + 148306 \beta_{15} - 148306 \beta_{14} + 74153 \beta_{13} - 148306 \beta_{12} + 74153 \beta_{11} - 148306 \beta_{10} + 156759 \beta_{9} + 103931 \beta_{8} + 74153 \beta_{7} + \cdots - 292662 ) / 2 \) |
\(\nu^{13}\) | \(=\) | \( ( - 461824 \beta_{18} - 230912 \beta_{16} + 489771 \beta_{14} + 324415 \beta_{13} + 542599 \beta_{12} + 377243 \beta_{11} - 461824 \beta_{9} + 230912 \beta_{8} + 746292 \beta_{7} + \cdots + 461824 \beta_{2} ) / 2 \) |
\(\nu^{14}\) | \(=\) | \( ( - 1441366 \beta_{17} - 1441366 \beta_{14} + 720683 \beta_{13} - 1441366 \beta_{12} + 720683 \beta_{11} - 1441366 \beta_{10} - 1176507 \beta_{9} + 1176507 \beta_{8} + 720683 \beta_{7} + \cdots - 720683 \beta_1 ) / 2 \) |
\(\nu^{15}\) | \(=\) | \( ( - 4492972 \beta_{19} + 2246486 \beta_{16} + 3668827 \beta_{14} - 3668827 \beta_{13} + 3154175 \beta_{12} - 3154175 \beta_{11} - 8868288 \beta_{10} + 2246486 \beta_{8} + \cdots - 1606722 \beta_1 ) / 2 \) |
\(\nu^{16}\) | \(=\) | \( ( - 5007624 \beta_{16} - 14014766 \beta_{15} + 14014766 \beta_{14} - 7007383 \beta_{13} + 14014766 \beta_{12} - 7007383 \beta_{11} + 14014766 \beta_{10} - 14842429 \beta_{9} + \cdots + 27660770 ) / 2 \) |
\(\nu^{17}\) | \(=\) | \( ( 43699624 \beta_{18} + 21849812 \beta_{16} - 46294061 \beta_{14} - 30672573 \beta_{13} - 51301685 \beta_{12} - 35680197 \beta_{11} + 43699624 \beta_{9} - 21849812 \beta_{8} + \cdots - 43699624 \beta_{2} ) / 2 \) |
\(\nu^{18}\) | \(=\) | \( ( 136287746 \beta_{17} + 136287746 \beta_{14} - 68143873 \beta_{13} + 136287746 \beta_{12} - 68143873 \beta_{11} + 136287746 \beta_{10} + 111270017 \beta_{9} + \cdots + 68143873 \beta_1 ) / 2 \) |
\(\nu^{19}\) | \(=\) | \( ( 424999300 \beta_{19} - 212499650 \beta_{16} - 346996293 \beta_{14} + 346996293 \beta_{13} - 298289045 \beta_{12} + 298289045 \beta_{11} + 838836392 \beta_{10} + \cdots + 151909234 \beta_1 ) / 2 \) |
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-\beta_{2}\) |
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 | \(\iota_m(\nu)\) | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
37.1 |
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−0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | − | 1.00000i | −1.29975 | + | 1.81952i | −1.00000 | −0.728588 | − | 0.728588i | 0.707107 | + | 0.707107i | 1.00000i | −0.367533 | − | 2.20566i | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
37.2 | −0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | − | 1.00000i | 0.114611 | − | 2.23313i | −1.00000 | −1.40368 | − | 1.40368i | 0.707107 | + | 0.707107i | 1.00000i | 1.49802 | + | 1.66010i | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
37.3 | −0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | − | 1.00000i | 0.528178 | + | 2.17279i | −1.00000 | 0.904140 | + | 0.904140i | 0.707107 | + | 0.707107i | 1.00000i | −1.90987 | − | 1.16292i | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
37.4 | −0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | − | 1.00000i | 1.42113 | − | 1.72638i | −1.00000 | 3.40461 | + | 3.40461i | 0.707107 | + | 0.707107i | 1.00000i | 0.215841 | + | 2.22563i | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
37.5 | −0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | − | 1.00000i | 2.23583 | − | 0.0328054i | −1.00000 | −3.17648 | − | 3.17648i | 0.707107 | + | 0.707107i | 1.00000i | −1.55777 | + | 1.60417i | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
