Newspace parameters
Level: | \( N \) | \(=\) | \( 192 = 2^{6} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 192.i (of order \(4\), degree \(2\), not minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(5.23162107572\) |
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: | \( x^{20} - 2 x^{18} + 6 x^{16} - 24 x^{14} - 24 x^{12} + 1216 x^{10} - 384 x^{8} - 6144 x^{6} + 24576 x^{4} - 131072 x^{2} + 1048576 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{23} \) |
Twist minimal: | no (minimal twist has level 48) |
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 \( x^{20} - 2 x^{18} + 6 x^{16} - 24 x^{14} - 24 x^{12} + 1216 x^{10} - 384 x^{8} - 6144 x^{6} + 24576 x^{4} - 131072 x^{2} + 1048576 \) :
\(\beta_{1}\) | \(=\) | \( ( - 33 \nu^{18} - 42 \nu^{16} + 1090 \nu^{14} - 528 \nu^{12} - 11816 \nu^{10} + 6496 \nu^{8} - 64512 \nu^{6} + 1111040 \nu^{4} + 1482752 \nu^{2} - 16842752 ) / 10158080 \) |
\(\beta_{2}\) | \(=\) | \( ( - 3 \nu^{19} - 90 \nu^{17} + 430 \nu^{15} + 1288 \nu^{13} - 5816 \nu^{11} - 3904 \nu^{9} - 19328 \nu^{7} + 278528 \nu^{5} + 2621440 \nu^{3} - 1638400 \nu ) / 4063232 \) |
\(\beta_{3}\) | \(=\) | \( ( 4 \nu^{18} + 51 \nu^{16} - 74 \nu^{14} - 790 \nu^{12} + 2736 \nu^{10} + 5240 \nu^{8} + 45664 \nu^{6} + 11520 \nu^{4} - 942080 \nu^{2} + 2064384 ) / 507904 \) |
\(\beta_{4}\) | \(=\) | \( ( - 4 \nu^{19} - 112 \nu^{18} - 101 \nu^{17} + 542 \nu^{16} - 410 \nu^{15} - 980 \nu^{14} + 1946 \nu^{13} - 5372 \nu^{12} - 368 \nu^{11} + 13216 \nu^{10} + 24248 \nu^{9} + \cdots + 18481152 ) / 10158080 \) |
\(\beta_{5}\) | \(=\) | \( ( 4 \nu^{19} - 112 \nu^{18} + 101 \nu^{17} + 542 \nu^{16} + 410 \nu^{15} - 980 \nu^{14} - 1946 \nu^{13} - 5372 \nu^{12} + 368 \nu^{11} + 13216 \nu^{10} - 24248 \nu^{9} - 64976 \nu^{8} + \cdots + 18481152 ) / 10158080 \) |
\(\beta_{6}\) | \(=\) | \( ( - 187 \nu^{18} - 858 \nu^{16} + 6590 \nu^{14} - 21592 \nu^{12} - 90104 \nu^{10} - 159936 \nu^{8} - 782208 \nu^{6} + 3809280 \nu^{4} + 4169728 \nu^{2} + \cdots - 139460608 ) / 10158080 \) |
\(\beta_{7}\) | \(=\) | \( ( - 43 \nu^{18} - 106 \nu^{16} - 258 \nu^{14} - 1400 \nu^{12} + 7432 \nu^{10} - 17984 \nu^{8} - 125824 \nu^{6} + 706560 \nu^{4} - 1171456 \nu^{2} + 1966080 ) / 2031616 \) |
\(\beta_{8}\) | \(=\) | \( ( 79 \nu^{19} + 592 \nu^{18} - 34 \nu^{17} - 3112 \nu^{16} - 2030 \nu^{15} + 2320 \nu^{14} - 4896 \nu^{13} + 18832 \nu^{12} - 12392 \nu^{11} - 77056 \nu^{10} + 68512 \nu^{9} + \cdots - 96468992 ) / 40632320 \) |
\(\beta_{9}\) | \(=\) | \( ( - 79 \nu^{19} + 592 \nu^{18} + 34 \nu^{17} - 3112 \nu^{16} + 2030 \nu^{15} + 2320 \nu^{14} + 4896 \nu^{13} + 18832 \nu^{12} + 12392 \nu^{11} - 77056 \nu^{10} - 68512 \nu^{9} + \cdots - 96468992 ) / 40632320 \) |
