Properties

Label 2646.2.m.a
Level $2646$
Weight $2$
Character orbit 2646.m
Analytic conductor $21.128$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.m (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(21.1284163748\)
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: \( 3^{4} \)
Twist minimal: no (minimal twist has level 126)
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.

\(f(q)\) \(=\) \( q + \beta_1 q^{2} + ( - \beta_{8} + 1) q^{4} + (\beta_{12} + \beta_{10} + \beta_{5}) q^{5} + (\beta_{7} + \beta_1) q^{8}+O(q^{10}) \) Copy content Toggle raw display \( q + \beta_1 q^{2} + ( - \beta_{8} + 1) q^{4} + (\beta_{12} + \beta_{10} + \beta_{5}) q^{5} + (\beta_{7} + \beta_1) q^{8} + (\beta_{15} + \beta_{13} + \beta_{11} - \beta_{9} + \beta_{3} - \beta_{2}) q^{10} + ( - \beta_{15} - \beta_{11} - \beta_{8} - \beta_{4} + \beta_{3} - \beta_{2} + 1) q^{11} + (\beta_{15} - \beta_{11} - \beta_{9} + \beta_{7} - \beta_{3} - \beta_{2} - \beta_1 - 2) q^{13} - \beta_{8} q^{16} + (\beta_{11} + \beta_{9} + \beta_{8} + \beta_{7} - \beta_{6} - \beta_{4} - \beta_{3} + \beta_{2} + 2) q^{17} + ( - \beta_{11} + \beta_{10} + \beta_{9} - \beta_{8} - \beta_{7} - \beta_{6} + \beta_{5} - \beta_{2} - 2 \beta_1) q^{19} + ( - \beta_{14} + \beta_{10} + \beta_{5}) q^{20} + ( - \beta_{12} - \beta_{10} - \beta_{6} - \beta_{5} - \beta_{2}) q^{22} + (\beta_{13} - \beta_{9} - \beta_{8} + \beta_{4} + 2 \beta_{3} - \beta_{2} + 1) q^{23} + (\beta_{15} + \beta_{14} - \beta_{13} - \beta_{12} - 2 \beta_{11} + \beta_{9} - 2 \beta_{8} - 3 \beta_{7} + \cdots - 1) q^{25}+ \cdots + (\beta_{15} + \beta_{13} - 2 \beta_{12} + 2 \beta_{11} - 2 \beta_{10} + \beta_{9} - \beta_{8} + \beta_{7} + \cdots + 5 \beta_1) q^{97}+O(q^{100}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 8 q^{4} + 12 q^{11} - 6 q^{13} - 8 q^{16} + 36 q^{17} - 6 q^{23} - 8 q^{25} - 24 q^{26} - 6 q^{29} - 6 q^{31} + 4 q^{37} - 6 q^{41} - 2 q^{43} - 12 q^{46} + 18 q^{47} + 12 q^{50} - 6 q^{52} + 6 q^{58} - 30 q^{59} + 60 q^{61} + 36 q^{62} - 16 q^{64} + 42 q^{65} + 14 q^{67} + 18 q^{68} + 18 q^{74} - 16 q^{79} - 12 q^{85} + 24 q^{86} + 48 q^{89} - 6 q^{92} - 66 q^{95} - 6 q^{97}+O(q^{100}) \) 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
\(\beta_{2}\)\(=\) \( ( 169 \nu^{15} - 866 \nu^{14} + 1319 \nu^{13} + 2308 \nu^{12} - 13199 \nu^{11} + 19055 \nu^{10} + 12131 \nu^{9} - 90010 \nu^{8} + 128722 \nu^{7} + 13734 \nu^{6} - 313347 \nu^{5} + \cdots - 244944 ) / 47385 \) Copy content Toggle raw display
