Properties

Label 192.3.i.b
Level $192$
Weight $3$
Character orbit 192.i
Analytic conductor $5.232$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

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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: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Defining polynomial: \( x^{20} - 2 x^{18} + 6 x^{16} - 24 x^{14} - 24 x^{12} + 1216 x^{10} - 384 x^{8} - 6144 x^{6} + 24576 x^{4} - 131072 x^{2} + 1048576 \) Copy content Toggle raw display
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.

\(f(q)\) \(=\) \( q + \beta_{4} q^{3} + ( - \beta_{10} - \beta_{9} + \beta_{8}) q^{5} - \beta_{6} q^{7} + \beta_{19} q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + \beta_{4} q^{3} + ( - \beta_{10} - \beta_{9} + \beta_{8}) q^{5} - \beta_{6} q^{7} + \beta_{19} q^{9} + ( - \beta_{18} + \beta_{15} + \beta_{13} - \beta_{11} + \beta_{10}) q^{11} + ( - \beta_{5} - \beta_{4} + \beta_{3} - 5 \beta_1 + 5) q^{13} + ( - \beta_{15} + \beta_{14} - \beta_{12} + \beta_{11} - \beta_{3} + 6) q^{15} + (\beta_{14} - \beta_{13} - \beta_{12} + \beta_{9} - \beta_{8} - \beta_{5} + \beta_{4} - \beta_{2}) q^{17} + (\beta_{19} - \beta_{16} + \beta_{14} + \beta_{12} + \beta_{7} + \beta_{6} - 3 \beta_{5} - 3 \beta_{4} - 4 \beta_1 + 4) q^{19} + ( - \beta_{19} - \beta_{18} + \beta_{15} + 4 \beta_{13} + \beta_{12} + \beta_{11} - \beta_{10} + 2 \beta_{9} + \cdots + 4) q^{21}+ \cdots + (\beta_{18} + 18 \beta_{17} + 4 \beta_{16} + \beta_{15} - 4 \beta_{14} - 9 \beta_{5} + 9 \beta_{4} + \cdots + 24) q^{99}+O(q^{100}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 6 q^{3}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 6 q^{3} + 92 q^{13} + 116 q^{15} + 52 q^{19} + 48 q^{21} - 18 q^{27} + 80 q^{31} + 60 q^{33} - 116 q^{37} - 172 q^{43} + 60 q^{45} - 364 q^{49} - 128 q^{51} - 244 q^{61} - 296 q^{63} - 356 q^{67} - 20 q^{69} + 146 q^{75} - 384 q^{79} - 188 q^{81} + 48 q^{85} - 136 q^{91} - 132 q^{93} + 472 q^{97} + 452 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Basis of coefficient ring in terms of a root \(\nu\) of \( x^{20} - 2 x^{18} + 6 x^{16} - 24 x^{14} - 24 x^{12} + 1216 x^{10} - 384 x^{8} - 6144 x^{6} + 24576 x^{4} - 131072 x^{2} + 1048576 \) : Copy content Toggle raw display

\(\beta_{1}\)\(=\) \( ( - 33 \nu^{18} - 42 \nu^{16} + 1090 \nu^{14} - 528 \nu^{12} - 11816 \nu^{10} + 6496 \nu^{8} - 64512 \nu^{6} + 1111040 \nu^{4} + 1482752 \nu^{2} - 16842752 ) / 10158080 \) Copy content Toggle raw display