37.6 | 0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | − | 1.00000i | −1.29975 | + | 1.81952i | −1.00000 | −0.728588 | − | 0.728588i | −0.707107 | − | 0.707107i | 1.00000i | 0.367533 | + | 2.20566i | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
37.7 | 0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | − | 1.00000i | 0.114611 | − | 2.23313i | −1.00000 | −1.40368 | − | 1.40368i | −0.707107 | − | 0.707107i | 1.00000i | −1.49802 | − | 1.66010i | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
37.8 | 0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | − | 1.00000i | 0.528178 | + | 2.17279i | −1.00000 | 0.904140 | + | 0.904140i | −0.707107 | − | 0.707107i | 1.00000i | 1.90987 | + | 1.16292i | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
37.9 | 0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | − | 1.00000i | 1.42113 | − | 1.72638i | −1.00000 | 3.40461 | + | 3.40461i | −0.707107 | − | 0.707107i | 1.00000i | −0.215841 | − | 2.22563i | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
37.10 | 0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | − | 1.00000i | 2.23583 | − | 0.0328054i | −1.00000 | −3.17648 | − | 3.17648i | −0.707107 | − | 0.707107i | 1.00000i | 1.55777 | − | 1.60417i | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
493.1 | −0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | 1.00000i | −1.29975 | − | 1.81952i | −1.00000 | −0.728588 | + | 0.728588i | 0.707107 | − | 0.707107i | − | 1.00000i | −0.367533 | + | 2.20566i | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
493.2 | −0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | 1.00000i | 0.114611 | + | 2.23313i | −1.00000 | −1.40368 | + | 1.40368i | 0.707107 | − | 0.707107i | − | 1.00000i | 1.49802 | − | 1.66010i | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
493.3 | −0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | 1.00000i | 0.528178 | − | 2.17279i | −1.00000 | 0.904140 | − | 0.904140i | 0.707107 | − | 0.707107i | − | 1.00000i | −1.90987 | + | 1.16292i | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
493.4 | −0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | 1.00000i | 1.42113 | + | 1.72638i | −1.00000 | 3.40461 | − | 3.40461i | 0.707107 | − | 0.707107i | − | 1.00000i | 0.215841 | − | 2.22563i | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
493.5 | −0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | 1.00000i | 2.23583 | + | 0.0328054i | −1.00000 | −3.17648 | + | 3.17648i | 0.707107 | − | 0.707107i | − | 1.00000i | −1.55777 | − | 1.60417i | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
493.6 | 0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | 1.00000i | −1.29975 | − | 1.81952i | −1.00000 | −0.728588 | + | 0.728588i | −0.707107 | + | 0.707107i | − | 1.00000i | 0.367533 | − | 2.20566i | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
493.7 | 0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | 1.00000i | 0.114611 | + | 2.23313i | −1.00000 | −1.40368 | + | 1.40368i | −0.707107 | + | 0.707107i | − | 1.00000i | −1.49802 | + | 1.66010i | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
493.8 | 0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | 1.00000i | 0.528178 | − | 2.17279i | −1.00000 | 0.904140 | − | 0.904140i | −0.707107 | + | 0.707107i | − | 1.00000i | 1.90987 | − | 1.16292i | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