\(\beta_{10}\) | \(=\) | \( ( - 117 \nu^{19} + 282 \nu^{17} + 2210 \nu^{15} - 8552 \nu^{13} - 18184 \nu^{11} + 45504 \nu^{9} - 161408 \nu^{7} + 3051520 \nu^{5} - 7176192 \nu^{3} + \cdots - 18546688 \nu ) / 20316160 \) |
\(\beta_{11}\) | \(=\) | \( ( 29 \nu^{18} - 100 \nu^{16} - 22 \nu^{14} + 1180 \nu^{12} - 280 \nu^{10} + 11696 \nu^{8} + 6976 \nu^{6} - 372224 \nu^{4} + 3276800 \nu^{2} - 327680 ) / 1015808 \) |
\(\beta_{12}\) | \(=\) | \( ( - 53 \nu^{19} - 48 \nu^{18} + 394 \nu^{17} + 320 \nu^{16} - 670 \nu^{15} - 2272 \nu^{14} - 392 \nu^{13} - 2624 \nu^{12} + 32824 \nu^{11} + 2944 \nu^{10} - 31936 \nu^{9} + \cdots + 15990784 ) / 8126464 \) |
\(\beta_{13}\) | \(=\) | \( ( 7 \nu^{19} - 38 \nu^{17} + 154 \nu^{15} + 136 \nu^{13} - 1640 \nu^{11} + 8448 \nu^{9} - 7808 \nu^{7} + 22016 \nu^{5} + 845824 \nu^{3} - 3457024 \nu ) / 1015808 \) |
\(\beta_{14}\) | \(=\) | \( ( 53 \nu^{19} - 48 \nu^{18} - 394 \nu^{17} + 320 \nu^{16} + 670 \nu^{15} - 2272 \nu^{14} + 392 \nu^{13} - 2624 \nu^{12} - 32824 \nu^{11} + 2944 \nu^{10} + 31936 \nu^{9} + 55040 \nu^{8} + \cdots + 15990784 ) / 8126464 \) |
\(\beta_{15}\) | \(=\) | \( ( - 25 \nu^{19} + 84 \nu^{18} + 1234 \nu^{17} - 808 \nu^{16} - 4022 \nu^{15} + 504 \nu^{14} - 5800 \nu^{13} + 11040 \nu^{12} + 22296 \nu^{11} - 23008 \nu^{10} - 69568 \nu^{9} + \cdots - 17825792 ) / 8126464 \) |
\(\beta_{16}\) | \(=\) | \( ( - 539 \nu^{19} - 1700 \nu^{18} - 386 \nu^{17} - 2840 \nu^{16} + 2190 \nu^{15} + 35560 \nu^{14} - 27464 \nu^{13} - 22240 \nu^{12} + 28232 \nu^{11} - 101280 \nu^{10} + \cdots - 399769600 ) / 40632320 \) |
\(\beta_{17}\) | \(=\) | \( ( 17 \nu^{19} - 37 \nu^{17} - 80 \nu^{15} + 302 \nu^{13} + 904 \nu^{11} + 8936 \nu^{9} + 6368 \nu^{7} - 250240 \nu^{5} + 686592 \nu^{3} + 2428928 \nu ) / 1269760 \) |
\(\beta_{18}\) | \(=\) | \( ( 597 \nu^{19} - 740 \nu^{18} - 962 \nu^{17} - 40 \nu^{16} - 530 \nu^{15} + 3400 \nu^{14} + 33272 \nu^{13} + 8000 \nu^{12} - 39736 \nu^{11} - 103840 \nu^{10} + 562176 \nu^{9} + \cdots - 76021760 ) / 40632320 \) |
\(\beta_{19}\) | \(=\) | \( ( - 539 \nu^{19} + 1700 \nu^{18} - 386 \nu^{17} + 2840 \nu^{16} + 2190 \nu^{15} - 35560 \nu^{14} - 27464 \nu^{13} + 22240 \nu^{12} + 28232 \nu^{11} + 101280 \nu^{10} + \cdots + 399769600 ) / 40632320 \) |
\(\nu\) | \(=\) | \( ( \beta_{17} - \beta_{13} + \beta_{10} + \beta_{2} ) / 4 \) |
\(\nu^{2}\) | \(=\) | \( ( \beta_{11} + \beta_{5} + \beta_{4} + 2\beta_1 ) / 2 \) |
\(\nu^{3}\) | \(=\) | \( ( \beta_{19} + \beta_{18} + \beta_{17} + \beta_{16} + \beta_{15} + \beta_{13} + \beta_{9} - \beta_{8} + \beta_{3} + 2\beta_{2} ) / 2 \) |
\(\nu^{4}\) | \(=\) | \( ( \beta_{19} - \beta_{16} - \beta_{14} - \beta_{12} - 2 \beta_{9} - 2 \beta_{8} + 2 \beta_{7} - 2 \beta_{5} - 2 \beta_{4} + 12 \beta_1 ) / 2 \) |