\(\beta_{2}\)\(=\) \( ( - 3 \nu^{19} - 90 \nu^{17} + 430 \nu^{15} + 1288 \nu^{13} - 5816 \nu^{11} - 3904 \nu^{9} - 19328 \nu^{7} + 278528 \nu^{5} + 2621440 \nu^{3} - 1638400 \nu ) / 4063232 \) Copy content Toggle raw display
\(\beta_{3}\)\(=\) \( ( 4 \nu^{18} + 51 \nu^{16} - 74 \nu^{14} - 790 \nu^{12} + 2736 \nu^{10} + 5240 \nu^{8} + 45664 \nu^{6} + 11520 \nu^{4} - 942080 \nu^{2} + 2064384 ) / 507904 \) Copy content Toggle raw display
\(\beta_{4}\)\(=\) \( ( - 4 \nu^{19} - 112 \nu^{18} - 101 \nu^{17} + 542 \nu^{16} - 410 \nu^{15} - 980 \nu^{14} + 1946 \nu^{13} - 5372 \nu^{12} - 368 \nu^{11} + 13216 \nu^{10} + 24248 \nu^{9} + \cdots + 18481152 ) / 10158080 \) Copy content Toggle raw display
\(\beta_{5}\)\(=\) \( ( 4 \nu^{19} - 112 \nu^{18} + 101 \nu^{17} + 542 \nu^{16} + 410 \nu^{15} - 980 \nu^{14} - 1946 \nu^{13} - 5372 \nu^{12} + 368 \nu^{11} + 13216 \nu^{10} - 24248 \nu^{9} - 64976 \nu^{8} + \cdots + 18481152 ) / 10158080 \) Copy content Toggle raw display
\(\beta_{6}\)\(=\) \( ( - 187 \nu^{18} - 858 \nu^{16} + 6590 \nu^{14} - 21592 \nu^{12} - 90104 \nu^{10} - 159936 \nu^{8} - 782208 \nu^{6} + 3809280 \nu^{4} + 4169728 \nu^{2} + \cdots - 139460608 ) / 10158080 \) Copy content Toggle raw display
\(\beta_{7}\)\(=\) \( ( - 43 \nu^{18} - 106 \nu^{16} - 258 \nu^{14} - 1400 \nu^{12} + 7432 \nu^{10} - 17984 \nu^{8} - 125824 \nu^{6} + 706560 \nu^{4} - 1171456 \nu^{2} + 1966080 ) / 2031616 \) Copy content Toggle raw display
\(\beta_{8}\)\(=\) \( ( 79 \nu^{19} + 592 \nu^{18} - 34 \nu^{17} - 3112 \nu^{16} - 2030 \nu^{15} + 2320 \nu^{14} - 4896 \nu^{13} + 18832 \nu^{12} - 12392 \nu^{11} - 77056 \nu^{10} + 68512 \nu^{9} + \cdots - 96468992 ) / 40632320 \) Copy content Toggle raw display
\(\beta_{9}\)\(=\) \( ( - 79 \nu^{19} + 592 \nu^{18} + 34 \nu^{17} - 3112 \nu^{16} + 2030 \nu^{15} + 2320 \nu^{14} + 4896 \nu^{13} + 18832 \nu^{12} + 12392 \nu^{11} - 77056 \nu^{10} - 68512 \nu^{9} + \cdots - 96468992 ) / 40632320 \) Copy content Toggle raw display
\(\beta_{10}\)\(=\) \( ( - 117 \nu^{19} + 282 \nu^{17} + 2210 \nu^{15} - 8552 \nu^{13} - 18184 \nu^{11} + 45504 \nu^{9} - 161408 \nu^{7} + 3051520 \nu^{5} - 7176192 \nu^{3} + \cdots - 18546688 \nu ) / 20316160 \) Copy content Toggle raw display
\(\beta_{11}\)\(=\) \( ( 29 \nu^{18} - 100 \nu^{16} - 22 \nu^{14} + 1180 \nu^{12} - 280 \nu^{10} + 11696 \nu^{8} + 6976 \nu^{6} - 372224 \nu^{4} + 3276800 \nu^{2} - 327680 ) / 1015808 \) Copy content Toggle raw display