\(\beta_{3}\)\(=\) \( ( 154 \nu^{15} - 1325 \nu^{14} + 3608 \nu^{13} - 224 \nu^{12} - 22478 \nu^{11} + 55022 \nu^{10} - 23518 \nu^{9} - 159688 \nu^{8} + 382978 \nu^{7} - 226785 \nu^{6} + \cdots - 1285227 ) / 47385 \) Copy content Toggle raw display
\(\beta_{4}\)\(=\) \( ( 1445 \nu^{15} - 9836 \nu^{14} + 21081 \nu^{13} + 15627 \nu^{12} - 172766 \nu^{11} + 334353 \nu^{10} + 13019 \nu^{9} - 1283242 \nu^{8} + 2419149 \nu^{7} - 693301 \nu^{6} + \cdots - 7117227 ) / 47385 \) Copy content Toggle raw display
\(\beta_{5}\)\(=\) \( ( 2858 \nu^{15} - 19265 \nu^{14} + 40866 \nu^{13} + 31392 \nu^{12} - 338066 \nu^{11} + 649239 \nu^{10} + 37829 \nu^{9} - 2521996 \nu^{8} + 4717386 \nu^{7} + \cdots - 14041269 ) / 47385 \) Copy content Toggle raw display
\(\beta_{6}\)\(=\) \( ( - 11192 \nu^{15} + 70123 \nu^{14} - 136087 \nu^{13} - 145859 \nu^{12} + 1215277 \nu^{11} - 2154880 \nu^{10} - 494788 \nu^{9} + 9027170 \nu^{8} - 15633236 \nu^{7} + \cdots + 42998607 ) / 142155 \) Copy content Toggle raw display
\(\beta_{7}\)\(=\) \( ( 16898 \nu^{15} - 108472 \nu^{14} + 217033 \nu^{13} + 208526 \nu^{12} - 1883968 \nu^{11} + 3436840 \nu^{10} + 565132 \nu^{9} - 13978340 \nu^{8} + 24892859 \nu^{7} + \cdots - 69445998 ) / 142155 \) Copy content Toggle raw display
\(\beta_{8}\)\(=\) \( ( - 4120 \nu^{15} + 25571 \nu^{14} - 48788 \nu^{13} - 55006 \nu^{12} + 441224 \nu^{11} - 771188 \nu^{10} - 200900 \nu^{9} + 3269857 \nu^{8} - 5585140 \nu^{7} + \cdots + 14963454 ) / 28431 \) Copy content Toggle raw display
\(\beta_{9}\)\(=\) \( ( 8586 \nu^{15} - 53254 \nu^{14} + 101261 \nu^{13} + 115567 \nu^{12} - 919066 \nu^{11} + 1601225 \nu^{10} + 428149 \nu^{9} - 6806990 \nu^{8} + 11591968 \nu^{7} + \cdots - 30865131 ) / 47385 \) Copy content Toggle raw display
\(\beta_{10}\)\(=\) \( ( - 26068 \nu^{15} + 165707 \nu^{14} - 325403 \nu^{13} - 334861 \nu^{12} + 2873363 \nu^{11} - 5145350 \nu^{10} - 1063457 \nu^{9} + 21324130 \nu^{8} + \cdots + 102032298 ) / 142155 \) Copy content Toggle raw display
\(\beta_{11}\)\(=\) \( ( - 31130 \nu^{15} + 194263 \nu^{14} - 374983 \nu^{13} - 405716 \nu^{12} + 3354958 \nu^{11} - 5936959 \nu^{10} - 1366837 \nu^{9} + 24841391 \nu^{8} + \cdots + 117273501 ) / 142155 \) Copy content Toggle raw display
\(\beta_{12}\)\(=\) \( ( 33311 \nu^{15} - 207064 \nu^{14} + 396466 \nu^{13} + 441842 \nu^{12} - 3574291 \nu^{11} + 6268915 \nu^{10} + 1580329 \nu^{9} - 26474600 \nu^{8} + \cdots - 121811526 ) / 142155 \) Copy content Toggle raw display