\(\nu^{5}\) | \(=\) | \( ( \beta_{19} + 2 \beta_{18} - 5 \beta_{17} + \beta_{16} - 3 \beta_{14} + 5 \beta_{13} + 3 \beta_{12} + \beta_{11} - 5 \beta_{10} - 11 \beta_{9} + 11 \beta_{8} + 3 \beta_{5} - 3 \beta_{4} + \beta_{3} + 7 \beta_{2} ) / 2 \) |
\(\nu^{6}\) | \(=\) | \( 3 \beta_{14} + 3 \beta_{12} + 3 \beta_{11} - 7 \beta_{9} - 7 \beta_{8} + \beta_{7} + \beta_{6} - 9 \beta_{5} - 9 \beta_{4} + \beta_{3} + 4 \beta _1 + 4 \) |
\(\nu^{7}\) | \(=\) | \( - 3 \beta_{19} - 13 \beta_{18} + 2 \beta_{17} - 3 \beta_{16} + 3 \beta_{15} - 2 \beta_{14} + 16 \beta_{13} + 2 \beta_{12} - 8 \beta_{11} - 3 \beta_{10} - \beta_{9} + \beta_{8} - 8 \beta_{5} + 8 \beta_{4} - 5 \beta_{3} + 7 \beta_{2} \) |
\(\nu^{8}\) | \(=\) | \( - \beta_{19} + \beta_{16} + 9 \beta_{14} + 9 \beta_{12} - 4 \beta_{11} + 28 \beta_{9} + 28 \beta_{8} + 6 \beta_{7} - 16 \beta_{6} + 14 \beta_{5} + 14 \beta_{4} + 14 \beta_{3} + 148 \beta _1 + 28 \) |
\(\nu^{9}\) | \(=\) | \( - \beta_{19} + 4 \beta_{18} + 37 \beta_{17} - \beta_{16} + 10 \beta_{15} - 7 \beta_{14} + 31 \beta_{13} + 7 \beta_{12} - 3 \beta_{11} + 95 \beta_{10} + 19 \beta_{9} - 19 \beta_{8} - 81 \beta_{5} + 81 \beta_{4} + 7 \beta_{3} - 17 \beta_{2} \) |
\(\nu^{10}\) | \(=\) | \( - 38 \beta_{19} + 38 \beta_{16} - 12 \beta_{14} - 12 \beta_{12} + 42 \beta_{11} + 18 \beta_{9} + 18 \beta_{8} + 30 \beta_{7} - 54 \beta_{6} + 14 \beta_{5} + 14 \beta_{4} + 78 \beta_{3} - 200 \beta _1 - 576 \) |
\(\nu^{11}\) | \(=\) | \( 56 \beta_{19} + 26 \beta_{18} + 30 \beta_{17} + 56 \beta_{16} - 18 \beta_{15} - 86 \beta_{14} + 182 \beta_{13} + 86 \beta_{12} + 22 \beta_{11} - 156 \beta_{10} + 148 \beta_{9} - 148 \beta_{8} + 18 \beta_{5} - 18 \beta_{4} + 4 \beta_{3} - 240 \beta_{2} \) |
\(\nu^{12}\) | \(=\) | \( - 26 \beta_{19} + 26 \beta_{16} - 18 \beta_{14} - 18 \beta_{12} - 236 \beta_{11} - 100 \beta_{9} - 100 \beta_{8} - 88 \beta_{7} - 276 \beta_{6} - 328 \beta_{5} - 328 \beta_{4} - 256 \beta_{3} + 168 \beta _1 - 1160 \) |
\(\nu^{13}\) | \(=\) | \( - 486 \beta_{19} - 100 \beta_{18} - 942 \beta_{17} - 486 \beta_{16} - 248 \beta_{15} - 150 \beta_{14} - 82 \beta_{13} + 150 \beta_{12} + 74 \beta_{11} - 662 \beta_{10} + 122 \beta_{9} - 122 \beta_{8} - 466 \beta_{5} + 466 \beta_{4} + \cdots + 34 \beta_{2} \) |
\(\nu^{14}\) | \(=\) | \( - 712 \beta_{19} + 712 \beta_{16} - 92 \beta_{14} - 92 \beta_{12} - 300 \beta_{11} + 388 \beta_{9} + 388 \beta_{8} - 1148 \beta_{7} - 332 \beta_{6} - 492 \beta_{5} - 492 \beta_{4} + 916 \beta_{3} - 2240 \beta _1 + 7024 \) |
\(\nu^{15}\) | \(=\) | \( - 1308 \beta_{19} - 1596 \beta_{18} + 2616 \beta_{17} - 1308 \beta_{16} - 908 \beta_{15} + 288 \beta_{14} - 1440 \beta_{13} - 288 \beta_{12} - 344 \beta_{11} + 4348 \beta_{10} + 5132 \beta_{9} - 5132 \beta_{8} + \cdots - 1068 \beta_{2} \) |