\(\beta_{12}\)\(=\) \( ( - 53 \nu^{19} - 48 \nu^{18} + 394 \nu^{17} + 320 \nu^{16} - 670 \nu^{15} - 2272 \nu^{14} - 392 \nu^{13} - 2624 \nu^{12} + 32824 \nu^{11} + 2944 \nu^{10} - 31936 \nu^{9} + \cdots + 15990784 ) / 8126464 \) Copy content Toggle raw display
\(\beta_{13}\)\(=\) \( ( 7 \nu^{19} - 38 \nu^{17} + 154 \nu^{15} + 136 \nu^{13} - 1640 \nu^{11} + 8448 \nu^{9} - 7808 \nu^{7} + 22016 \nu^{5} + 845824 \nu^{3} - 3457024 \nu ) / 1015808 \) Copy content Toggle raw display
\(\beta_{14}\)\(=\) \( ( 53 \nu^{19} - 48 \nu^{18} - 394 \nu^{17} + 320 \nu^{16} + 670 \nu^{15} - 2272 \nu^{14} + 392 \nu^{13} - 2624 \nu^{12} - 32824 \nu^{11} + 2944 \nu^{10} + 31936 \nu^{9} + 55040 \nu^{8} + \cdots + 15990784 ) / 8126464 \) Copy content Toggle raw display
\(\beta_{15}\)\(=\) \( ( - 25 \nu^{19} + 84 \nu^{18} + 1234 \nu^{17} - 808 \nu^{16} - 4022 \nu^{15} + 504 \nu^{14} - 5800 \nu^{13} + 11040 \nu^{12} + 22296 \nu^{11} - 23008 \nu^{10} - 69568 \nu^{9} + \cdots - 17825792 ) / 8126464 \) Copy content Toggle raw display
\(\beta_{16}\)\(=\) \( ( - 539 \nu^{19} - 1700 \nu^{18} - 386 \nu^{17} - 2840 \nu^{16} + 2190 \nu^{15} + 35560 \nu^{14} - 27464 \nu^{13} - 22240 \nu^{12} + 28232 \nu^{11} - 101280 \nu^{10} + \cdots - 399769600 ) / 40632320 \) Copy content Toggle raw display
\(\beta_{17}\)\(=\) \( ( 17 \nu^{19} - 37 \nu^{17} - 80 \nu^{15} + 302 \nu^{13} + 904 \nu^{11} + 8936 \nu^{9} + 6368 \nu^{7} - 250240 \nu^{5} + 686592 \nu^{3} + 2428928 \nu ) / 1269760 \) Copy content Toggle raw display
\(\beta_{18}\)\(=\) \( ( 597 \nu^{19} - 740 \nu^{18} - 962 \nu^{17} - 40 \nu^{16} - 530 \nu^{15} + 3400 \nu^{14} + 33272 \nu^{13} + 8000 \nu^{12} - 39736 \nu^{11} - 103840 \nu^{10} + 562176 \nu^{9} + \cdots - 76021760 ) / 40632320 \) Copy content Toggle raw display
\(\beta_{19}\)\(=\) \( ( - 539 \nu^{19} + 1700 \nu^{18} - 386 \nu^{17} + 2840 \nu^{16} + 2190 \nu^{15} - 35560 \nu^{14} - 27464 \nu^{13} + 22240 \nu^{12} + 28232 \nu^{11} + 101280 \nu^{10} + \cdots + 399769600 ) / 40632320 \) Copy content Toggle raw display
\(\nu\)\(=\) \( ( \beta_{17} - \beta_{13} + \beta_{10} + \beta_{2} ) / 4 \) Copy content Toggle raw display
\(\nu^{2}\)\(=\) \( ( \beta_{11} + \beta_{5} + \beta_{4} + 2\beta_1 ) / 2 \) Copy content Toggle raw display
\(\nu^{3}\)\(=\) \( ( \beta_{19} + \beta_{18} + \beta_{17} + \beta_{16} + \beta_{15} + \beta_{13} + \beta_{9} - \beta_{8} + \beta_{3} + 2\beta_{2} ) / 2 \) Copy content Toggle raw display
