Properties

Label 126.2.l.a
Level $126$
Weight $2$
Character orbit 126.l
Analytic conductor $1.006$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 126.l (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.00611506547\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \( x^{16} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + 2785 x^{8} - 2640 x^{7} - 2601 x^{6} + 10260 x^{5} - 10611 x^{4} - 1944 x^{3} + \cdots + 6561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3^{2} \)
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.

\(f(q)\) \(=\) \( q - \beta_{6} q^{2} - \beta_{11} q^{3} - q^{4} + ( - \beta_{13} + \beta_{12} - \beta_{9} + \beta_{7} + \beta_{5} - \beta_{4} + \beta_{2} + 1) q^{5} + ( - \beta_{9} - \beta_{4}) q^{6} + (\beta_{15} - \beta_{14} + \beta_{12} - \beta_{11} - \beta_{6} - \beta_{4} + \beta_{2} + 1) q^{7} + \beta_{6} q^{8} + ( - \beta_{15} - \beta_{9} + \beta_{8} + \beta_{7} - \beta_{6} - \beta_{2} + \beta_1) q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - \beta_{6} q^{2} - \beta_{11} q^{3} - q^{4} + ( - \beta_{13} + \beta_{12} - \beta_{9} + \beta_{7} + \beta_{5} - \beta_{4} + \beta_{2} + 1) q^{5} + ( - \beta_{9} - \beta_{4}) q^{6} + (\beta_{15} - \beta_{14} + \beta_{12} - \beta_{11} - \beta_{6} - \beta_{4} + \beta_{2} + 1) q^{7} + \beta_{6} q^{8} + ( - \beta_{15} - \beta_{9} + \beta_{8} + \beta_{7} - \beta_{6} - \beta_{2} + \beta_1) q^{9} + ( - \beta_{15} + \beta_{13} + \beta_{11} + \beta_{10} - \beta_{3} - \beta_1) q^{10} + (\beta_{15} - \beta_{13} - \beta_{12} - \beta_{11} + \beta_{8} - \beta_{6} - \beta_{5} + \beta_{4} - \beta_{3} + \beta_{2} + \beta_1) q^{11} + \beta_{11} q^{12} + (\beta_{13} + \beta_{11} + \beta_{10} - \beta_{8} + 2 \beta_{6} + \beta_{3} - \beta_{2} - 2 \beta_1) q^{13} + ( - \beta_{14} + \beta_{10} - \beta_{9} + \beta_{8} - \beta_{6} - \beta_{3} - 1) q^{14} + (\beta_{14} - 2 \beta_{10} + \beta_{9} - 2 \beta_{8} - \beta_{7} + \beta_{6} - \beta_{5} + 2 \beta_{3} + \cdots - 1) q^{15}+ \cdots + ( - 2 \beta_{15} - \beta_{14} - \beta_{13} + 2 \beta_{12} + \beta_{11} + \beta_{10} - 2 \beta_{9} + \cdots - 5 \beta_1) q^{99}+O(q^{100}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 16 q^{4} + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 16 q^{4} + 2 q^{7} + 12 q^{11} + 6 q^{13} - 6 q^{14} - 18 q^{15} + 16 q^{16} - 18 q^{17} - 12 q^{18} - 12 q^{21} - 6 q^{23} - 8 q^{25} + 12 q^{26} + 36 q^{27} - 2 q^{28} + 6 q^{29} + 30 q^{35} - 2 q^{37} - 12 q^{39} - 6 q^{41} - 2 q^{43} - 12 q^{44} - 30 q^{45} + 6 q^{46} - 36 q^{47} - 8 q^{49} - 12 q^{50} + 6 q^{51} - 6 q^{52} - 36 q^{53} + 18 q^{54} + 6 q^{56} + 6 q^{57} + 6 q^{58} + 60 q^{59} + 18 q^{60} + 36 q^{62} + 36 q^{63} - 16 q^{64} + 24 