\(\nu^{16}\) | \(=\) | \( 36 \beta_{19} - 36 \beta_{16} - 1940 \beta_{14} - 1940 \beta_{12} + 1152 \beta_{11} + 2416 \beta_{9} + 2416 \beta_{8} - 5832 \beta_{7} - 1904 \beta_{6} + 11192 \beta_{5} + 11192 \beta_{4} + 264 \beta_{3} + \cdots - 21584 \) |
\(\nu^{17}\) | \(=\) | \( 340 \beta_{19} + 9200 \beta_{18} - 2164 \beta_{17} + 340 \beta_{16} + 7096 \beta_{15} + 1100 \beta_{14} + 1636 \beta_{13} - 1100 \beta_{12} + 1052 \beta_{11} + 7748 \beta_{10} + 15716 \beta_{9} - 15716 \beta_{8} + \cdots + 708 \beta_{2} \) |
\(\nu^{18}\) | \(=\) | \( 7096 \beta_{19} - 7096 \beta_{16} - 16912 \beta_{14} - 16912 \beta_{12} - 6824 \beta_{11} - 9576 \beta_{9} - 9576 \beta_{8} - 6936 \beta_{7} + 10104 \beta_{6} - 21112 \beta_{5} - 21112 \beta_{4} + \cdots - 28416 \) |
\(\nu^{19}\) | \(=\) | \( - 10944 \beta_{19} + 10200 \beta_{18} - 15480 \beta_{17} - 10944 \beta_{16} - 10040 \beta_{15} - 6664 \beta_{14} + 18600 \beta_{13} + 6664 \beta_{12} + 10120 \beta_{11} - 63952 \beta_{10} - 62448 \beta_{9} + \cdots - 9600 \beta_{2} \) |
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/192\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(133\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(\beta_{1}\) |
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 | \(\iota_m(\nu)\) | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
17.1 |
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0 | −2.77106 | − | 1.14944i | 0 | −4.80434 | − | 4.80434i | 0 | 7.36187i | 0 | 6.35757 | + | 6.37035i | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
17.2 | 0 | −2.75602 | + | 1.18505i | 0 | 0.00985921 | + | 0.00985921i | 0 | − | 6.42277i | 0 | 6.19134 | − | 6.53203i | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
17.3 | 0 | −1.50491 | + | 2.59524i | 0 | −2.59897 | − | 2.59897i | 0 | 7.30027i | 0 | −4.47050 | − | 7.81118i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
17.4 | 0 | −1.14944 | − | 2.77106i | 0 | 4.80434 | + | 4.80434i | 0 | 7.36187i | 0 | −6.35757 | + | 6.37035i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
17.5 | 0 | 0.164573 | + | 2.99548i | 0 | −3.61305 | − | 3.61305i | 0 | − | 12.2792i | 0 | −8.94583 | + | 0.985948i | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
17.6 | 0 | 1.18505 | − | 2.75602i | 0 | −0.00985921 | − | 0.00985921i | 0 | − | 6.42277i | 0 | −6.19134 | − | 6.53203i | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
17.7 | 0 | 2.06336 | + | 2.17774i | 0 | −3.17955 | − | 3.17955i | 0 | 6.03979i | 0 | −0.485128 | + | 8.98692i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
17.8 | 0 | 2.17774 | + | 2.06336i | 0 | 3.17955 | + | 3.17955i | 0 | 6.03979i | 0 | 0.485128 | + | 8.98692i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