\(\nu^{4}\)\(=\) \( ( \beta_{19} - \beta_{16} - \beta_{14} - \beta_{12} - 2 \beta_{9} - 2 \beta_{8} + 2 \beta_{7} - 2 \beta_{5} - 2 \beta_{4} + 12 \beta_1 ) / 2 \) Copy content Toggle raw display
\(\nu^{5}\)\(=\) \( ( \beta_{19} + 2 \beta_{18} - 5 \beta_{17} + \beta_{16} - 3 \beta_{14} + 5 \beta_{13} + 3 \beta_{12} + \beta_{11} - 5 \beta_{10} - 11 \beta_{9} + 11 \beta_{8} + 3 \beta_{5} - 3 \beta_{4} + \beta_{3} + 7 \beta_{2} ) / 2 \) Copy content Toggle raw display
\(\nu^{6}\)\(=\) \( 3 \beta_{14} + 3 \beta_{12} + 3 \beta_{11} - 7 \beta_{9} - 7 \beta_{8} + \beta_{7} + \beta_{6} - 9 \beta_{5} - 9 \beta_{4} + \beta_{3} + 4 \beta _1 + 4 \) Copy content Toggle raw display
\(\nu^{7}\)\(=\) \( - 3 \beta_{19} - 13 \beta_{18} + 2 \beta_{17} - 3 \beta_{16} + 3 \beta_{15} - 2 \beta_{14} + 16 \beta_{13} + 2 \beta_{12} - 8 \beta_{11} - 3 \beta_{10} - \beta_{9} + \beta_{8} - 8 \beta_{5} + 8 \beta_{4} - 5 \beta_{3} + 7 \beta_{2} \) Copy content Toggle raw display
\(\nu^{8}\)\(=\) \( - \beta_{19} + \beta_{16} + 9 \beta_{14} + 9 \beta_{12} - 4 \beta_{11} + 28 \beta_{9} + 28 \beta_{8} + 6 \beta_{7} - 16 \beta_{6} + 14 \beta_{5} + 14 \beta_{4} + 14 \beta_{3} + 148 \beta _1 + 28 \) Copy content Toggle raw display
\(\nu^{9}\)\(=\) \( - \beta_{19} + 4 \beta_{18} + 37 \beta_{17} - \beta_{16} + 10 \beta_{15} - 7 \beta_{14} + 31 \beta_{13} + 7 \beta_{12} - 3 \beta_{11} + 95 \beta_{10} + 19 \beta_{9} - 19 \beta_{8} - 81 \beta_{5} + 81 \beta_{4} + 7 \beta_{3} - 17 \beta_{2} \) Copy content Toggle raw display
\(\nu^{10}\)\(=\) \( - 38 \beta_{19} + 38 \beta_{16} - 12 \beta_{14} - 12 \beta_{12} + 42 \beta_{11} + 18 \beta_{9} + 18 \beta_{8} + 30 \beta_{7} - 54 \beta_{6} + 14 \beta_{5} + 14 \beta_{4} + 78 \beta_{3} - 200 \beta _1 - 576 \) Copy content Toggle raw display
\(\nu^{11}\)\(=\) \( 56 \beta_{19} + 26 \beta_{18} + 30 \beta_{17} + 56 \beta_{16} - 18 \beta_{15} - 86 \beta_{14} + 182 \beta_{13} + 86 \beta_{12} + 22 \beta_{11} - 156 \beta_{10} + 148 \beta_{9} - 148 \beta_{8} + 18 \beta_{5} - 18 \beta_{4} + 4 \beta_{3} - 240 \beta_{2} \) Copy content Toggle raw display
\(\nu^{12}\)\(=\) \( - 26 \beta_{19} + 26 \beta_{16} - 18 \beta_{14} - 18 \beta_{12} - 236 \beta_{11} - 100 \beta_{9} - 100 \beta_{8} - 88 \beta_{7} - 276 \beta_{6} - 328 \beta_{5} - 328 \beta_{4} - 256 \beta_{3} + 168 \beta _1 - 1160 \) Copy content Toggle raw display
\(\nu^{13}\)\(=\) \( - 486 \beta_{19} - 100 \beta_{18} - 942 \beta_{17} - 486 \beta_{16} - 248 \beta_{15} - 150 \beta_{14} - 82 \beta_{13} + 150 \beta_{12} + 74 \beta_{11} - 662 \beta_{10} + 122 \beta_{9} - 122 \beta_{8} - 466 \beta_{5} + 466 \beta_{4} + \cdots + 34 \beta_{2} \) Copy content Toggle raw display