493.9 | 0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | 1.00000i | 1.42113 | + | 1.72638i | −1.00000 | 3.40461 | − | 3.40461i | −0.707107 | + | 0.707107i | − | 1.00000i | −0.215841 | + | 2.22563i | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
493.10 | 0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | 1.00000i | 2.23583 | + | 0.0328054i | −1.00000 | −3.17648 | + | 3.17648i | −0.707107 | + | 0.707107i | − | 1.00000i | 1.55777 | + | 1.60417i | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
5.c | odd | 4 | 1 | inner |
19.b | odd | 2 | 1 | inner |
95.g | even | 4 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 570.2.m.b | ✓ | 20 |
3.b | odd | 2 | 1 | 1710.2.p.c | 20 | ||
5.c | odd | 4 | 1 | inner | 570.2.m.b | ✓ | 20 |
15.e | even | 4 | 1 | 1710.2.p.c | 20 | ||
19.b | odd | 2 | 1 | inner | 570.2.m.b | ✓ | 20 |
57.d | even | 2 | 1 | 1710.2.p.c | 20 | ||
95.g | even | 4 | 1 | inner | 570.2.m.b | ✓ | 20 |
285.j | odd | 4 | 1 | 1710.2.p.c | 20 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
570.2.m.b | ✓ | 20 | 1.a | even | 1 | 1 | trivial |
570.2.m.b | ✓ | 20 | 5.c | odd | 4 | 1 | inner |
570.2.m.b | ✓ | 20 | 19.b | odd | 2 | 1 | inner |
570.2.m.b | ✓ | 20 | 95.g | even | 4 | 1 | inner |
1710.2.p.c | 20 | 3.b | odd | 2 | 1 | ||
1710.2.p.c | 20 | 15.e | even | 4 | 1 | ||
1710.2.p.c | 20 | 57.d | even | 2 | 1 | ||
1710.2.p.c | 20 | 285.j | odd | 4 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{7}^{10} + 2 T_{7}^{9} + 2 T_{7}^{8} + 8 T_{7}^{7} + 496 T_{7}^{6} + 1184 T_{7}^{5} + 1408 T_{7}^{4} - 320 T_{7}^{3} + 1600 T_{7}^{2} + 3200 T_{7} + 3200 \)
acting on \(S_{2}^{\mathrm{new}}(570, [\chi])\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( (T^{4} + 1)^{5} \)
$3$
\( (T^{4} + 1)^{5} \)
$5$
\( (T^{10} - 6 T^{9} + 25 T^{8} - 80 T^{7} + \cdots + 3125)^{2} \)
$7$
\( (T^{10} + 2 T^{9} + 2 T^{8} + 8 T^{7} + \cdots + 3200)^{2} \)
$11$
\( (T^{5} + 2 T^{4} - 36 T^{3} - 16 T^{2} + \cdots - 400)^{4} \)
$13$
\( T^{20} + 1248 T^{16} + 203872 T^{12} + \cdots + 4096 \)
$17$
\( (T^{10} + 6 T^{9} + 18 T^{8} - 64 T^{7} + \cdots + 12800)^{2} \)
$19$
\( T^{20} - 58 T^{18} + \cdots + 6131066257801 \)
$23$
\( (T^{10} + 2 T^{9} + 2 T^{8} - 24 T^{7} + \cdots + 156800)^{2} \)
$29$
\( (T^{10} - 112 T^{8} + 4320 T^{6} + \cdots - 51200)^{2} \)
$31$
\( (T^{10} + 192 T^{8} + 12544 T^{6} + \cdots + 204800)^{2} \)
$37$
\( T^{20} + 8928 T^{16} + \cdots + 362615934976 \)
$41$
\( (T^{10} + 64 T^{8} + 1320 T^{6} + \cdots + 51200)^{2} \)
$43$
\( (T^{10} + 6 T^{9} + 18 T^{8} + 224 T^{7} + \cdots + 768800)^{2} \)
$47$
\( (T^{10} + 22 T^{9} + 242 T^{8} + \cdots + 2000000)^{2} \)
$53$
\( T^{20} + 30928 T^{16} + \cdots + 12\!\cdots\!56 \)
$59$
\( (T^{10} - 160 T^{8} + 1944 T^{6} + \cdots - 3200)^{2} \)
$61$
\( (T^{5} - 248 T^{3} - 816 T^{2} + \cdots + 56000)^{4} \)
$67$
\( T^{20} + 85248 T^{16} + \cdots + 91\!\cdots\!96 \)
$71$
\( (T^{10} + 200 T^{8} + 12288 T^{6} + \cdots + 3276800)^{2} \)
$73$
\( (T^{10} + 2 T^{9} + 2 T^{8} + \cdots + 1468820000)^{2} \)
$79$
\( (T^{10} - 384 T^{8} + 28256 T^{6} + \cdots - 2508800)^{2} \)
$83$
\( (T^{10} - 38 T^{9} + 722 T^{8} + \cdots + 356979200)^{2} \)
$89$
\( (T^{10} - 192 T^{8} + 12680 T^{6} + \cdots - 3699200)^{2} \)
$97$
\( T^{20} + 113680 T^{16} + \cdots + 18\!\cdots\!36 \)
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