q^{66} - 28 q^{67} + 18 q^{68} - 42 q^{69} - 18 q^{70} + 12 q^{72} + 18 q^{74} + 60 q^{75} - 42 q^{77} + 32 q^{79} - 36 q^{81} + 12 q^{84} - 12 q^{85} + 24 q^{86} - 24 q^{87} - 24 q^{89} + 18 q^{90} - 12 q^{91} + 6 q^{92} - 42 q^{93} + 6 q^{97} - 24 q^{98} + 18 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Basis of coefficient ring in terms of a root \(\nu\) of \( x^{16} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + 2785 x^{8} - 2640 x^{7} - 2601 x^{6} + 10260 x^{5} - 10611 x^{4} - 1944 x^{3} + \cdots + 6561 \) : Copy content Toggle raw display

\(\beta_{1}\)\(=\) \( ( - 50 \nu^{15} - 1352 \nu^{14} + 6827 \nu^{13} - 7676 \nu^{12} - 27422 \nu^{11} + 107246 \nu^{10} - 107467 \nu^{9} - 206194 \nu^{8} + 757363 \nu^{7} - 724572 \nu^{6} + \cdots - 2825604 ) / 142155 \) Copy content Toggle raw display
\(\beta_{2}\)\(=\) \( ( 1292 \nu^{15} - 10486 \nu^{14} + 25660 \nu^{13} + 10145 \nu^{12} - 192280 \nu^{11} + 408694 \nu^{10} - 51650 \nu^{9} - 1459361 \nu^{8} + 2979638 \nu^{7} + \cdots - 9270693 ) / 142155 \) Copy content Toggle raw display
\(\beta_{3}\)\(=\) \( ( 2846 \nu^{15} - 22369 \nu^{14} + 55246 \nu^{13} + 17972 \nu^{12} - 402586 \nu^{11} + 878875 \nu^{10} - 166676 \nu^{9} - 3023495 \nu^{8} + 6386423 \nu^{7} + \cdots - 20783061 ) / 142155 \) Copy content Toggle raw display
\(\beta_{4}\)\(=\) \( ( - 2782 \nu^{15} + 15918 \nu^{14} - 26947 \nu^{13} - 42629 \nu^{12} + 270897 \nu^{11} - 425335 \nu^{10} - 220488 \nu^{9} + 2001225 \nu^{8} - 3082271 \nu^{7} + \cdots + 7405182 ) / 47385 \) Copy content Toggle raw display
\(\beta_{5}\)\(=\) \( ( - 3648 \nu^{15} + 23120 \nu^{14} - 45376 \nu^{13} - 47012 \nu^{12} + 401996 \nu^{11} - 719704 \nu^{10} - 150629 \nu^{9} + 2988436 \nu^{8} - 5221301 \nu^{7} + \cdots + 14281839 ) / 47385 \) Copy content Toggle raw display
\(\beta_{6}\)\(=\) \( ( - 16948 \nu^{15} + 107120 \nu^{14} - 210206 \nu^{13} - 216202 \nu^{12} + 1856546 \nu^{11} - 3329594 \nu^{10} - 672599 \nu^{9} + 13772146 \nu^{8} + \cdots + 66620394 ) / 142155 \) Copy content Toggle raw display
\(\beta_{7}\)\(=\) \( ( - 4120 \nu^{15} + 25571 \nu^{14} - 48788 \nu^{13} - 55006 \nu^{12} + 441224 \nu^{11} - 771188 \nu^{10} - 200900 \nu^{9} + 3269857 \nu^{8} - 5585140 \nu^{7} + \cdots + 14935023 ) / 28431 \) Copy content Toggle raw display
\(\beta_{8}\)\(=\) \( ( 24706 \nu^{15} - 155855 \nu^{14} + 305147 \nu^{13} + 316579 \nu^{12} - 2700647 \nu^{11} + 4831208 \nu^{10} + 1007453 \nu^{9} - 20043787 \nu^{8} + 35017972 \nu^{7} + \cdots - 96324228 ) / 142155 \) Copy content Toggle raw display
\(\beta_{9}\)\(=\) \( ( 2015 \nu^{15} - 12538 \nu^{14} + 24088 \nu^{13} + 26576 \nu^{12} - 216643 \nu^{11} + 381184 \nu^{10} + 93322 \nu^{9} - 1605386 \nu^{8} + 2760692 \nu^{7} - 423483 \nu^{6} + \cdots - 7453296 ) / 10935 \) Copy content Toggle raw display