\(\beta_{13}\)\(=\) \( ( 5368 \nu^{15} - 32959 \nu^{14} + 62025 \nu^{13} + 72930 \nu^{12} - 567820 \nu^{11} + 981351 \nu^{10} + 280045 \nu^{9} - 4204439 \nu^{8} + 7108452 \nu^{7} + \cdots - 18826182 ) / 15795 \) Copy content Toggle raw display
\(\beta_{14}\)\(=\) \( ( - 62668 \nu^{15} + 397070 \nu^{14} - 778856 \nu^{13} - 802747 \nu^{12} + 6878696 \nu^{11} - 12322064 \nu^{10} - 2527469 \nu^{9} + 51016561 \nu^{8} + \cdots + 244346949 ) / 142155 \) Copy content Toggle raw display
\(\beta_{15}\)\(=\) \( ( 5105 \nu^{15} - 31804 \nu^{14} + 61039 \nu^{13} + 67583 \nu^{12} - 549514 \nu^{11} + 965497 \nu^{10} + 239686 \nu^{9} - 4072523 \nu^{8} + 6992981 \nu^{7} + \cdots - 18816948 ) / 10935 \) Copy content Toggle raw display
\(\nu\)\(=\) \( ( -\beta_{15} + 2\beta_{9} + \beta_{8} + \beta_{7} - 2\beta_{6} - \beta_{4} - \beta_{3} + 2\beta_{2} - \beta _1 + 2 ) / 3 \) Copy content Toggle raw display
\(\nu^{2}\)\(=\) \( ( \beta_{14} - 2 \beta_{13} - \beta_{11} + \beta_{10} + 3 \beta_{9} - 2 \beta_{8} + 2 \beta_{7} - \beta_{6} - 2 \beta_{4} - \beta_{3} - 2 \beta _1 + 3 ) / 3 \) Copy content Toggle raw display
\(\nu^{3}\)\(=\) \( ( - 2 \beta_{13} + \beta_{12} + 2 \beta_{11} + 3 \beta_{10} + 6 \beta_{9} + 2 \beta_{8} + 5 \beta_{7} + 2 \beta_{5} - 3 \beta_{4} - 5 \beta_{3} + 8 \beta_{2} + \beta _1 - 4 ) / 3 \) Copy content Toggle raw display
\(\nu^{4}\)\(=\) \( ( 5 \beta_{15} - 3 \beta_{13} - \beta_{12} + 3 \beta_{11} + 6 \beta_{10} + 2 \beta_{9} - 3 \beta_{8} + \beta_{7} + 7 \beta_{6} + 4 \beta_{5} + 2 \beta_{4} + 4 \beta_{3} - 2 \beta_{2} + 11 \beta _1 + 8 ) / 3 \) Copy content Toggle raw display
\(\nu^{5}\)\(=\) \( ( - 10 \beta_{14} + 3 \beta_{13} + 3 \beta_{12} + 9 \beta_{11} + 5 \beta_{10} + 6 \beta_{9} + 30 \beta_{8} - 3 \beta_{7} - 2 \beta_{6} + 6 \beta_{5} - 7 \beta_{4} + \beta_{3} + 16 \beta_{2} + 21 \beta _1 - 1 ) / 3 \) Copy content Toggle raw display
\(\nu^{6}\)\(=\) \( ( - 7 \beta_{15} - 2 \beta_{14} + 7 \beta_{13} - 2 \beta_{12} + 11 \beta_{11} - 2 \beta_{10} + 8 \beta_{9} + 15 \beta_{8} + 30 \beta_{7} - 3 \beta_{6} - 4 \beta_{5} - 12 \beta_{4} + 32 \beta_{3} - 21 \beta_{2} + 51 \beta _1 + 20 ) / 3 \) Copy content Toggle raw display
\(\nu^{7}\)\(=\) \( ( - 36 \beta_{15} + 3 \beta_{14} + 6 \beta_{13} + 37 \beta_{12} + 24 \beta_{11} - 21 \beta_{10} + 33 \beta_{9} + 49 \beta_{8} + 93 \beta_{7} - \beta_{5} - 39 \beta_{4} - 17 \beta_{3} + 46 \beta_{2} + 90 \beta _1 - 3 ) / 3 \) Copy content Toggle raw display