17.9 | 0 | 2.59524 | − | 1.50491i | 0 | 2.59897 | + | 2.59897i | 0 | 7.30027i | 0 | 4.47050 | − | 7.81118i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
17.10 | 0 | 2.99548 | + | 0.164573i | 0 | 3.61305 | + | 3.61305i | 0 | − | 12.2792i | 0 | 8.94583 | + | 0.985948i | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
113.1 | 0 | −2.77106 | + | 1.14944i | 0 | −4.80434 | + | 4.80434i | 0 | − | 7.36187i | 0 | 6.35757 | − | 6.37035i | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
113.2 | 0 | −2.75602 | − | 1.18505i | 0 | 0.00985921 | − | 0.00985921i | 0 | 6.42277i | 0 | 6.19134 | + | 6.53203i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
113.3 | 0 | −1.50491 | − | 2.59524i | 0 | −2.59897 | + | 2.59897i | 0 | − | 7.30027i | 0 | −4.47050 | + | 7.81118i | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
113.4 | 0 | −1.14944 | + | 2.77106i | 0 | 4.80434 | − | 4.80434i | 0 | − | 7.36187i | 0 | −6.35757 | − | 6.37035i | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
113.5 | 0 | 0.164573 | − | 2.99548i | 0 | −3.61305 | + | 3.61305i | 0 | 12.2792i | 0 | −8.94583 | − | 0.985948i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
113.6 | 0 | 1.18505 | + | 2.75602i | 0 | −0.00985921 | + | 0.00985921i | 0 | 6.42277i | 0 | −6.19134 | + | 6.53203i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
113.7 | 0 | 2.06336 | − | 2.17774i | 0 | −3.17955 | + | 3.17955i | 0 | − | 6.03979i | 0 | −0.485128 | − | 8.98692i | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
113.8 | 0 | 2.17774 | − | 2.06336i | 0 | 3.17955 | − | 3.17955i | 0 | − | 6.03979i | 0 | 0.485128 | − | 8.98692i | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
113.9 | 0 | 2.59524 | + | 1.50491i | 0 | 2.59897 | − | 2.59897i | 0 | − | 7.30027i | 0 | 4.47050 | + | 7.81118i | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
113.10 | 0 | 2.99548 | − | 0.164573i | 0 | 3.61305 | − | 3.61305i | 0 | 12.2792i | 0 | 8.94583 | − | 0.985948i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
3.b | odd | 2 | 1 | inner |
16.e | even | 4 | 1 | inner |
48.i | odd | 4 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 192.3.i.b | 20 | |
3.b | odd | 2 | 1 | inner | 192.3.i.b | 20 | |
4.b | odd | 2 | 1 | 48.3.i.b | ✓ | 20 | |
8.b | even | 2 | 1 | 384.3.i.c | 20 | ||
8.d | odd | 2 | 1 | 384.3.i.d | 20 | ||
12.b | even | 2 | 1 | 48.3.i.b | ✓ | 20 | |
16.e | even | 4 | 1 | inner | 192.3.i.b | 20 | |
16.e | even | 4 | 1 | 384.3.i.c | 20 | ||
16.f | odd | 4 | 1 | 48.3.i.b | ✓ | 20 | |
16.f | odd | 4 | 1 | 384.3.i.d | 20 | ||
24.f | even | 2 | 1 | 384.3.i.d | 20 | ||
24.h | odd | 2 | 1 | 384.3.i.c | 20 | ||
48.i | odd | 4 | 1 | inner | 192.3.i.b | 20 | |