\(\beta_{10}\)\(=\) \( ( - 26777 \nu^{15} + 172141 \nu^{14} - 345205 \nu^{13} - 329150 \nu^{12} + 2992915 \nu^{11} - 5473354 \nu^{10} - 873115 \nu^{9} + 22225271 \nu^{8} + \cdots + 112005018 ) / 142155 \) Copy content Toggle raw display
\(\beta_{11}\)\(=\) \( ( 32006 \nu^{15} - 201190 \nu^{14} + 390892 \nu^{13} + 415394 \nu^{12} - 3479542 \nu^{11} + 6180118 \nu^{10} + 1385833 \nu^{9} - 25793657 \nu^{8} + \cdots - 121376313 ) / 142155 \) Copy content Toggle raw display
\(\beta_{12}\)\(=\) \( ( - 10990 \nu^{15} + 68842 \nu^{14} - 133062 \nu^{13} - 143724 \nu^{12} + 1190062 \nu^{11} - 2105781 \nu^{10} - 489283 \nu^{9} + 8822519 \nu^{8} - 15253998 \nu^{7} + \cdots + 41433444 ) / 47385 \) Copy content Toggle raw display
\(\beta_{13}\)\(=\) \( ( - 35897 \nu^{15} + 219337 \nu^{14} - 409846 \nu^{13} - 492632 \nu^{12} + 3774151 \nu^{11} - 6478657 \nu^{10} - 1950109 \nu^{9} + 27930713 \nu^{8} + \cdots + 122931270 ) / 142155 \) Copy content Toggle raw display
\(\beta_{14}\)\(=\) \( ( - 14807 \nu^{15} + 92828 \nu^{14} - 179757 \nu^{13} - 193044 \nu^{12} + 1605257 \nu^{11} - 2844540 \nu^{10} - 652043 \nu^{9} + 11900965 \nu^{8} - 20604021 \nu^{7} + \cdots + 55960227 ) / 47385 \) Copy content Toggle raw display
\(\beta_{15}\)\(=\) \( ( - 68699 \nu^{15} + 433198 \nu^{14} - 844756 \nu^{13} - 889547 \nu^{12} + 7506256 \nu^{11} - 13372516 \nu^{10} - 2912329 \nu^{9} + 55693424 \nu^{8} + \cdots + 264515463 ) / 142155 \) Copy content Toggle raw display
\(\nu\)\(=\) \( ( -\beta_{15} - \beta_{9} - \beta_{8} + \beta_{7} + \beta_{6} - 2\beta_{4} + 2\beta_{3} - 2\beta_{2} + \beta _1 + 2 ) / 3 \) Copy content Toggle raw display
\(\nu^{2}\)\(=\) \( ( - \beta_{15} + 4 \beta_{14} + \beta_{13} - 2 \beta_{12} + 2 \beta_{11} - \beta_{10} - \beta_{9} - \beta_{8} - \beta_{6} - \beta_{5} - 2 \beta_{4} - \beta_{3} - 2 \beta_{2} + 2 \beta _1 + 3 ) / 3 \) Copy content Toggle raw display
\(\nu^{3}\)\(=\) \( ( - 3 \beta_{15} - \beta_{14} + 5 \beta_{13} + 2 \beta_{12} + \beta_{11} + \beta_{10} - 3 \beta_{8} - 2 \beta_{7} - \beta_{6} - 2 \beta_{5} - 3 \beta_{3} - 6 \beta_{2} - \beta _1 - 4 ) / 3 \) Copy content Toggle raw display
\(\nu^{4}\)\(=\) \( ( - \beta_{15} + 2 \beta_{14} + 11 \beta_{13} - 4 \beta_{12} + 7 \beta_{11} + 4 \beta_{10} + 8 \beta_{9} - 4 \beta_{8} - \beta_{7} - 6 \beta_{6} - 2 \beta_{5} + 7 \beta_{4} - 10 \beta_{3} - 2 \beta_{2} - 15 \beta _1 + 7 ) / 3 \) Copy content Toggle raw display
\(\nu^{5}\)\(=\) \( ( - 11 \beta_{15} - 6 \beta_{14} + 9 \beta_{13} + 12 \beta_{11} + 6 \beta_{10} - 2 \beta_{9} + \beta_{8} + 23 \beta_{7} + 17 \beta_{6} + 3 \beta_{5} + 8 \beta_{4} - 5 \beta_{3} - 16 \beta_{2} - 31 \beta _1 + 10 ) / 3 \) Copy content Toggle raw display