\(\nu^{8}\)\(=\) \( ( - 42 \beta_{15} + 68 \beta_{14} + 10 \beta_{13} + 66 \beta_{12} + 50 \beta_{11} - 25 \beta_{10} + 42 \beta_{9} - 71 \beta_{8} + 179 \beta_{7} + 61 \beta_{6} + 18 \beta_{5} + 50 \beta_{4} + 31 \beta_{3} - 16 \beta_{2} + 163 \beta _1 + 94 ) / 3 \) Copy content Toggle raw display
\(\nu^{9}\)\(=\) \( ( - 44 \beta_{15} + 32 \beta_{14} + 216 \beta_{12} + 72 \beta_{11} + 14 \beta_{10} + 40 \beta_{9} + 50 \beta_{8} - 19 \beta_{7} + 66 \beta_{6} + 126 \beta_{5} + 66 \beta_{4} - 64 \beta_{3} + 110 \beta_{2} + 67 \beta _1 + 168 ) / 3 \) Copy content Toggle raw display
\(\nu^{10}\)\(=\) \( ( - 58 \beta_{15} - 18 \beta_{14} + 90 \beta_{13} + 172 \beta_{12} + 126 \beta_{11} + 162 \beta_{10} + 62 \beta_{9} + 14 \beta_{8} - 161 \beta_{7} - 8 \beta_{6} + 167 \beta_{5} + 158 \beta_{4} + 153 \beta_{3} - 144 \beta_{2} - 61 \beta _1 + 188 ) / 3 \) Copy content Toggle raw display
\(\nu^{11}\)\(=\) \( ( - 126 \beta_{15} - 351 \beta_{14} - 100 \beta_{13} + 231 \beta_{12} + 13 \beta_{11} + 333 \beta_{10} + 48 \beta_{9} + 80 \beta_{8} - 482 \beta_{7} - 81 \beta_{6} + 141 \beta_{5} - 219 \beta_{4} - 138 \beta_{3} + 86 \beta_{2} + \cdots + 217 ) / 3 \) Copy content Toggle raw display
\(\nu^{12}\)\(=\) \( ( - 209 \beta_{15} - 418 \beta_{14} - 251 \beta_{13} - 170 \beta_{12} + 68 \beta_{11} + 416 \beta_{10} + 301 \beta_{9} - 320 \beta_{8} + 325 \beta_{7} - 36 \beta_{6} - 298 \beta_{5} + 153 \beta_{4} - 357 \beta_{3} + 376 \beta_{2} + \cdots - 97 ) / 3 \) Copy content Toggle raw display
\(\nu^{13}\)\(=\) \( ( 385 \beta_{15} - 609 \beta_{14} - 1440 \beta_{13} + 402 \beta_{12} - 186 \beta_{11} + 414 \beta_{10} - 155 \beta_{9} - 478 \beta_{8} - 220 \beta_{7} + 98 \beta_{6} - 597 \beta_{5} + 277 \beta_{4} - 1199 \beta_{3} + 1540 \beta_{2} + \cdots + 1243 ) / 3 \) Copy content Toggle raw display
\(\nu^{14}\)\(=\) \( ( 1281 \beta_{15} - 511 \beta_{14} - 835 \beta_{13} + 960 \beta_{12} + 1042 \beta_{11} + 812 \beta_{10} - 27 \beta_{9} + 3809 \beta_{8} + 541 \beta_{7} - 1481 \beta_{6} - 882 \beta_{5} + 1178 \beta_{4} - 1454 \beta_{3} + \cdots - 1641 ) / 3 \) Copy content Toggle raw display
\(\nu^{15}\)\(=\) \( ( 2826 \beta_{15} - 1179 \beta_{14} - 1012 \beta_{13} + 2828 \beta_{12} + 1522 \beta_{11} + 2838 \beta_{10} - 2730 \beta_{9} + 6361 \beta_{8} - 11 \beta_{7} - 2559 \beta_{6} - 431 \beta_{5} - 2124 \beta_{4} + 809 \beta_{3} + \cdots + 208 ) / 3 \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(1 - \beta_{8}\) \(-1\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
881.1
1.71298 + 0.256290i
1.58110 + 0.707199i