\(\nu^{14}\)\(=\) \( - 712 \beta_{19} + 712 \beta_{16} - 92 \beta_{14} - 92 \beta_{12} - 300 \beta_{11} + 388 \beta_{9} + 388 \beta_{8} - 1148 \beta_{7} - 332 \beta_{6} - 492 \beta_{5} - 492 \beta_{4} + 916 \beta_{3} - 2240 \beta _1 + 7024 \) Copy content Toggle raw display
\(\nu^{15}\)\(=\) \( - 1308 \beta_{19} - 1596 \beta_{18} + 2616 \beta_{17} - 1308 \beta_{16} - 908 \beta_{15} + 288 \beta_{14} - 1440 \beta_{13} - 288 \beta_{12} - 344 \beta_{11} + 4348 \beta_{10} + 5132 \beta_{9} - 5132 \beta_{8} + \cdots - 1068 \beta_{2} \) Copy content Toggle raw display
\(\nu^{16}\)\(=\) \( 36 \beta_{19} - 36 \beta_{16} - 1940 \beta_{14} - 1940 \beta_{12} + 1152 \beta_{11} + 2416 \beta_{9} + 2416 \beta_{8} - 5832 \beta_{7} - 1904 \beta_{6} + 11192 \beta_{5} + 11192 \beta_{4} + 264 \beta_{3} + \cdots - 21584 \) Copy content Toggle raw display
\(\nu^{17}\)\(=\) \( 340 \beta_{19} + 9200 \beta_{18} - 2164 \beta_{17} + 340 \beta_{16} + 7096 \beta_{15} + 1100 \beta_{14} + 1636 \beta_{13} - 1100 \beta_{12} + 1052 \beta_{11} + 7748 \beta_{10} + 15716 \beta_{9} - 15716 \beta_{8} + \cdots + 708 \beta_{2} \) Copy content Toggle raw display
\(\nu^{18}\)\(=\) \( 7096 \beta_{19} - 7096 \beta_{16} - 16912 \beta_{14} - 16912 \beta_{12} - 6824 \beta_{11} - 9576 \beta_{9} - 9576 \beta_{8} - 6936 \beta_{7} + 10104 \beta_{6} - 21112 \beta_{5} - 21112 \beta_{4} + \cdots - 28416 \) Copy content Toggle raw display
\(\nu^{19}\)\(=\) \( - 10944 \beta_{19} + 10200 \beta_{18} - 15480 \beta_{17} - 10944 \beta_{16} - 10040 \beta_{15} - 6664 \beta_{14} + 18600 \beta_{13} + 6664 \beta_{12} + 10120 \beta_{11} - 63952 \beta_{10} - 62448 \beta_{9} + \cdots - 9600 \beta_{2} \) Copy content Toggle raw display

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
−1.21144 + 1.59136i
−0.312316 1.97546i
1.85381 0.750590i
1.21144 1.59136i
−1.96139 + 0.391068i
0.312316 + 1.97546i
1.28499 + 1.53258i
−1.28499 1.53258i
−1.85381 + 0.750590i
1.96139 0.391068i
−1.21144 1.59136i
−0.312316 + 1.97546i
1.85381 + 0.750590i
1.21144 + 1.59136i
−1.96139 0.391068i
0.312316 1.97546i
1.28499 1.53258i
−1.28499 + 1.53258i
−1.85381 0.750590i
1.96139 + 0.391068i
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
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 113.10
Significant digits:
Format:

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 \(S_{3}^{\mathrm{new}}(192, [\chi])\). Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T^{20} \) Copy content Toggle raw display
$3$ \( T^{20} - 6 T^{19} + \cdots + 3486784401 \) Copy content Toggle raw display
$5$ \( T^{20} + 3404 T^{16} + 3190384 T^{12} + \cdots + 4096 \) Copy content Toggle raw display
$7$ \( (T^{10} + 336 T^{8} + 40676 T^{6} + \cdots + 655360000)^{2} \) Copy content Toggle raw display
$11$ \( T^{20} + 207308 T^{16} + \cdots + 22\!\cdots\!00 \) Copy content Toggle raw display
$13$ \( (T^{10} - 46 T^{9} + 1058 T^{8} + \cdots + 33620000)^{2} \) Copy content Toggle raw display
$17$ \( (T^{10} + 952 T^{8} + \cdots + 15510536192)^{2} \) Copy content Toggle raw display
$19$ \( (T^{10} - 26 T^{9} + 338 T^{8} + \cdots + 23975244288)^{2} \) Copy content Toggle raw display
$23$ \( (T^{10} - 2236 T^{8} + \cdots - 2157878476800)^{2} \) Copy content Toggle raw display
$29$ \( T^{20} + 8250700 T^{16} + \cdots + 14\!\cdots\!00 \) Copy content Toggle raw display
$31$ \( (T^{5} - 20 T^{4} - 2750 T^{3} + \cdots - 6473680)^{4} \) Copy content Toggle raw display
$37$ \( (T^{10} + 58 T^{9} + \cdots + 93878430976800)^{2} \) Copy content Toggle raw display
$41$ \( (T^{10} - 8644 T^{8} + \cdots - 89172136396800)^{2} \) Copy content Toggle raw display
$43$ \( (T^{10} + 86 T^{9} + \cdots + 398518394892800)^{2} \) Copy content Toggle raw display
$47$ \( (T^{10} + 4944 T^{8} + \cdots + 2199023255552)^{2} \) Copy content Toggle raw display
$53$ \( T^{20} + 33387084 T^{16} + \cdots + 51\!\cdots\!00 \) Copy content Toggle raw display
$59$ \( T^{20} + 96029644 T^{16} + \cdots + 55\!\cdots\!00 \) Copy content Toggle raw display
$61$ \( (T^{10} + 122 T^{9} + \cdots + 79\!\cdots\!68)^{2} \) Copy content Toggle raw display
$67$ \( (T^{10} + 178 T^{9} + \cdots + 14\!\cdots\!00)^{2} \) Copy content Toggle raw display
$71$ \( (T^{10} - 12876 T^{8} + \cdots - 63\!\cdots\!00)^{2} \) Copy content Toggle raw display
$73$ \( (T^{10} + 16160 T^{8} + \cdots + 900192010240000)^{2} \) Copy content Toggle raw display
$79$ \( (T^{5} + 96 T^{4} - 3534 T^{3} + \cdots + 147403248)^{4} \) Copy content Toggle raw display
$83$ \( T^{20} + 433330892 T^{16} + \cdots + 53\!\cdots\!00 \) Copy content Toggle raw display
$89$ \( (T^{10} - 49740 T^{8} + \cdots - 15\!\cdots\!00)^{2} \) Copy content Toggle raw display
$97$ \( (T^{5} - 118 T^{4} - 11780 T^{3} + \cdots - 2657552000)^{4} \) Copy content Toggle raw display
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