\(\nu^{6}\)\(=\) \( ( - 5 \beta_{15} + 26 \beta_{14} + 2 \beta_{13} - 31 \beta_{12} + 28 \beta_{11} + 13 \beta_{10} - 14 \beta_{9} + 4 \beta_{8} + 39 \beta_{7} - 20 \beta_{6} - 5 \beta_{5} - \beta_{4} - 2 \beta_{3} - 10 \beta_{2} - 20 \beta _1 + 15 ) / 3 \) Copy content Toggle raw display
\(\nu^{7}\)\(=\) \( ( - 15 \beta_{15} + 16 \beta_{14} - 20 \beta_{13} + 16 \beta_{12} + 29 \beta_{11} - 13 \beta_{10} - 60 \beta_{9} + 6 \beta_{8} + 26 \beta_{7} - 5 \beta_{6} - 10 \beta_{5} - 3 \beta_{4} - 3 \beta_{3} - 30 \beta_{2} - 14 \beta _1 - 11 ) / 3 \) Copy content Toggle raw display
\(\nu^{8}\)\(=\) \( ( 43 \beta_{15} + 28 \beta_{14} - 8 \beta_{13} + 10 \beta_{12} + 44 \beta_{11} - 16 \beta_{10} + 25 \beta_{9} - 92 \beta_{8} - 65 \beta_{7} - 114 \beta_{6} - 52 \beta_{5} - 7 \beta_{4} + 31 \beta_{3} + 26 \beta_{2} - 27 \beta _1 - 1 ) / 3 \) Copy content Toggle raw display
\(\nu^{9}\)\(=\) \( ( 50 \beta_{15} - 12 \beta_{14} - 18 \beta_{13} + 102 \beta_{12} + 102 \beta_{11} - 144 \beta_{10} + 80 \beta_{9} - 106 \beta_{8} - 104 \beta_{7} + 229 \beta_{6} - 84 \beta_{5} + 34 \beta_{4} + 44 \beta_{3} - 8 \beta_{2} - 194 \beta _1 + 134 ) / 3 \) Copy content Toggle raw display
\(\nu^{10}\)\(=\) \( ( 140 \beta_{15} + 139 \beta_{14} + 31 \beta_{13} - 224 \beta_{12} + 95 \beta_{11} - 46 \beta_{10} + 320 \beta_{9} - 220 \beta_{8} - 117 \beta_{7} + 251 \beta_{6} - 337 \beta_{5} + 10 \beta_{4} + 224 \beta_{3} - 80 \beta_{2} - 109 \beta_1 ) / 3 \) Copy content Toggle raw display
\(\nu^{11}\)\(=\) \( ( 60 \beta_{15} + 503 \beta_{14} + 23 \beta_{13} - 313 \beta_{12} + 133 \beta_{11} - 218 \beta_{10} + 114 \beta_{9} + 171 \beta_{8} - 482 \beta_{7} + 779 \beta_{6} - 524 \beta_{5} + 270 \beta_{4} - 12 \beta_{3} - 399 \beta_{2} + \cdots - 193 ) / 3 \) Copy content Toggle raw display
\(\nu^{12}\)\(=\) \( ( - 94 \beta_{15} + 722 \beta_{14} + 191 \beta_{13} - 343 \beta_{12} - 182 \beta_{11} + 238 \beta_{10} + 569 \beta_{9} - 454 \beta_{8} - 1069 \beta_{7} - 192 \beta_{6} - 674 \beta_{5} + 382 \beta_{4} + 398 \beta_{3} + \cdots - 1112 ) / 3 \) Copy content Toggle raw display
\(\nu^{13}\)\(=\) \( ( - 425 \beta_{15} + 1353 \beta_{14} + 255 \beta_{13} + 1086 \beta_{12} + 1068 \beta_{11} - 588 \beta_{10} + 691 \beta_{9} - 122 \beta_{8} - 1675 \beta_{7} + 662 \beta_{6} + 498 \beta_{5} + 707 \beta_{4} - 206 \beta_{3} + \cdots + 727 ) / 3 \) Copy content Toggle raw display
\(\nu^{14}\)\(=\) \( ( - 953 \beta_{15} + 446 \beta_{14} + 35 \beta_{13} + 2231 \beta_{12} + 1294 \beta_{11} + 82 \beta_{10} + 1990 \beta_{9} - 1151 \beta_{8} + 1755 \beta_{7} + 91 \beta_{6} + 688 \beta_{5} - 970 \beta_{4} + 1378 \beta_{3} + \cdots + 1896 ) / 3 \) Copy content Toggle raw display