48.i | odd | 4 | 1 | 384.3.i.c | 20 | ||
48.k | even | 4 | 1 | 48.3.i.b | ✓ | 20 | |
48.k | even | 4 | 1 | 384.3.i.d | 20 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
48.3.i.b | ✓ | 20 | 4.b | odd | 2 | 1 | |
48.3.i.b | ✓ | 20 | 12.b | even | 2 | 1 | |
48.3.i.b | ✓ | 20 | 16.f | odd | 4 | 1 | |
48.3.i.b | ✓ | 20 | 48.k | even | 4 | 1 | |
192.3.i.b | 20 | 1.a | even | 1 | 1 | trivial | |
192.3.i.b | 20 | 3.b | odd | 2 | 1 | inner | |
192.3.i.b | 20 | 16.e | even | 4 | 1 | inner | |
192.3.i.b | 20 | 48.i | odd | 4 | 1 | inner | |
384.3.i.c | 20 | 8.b | even | 2 | 1 | ||
384.3.i.c | 20 | 16.e | even | 4 | 1 | ||
384.3.i.c | 20 | 24.h | odd | 2 | 1 | ||
384.3.i.c | 20 | 48.i | odd | 4 | 1 | ||
384.3.i.d | 20 | 8.d | odd | 2 | 1 | ||
384.3.i.d | 20 | 16.f | odd | 4 | 1 | ||
384.3.i.d | 20 | 24.f | even | 2 | 1 | ||
384.3.i.d | 20 | 48.k | even | 4 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5}^{20} + 3404T_{5}^{16} + 3190384T_{5}^{12} + 1068787520T_{5}^{8} + 108375444480T_{5}^{4} + 4096 \)
acting on \(S_{3}^{\mathrm{new}}(192, [\chi])\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T^{20} \)
$3$
\( T^{20} - 6 T^{19} + \cdots + 3486784401 \)
$5$
\( T^{20} + 3404 T^{16} + 3190384 T^{12} + \cdots + 4096 \)
$7$
\( (T^{10} + 336 T^{8} + 40676 T^{6} + \cdots + 655360000)^{2} \)
$11$
\( T^{20} + 207308 T^{16} + \cdots + 22\!\cdots\!00 \)
$13$
\( (T^{10} - 46 T^{9} + 1058 T^{8} + \cdots + 33620000)^{2} \)
$17$
\( (T^{10} + 952 T^{8} + \cdots + 15510536192)^{2} \)
$19$
\( (T^{10} - 26 T^{9} + 338 T^{8} + \cdots + 23975244288)^{2} \)
$23$
\( (T^{10} - 2236 T^{8} + \cdots - 2157878476800)^{2} \)
$29$
\( T^{20} + 8250700 T^{16} + \cdots + 14\!\cdots\!00 \)
$31$
\( (T^{5} - 20 T^{4} - 2750 T^{3} + \cdots - 6473680)^{4} \)
$37$
\( (T^{10} + 58 T^{9} + \cdots + 93878430976800)^{2} \)
$41$
\( (T^{10} - 8644 T^{8} + \cdots - 89172136396800)^{2} \)
$43$
\( (T^{10} + 86 T^{9} + \cdots + 398518394892800)^{2} \)
$47$
\( (T^{10} + 4944 T^{8} + \cdots + 2199023255552)^{2} \)
$53$
\( T^{20} + 33387084 T^{16} + \cdots + 51\!\cdots\!00 \)
$59$
\( T^{20} + 96029644 T^{16} + \cdots + 55\!\cdots\!00 \)
$61$
\( (T^{10} + 122 T^{9} + \cdots + 79\!\cdots\!68)^{2} \)
$67$
\( (T^{10} + 178 T^{9} + \cdots + 14\!\cdots\!00)^{2} \)
$71$
\( (T^{10} - 12876 T^{8} + \cdots - 63\!\cdots\!00)^{2} \)
$73$
\( (T^{10} + 16160 T^{8} + \cdots + 900192010240000)^{2} \)
$79$
\( (T^{5} + 96 T^{4} - 3534 T^{3} + \cdots + 147403248)^{4} \)
$83$
\( T^{20} + 433330892 T^{16} + \cdots + 53\!\cdots\!00 \)
$89$
\( (T^{10} - 49740 T^{8} + \cdots - 15\!\cdots\!00)^{2} \)
$97$
\( (T^{5} - 118 T^{4} - 11780 T^{3} + \cdots - 2657552000)^{4} \)
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