\(\nu^{15}\)\(=\) \( ( 1563 \beta_{15} + 1963 \beta_{14} - 725 \beta_{13} + 2308 \beta_{12} + 3086 \beta_{11} - 1306 \beta_{10} + 714 \beta_{9} + 4854 \beta_{8} + 2906 \beta_{7} - 1550 \beta_{6} + 32 \beta_{5} - 1380 \beta_{4} - 2391 \beta_{3} + \cdots + 6694 ) / 3 \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\)
\(\chi(n)\) \(-\beta_{7}\) \(-\beta_{7}\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
5.1
1.73109 0.0577511i
0.320287 + 1.70218i
−1.68301 + 0.409224i
0.765614 1.55365i
1.71298 + 0.256290i
1.27866 1.16834i
−1.70672 0.295146i
1.58110 + 0.707199i
1.71298 0.256290i
1.27866 + 1.16834i
−1.70672 + 0.295146i
1.58110 0.707199i
1.73109 + 0.0577511i
0.320287 1.70218i
−1.68301 0.409224i
0.765614 + 1.55365i
1.00000i −0.890915 + 1.48535i −1.00000 1.14095 + 1.97618i 1.48535 + 0.890915i 1.42337 + 2.23025i 1.00000i −1.41254 2.64665i 1.97618 1.14095i
5.2 1.00000i −0.290993 1.70743i −1.00000 −0.0338034 0.0585493i −1.70743 + 0.290993i 1.19767 2.35915i 1.00000i −2.83065 + 0.993700i −0.0585493 + 0.0338034i
5.3 1.00000i 1.38631 + 1.03834i −1.00000 0.714925 + 1.23829i 1.03834 1.38631i 0.327442 2.62541i 1.00000i 0.843698 + 2.87892i 1.23829 0.714925i
5.4 1.00000i 1.52765 0.816261i −1.00000 −1.82207 3.15592i −0.816261 1.52765i −1.58246 + 2.12034i 1.00000i 1.66744 2.49392i −3.15592 + 1.82207i
5.5 1.00000i −1.56012 0.752355i −1.00000 −1.80966 3.13442i 0.752355 1.56012i −2.41308 1.08492i 1.00000i 1.86792 + 2.34752i 3.13442 1.80966i
5.6 1.00000i −1.08509 1.35003i −1.00000 1.77612 + 3.07634i 1.35003 1.08509i 2.63804 0.201867i 1.00000i −0.645160 + 2.92981i −3.07634 + 1.77612i
5.7 1.00000i −0.734581 + 1.56856i −1.00000 0.483662 + 0.837727i −1.56856 0.734581i −2.16249 + 1.52435i 1.00000i −1.92078 2.30447i −0.837727 + 0.483662i
5.8 1.00000i 1.64774 + 0.533822i −1.00000 −0.450129 0.779646i −0.533822 + 1.64774i 1.57151 + 2.12847i 1.00000i 2.43007 + 1.75919i 0.779646 0.450129i
101.1 1.00000i −1.56012 + 0.752355i −1.00000 −1.80966 + 3.13442i 0.752355 + 1.56012i −2.41308 + 1.08492i 1.00000i 1.86792 2.34752i 3.13442 + 1.80966i
101.2 1.00000i −1.08509 + 1.35003i −1.00000 1.77612 3.07634i 1.35003 + 1.08509i 2.63804 + 0.201867i 1.00000i −0.645160 2.92981i −3.07634 1.77612i
101.3 1.00000i −0.734581 1.56856i −1.00000 0.483662 0.837727i −1.56856 + 0.734581i −2.16249 1.52435i 1.00000i −1.92078 + 2.30447i −0.837727 0.483662i
101.4 1.00000i 1.64774 0.533822i −1.00000 −0.450129 + 0.779646i −0.533822 1.64774i 1.57151 2.12847i 1.00000i 2.43007 1.75919i 0.779646 + 0.450129i
101.5 1.00000i −0.890915 1.48535i −1.00000 1.14095 1.97618i 1.48535 0.890915i 1.42337 2.23025i 1.00000i −1.41254 + 2.64665i 1.97618 + 1.14095i
101.6 1.00000i −0.290993 + 1.70743i −1.00000 −0.0338034 + 0.0585493i −1.70743 0.290993i 1.19767 + 2.35915i 1.00000i −2.83065 0.993700i −0.0585493 0.0338034i
101.7 1.00000i 1.38631 1.03834i −1.00000 0.714925 1.23829i 1.03834 + 1.38631i 0.327442 + 2.62541i 1.00000i 0.843698 2.87892i 1.23829 + 0.714925i
101.8 1.00000i 1.52765 + 0.816261i −1.00000 −1.82207 + 3.15592i −0.816261 + 1.52765i −1.58246 2.12034i 1.00000i 1.66744 + 2.49392i −3.15592 1.82207i
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 101.8
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
63.i even 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 126.2.l.a 16
3.b odd 2 1 378.2.l.a 16
4.b odd 2 1 1008.2.ca.c 16
7.b odd 2 1 882.2.l.b 16
7.c even 3 1 882.2.m.b 16
7.c even 3 1 882.2.t.a 16
7.d odd 6 1 126.2.t.a yes 16
7.d odd 6 1 882.2.m.a 16
9.c even 3 1 378.2.t.a 16
9.c even 3 1 1134.2.k.a 16
9.d odd 6 1 126.2.t.a yes 16
9.d odd 6 1 1134.2.k.b 16
12.b even 2 1 3024.2.ca.c 16
21.c even 2 1 2646.2.l.a 16
21.g even 6 1 378.2.t.a 16
21.g even 6 1 2646.2.m.a 16
21.h odd 6 1 2646.2.m.b 16
21.h odd 6 1 2646.2.t.b 16
28.f even 6 1 1008.2.df.c 16
36.f odd 6 1 3024.2.df.c 16
36.h even 6 1 1008.2.df.c 16
63.g even 3 1 2646.2.m.a 16
63.h even 3 1 2646.2.l.a 16
63.i even 6 1 inner 126.2.l.a 16
63.j odd 6 1 882.2.l.b 16
63.k odd 6 1 1134.2.k.b 16
63.k odd 6 1 2646.2.m.b 16
63.l odd 6 1 2646.2.t.b 16
63.n odd 6 1 882.2.m.a 16
63.o even 6 1 882.2.t.a 16
63.s even 6 1 882.2.m.b 16
63.s even 6 1 1134.2.k.a 16
63.t odd 6 1 378.2.l.a 16
84.j odd 6 1 3024.2.df.c 16
252.r odd 6 1 1008.2.ca.c 16
252.bj even 6 1 3024.2.ca.c 16
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
126.2.l.a 16 1.a even 1 1 trivial
126.2.l.a 16 63.i even 6 1 inner
126.2.t.a yes 16 7.d odd 6 1
126.2.t.a yes 16 9.d odd 6 1
378.2.l.a 16 3.b odd 2 1
378.2.l.a 16 63.t odd 6 1
378.2.t.a 16 9.c even 3 1
378.2.t.a 16 21.g even 6 1
882.2.l.b 16 7.b odd 2 1
882.2.l.b 16 63.j odd 6 1
882.2.m.a 16 7.d odd 6 1
882.2.m.a 16 63.n odd 6 1
882.2.m.b 16 7.c even 3 1
882.2.m.b 16 63.s even 6 1
882.2.t.a 16 7.c even 3 1
882.2.t.a 16 63.o even 6 1
1008.2.ca.c 16 4.b odd 2 1
1008.2.ca.c 16 252.r odd 6 1
1008.2.df.c 16 28.f even 6 1
1008.2.df.c 16 36.h even 6 1
1134.2.k.a 16 9.c even 3 1
1134.2.k.a 16 63.s even 6 1
1134.2.k.b 16 9.d odd 6 1
1134.2.k.b 16 63.k odd 6 1
2646.2.l.a 16 21.c even 2 1
2646.2.l.a 16 63.h even 3 1
2646.2.m.a 16 21.g even 6 1
2646.2.m.a 16 63.g even 3 1
2646.2.m.b 16 21.h odd 6 1
2646.2.m.b 16 63.k odd 6 1
2646.2.t.b 16 21.h odd 6 1
2646.2.t.b 16 63.l odd 6 1
3024.2.ca.c 16 12.b even 2 1
3024.2.ca.c 16 252.bj even 6 1
3024.2.df.c 16 36.f odd 6 1
3024.2.df.c 16 84.j odd 6 1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(126, [\chi])\).

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( (T^{2} + 1)^{8} \) Copy content Toggle raw display
$3$ \( T^{16} - 12 T^{13} + 9 T^{12} + \cdots + 6561 \) Copy content Toggle raw display
$5$ \( T^{16} + 24 T^{14} - 24 T^{13} + 423 T^{12} + \cdots + 81 \) Copy content Toggle raw display
$7$ \( T^{16} - 2 T^{15} + 6 T^{14} + \cdots + 5764801 \) Copy content Toggle raw display
$11$ \( T^{16} - 12 T^{15} + 18 T^{14} + \cdots + 61732449 \) Copy content Toggle raw display
$13$ \( T^{16} - 6 T^{15} - 57 T^{14} + \cdots + 390971529 \) Copy content Toggle raw display
$17$ \( T^{16} + 18 T^{15} + 231 T^{14} + \cdots + 56070144 \) Copy content Toggle raw display
$19$ \( T^{16} - 72 T^{14} + 4167 T^{12} + \cdots + 9199089 \) Copy content Toggle raw display
$23$ \( T^{16} + 6 T^{15} - 54 T^{14} + \cdots + 187388721 \) Copy content Toggle raw display
$29$ \( T^{16} - 6 T^{15} - 36 T^{14} + \cdots + 1108809 \) Copy content Toggle raw display
$31$ \( T^{16} + 204 T^{14} + \cdots + 65610000 \) Copy content Toggle raw display
$37$ \( T^{16} + 2 T^{15} + \cdots + 32746159681 \) Copy content Toggle raw display
$41$ \( T^{16} + 6 T^{15} + 105 T^{14} - 210 T^{13} + \cdots + 81 \) Copy content Toggle raw display
$43$ \( T^{16} + 2 T^{15} + \cdots + 2999643361 \) Copy content Toggle raw display
$47$ \( (T^{8} + 18 T^{7} + 3 T^{6} - 1650 T^{5} + \cdots + 766944)^{2} \) Copy content Toggle raw display
$53$ \( T^{16} + 36 T^{15} + \cdots + 36759242529 \) Copy content Toggle raw display
$59$ \( (T^{8} - 30 T^{7} + 228 T^{6} + \cdots + 465300)^{2} \) Copy content Toggle raw display
$61$ \( T^{16} + 504 T^{14} + \cdots + 547560000 \) Copy content Toggle raw display
$67$ \( (T^{8} + 14 T^{7} - 101 T^{6} + \cdots + 51028)^{2} \) Copy content Toggle raw display
$71$ \( T^{16} + 486 T^{14} + \cdots + 65610000 \) Copy content Toggle raw display
$73$ \( T^{16} - 150 T^{14} + \cdots + 71115489 \) Copy content Toggle raw display
$79$ \( (T^{8} - 16 T^{7} - 149 T^{6} + \cdots - 985100)^{2} \) Copy content Toggle raw display
$83$ \( T^{16} + 177 T^{14} + \cdots + 953512641 \) Copy content Toggle raw display
$89$ \( T^{16} + \cdots + 131145120363321 \) Copy content Toggle raw display
$97$ \( T^{16} - 6 T^{15} + \cdots + 9120206721024 \) Copy content Toggle raw display
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