−1.70672 0.295146i
1.27866 1.16834i
0.765614 1.55365i
0.320287 + 1.70218i
−1.68301 + 0.409224i
1.73109 0.0577511i
1.71298 0.256290i
1.58110 0.707199i
−1.70672 + 0.295146i
1.27866 + 1.16834i
0.765614 + 1.55365i
0.320287 1.70218i
−1.68301 0.409224i
1.73109 + 0.0577511i
−0.866025 + 0.500000i 0 0.500000 0.866025i −1.80966 + 3.13442i 0 0 1.00000i 0 3.61932i
881.2 −0.866025 + 0.500000i 0 0.500000 0.866025i −0.450129 + 0.779646i 0 0 1.00000i 0 0.900258i
881.3 −0.866025 + 0.500000i 0 0.500000 0.866025i 0.483662 0.837727i 0 0 1.00000i 0 0.967324i
881.4 −0.866025 + 0.500000i 0 0.500000 0.866025i 1.77612 3.07634i 0 0 1.00000i 0 3.55225i
881.5 0.866025 0.500000i 0 0.500000 0.866025i −1.82207 + 3.15592i 0 0 1.00000i 0 3.64414i
881.6 0.866025 0.500000i 0 0.500000 0.866025i −0.0338034 + 0.0585493i 0 0 1.00000i 0 0.0676069i
881.7 0.866025 0.500000i 0 0.500000 0.866025i 0.714925 1.23829i 0 0 1.00000i 0 1.42985i
881.8 0.866025 0.500000i 0 0.500000 0.866025i 1.14095 1.97618i 0 0 1.00000i 0 2.28190i
1763.1 −0.866025 0.500000i 0 0.500000 + 0.866025i −1.80966 3.13442i 0 0 1.00000i 0 3.61932i
1763.2 −0.866025 0.500000i 0 0.500000 + 0.866025i −0.450129 0.779646i 0 0 1.00000i 0 0.900258i
1763.3 −0.866025 0.500000i 0 0.500000 + 0.866025i 0.483662 + 0.837727i 0 0 1.00000i 0 0.967324i
1763.4 −0.866025 0.500000i 0 0.500000 + 0.866025i 1.77612 + 3.07634i 0 0 1.00000i 0 3.55225i
1763.5 0.866025 + 0.500000i 0 0.500000 + 0.866025i −1.82207 3.15592i 0 0 1.00000i 0 3.64414i
1763.6 0.866025 + 0.500000i 0 0.500000 + 0.866025i −0.0338034 0.0585493i 0 0 1.00000i 0 0.0676069i
1763.7 0.866025 + 0.500000i 0 0.500000 + 0.866025i 0.714925 + 1.23829i 0 0 1.00000i 0 1.42985i
1763.8 0.866025 + 0.500000i 0 0.500000 + 0.866025i 1.14095 + 1.97618i 0 0 1.00000i 0 2.28190i
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1763.8
Significant digits:
Format:

Inner twists

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

Twists

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

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5}^{16} + 24 T_{5}^{14} - 24 T_{5}^{13} + 423 T_{5}^{12} - 450 T_{5}^{11} + 3582 T_{5}^{10} - 5814 T_{5}^{9} + 22536 T_{5}^{8} - 25002 T_{5}^{7} + 42201 T_{5}^{6} - 19494 T_{5}^{5} + 32724 T_{5}^{4} - 11826 T_{5}^{3} + \cdots + 81 \) acting on \(S_{2}^{\mathrm{new}}(2646, [\chi])\). Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( (T^{4} - T^{2} + 1)^{4} \) Copy content Toggle raw display
$3$ \( T^{16} \) Copy content Toggle raw display
$5$ \( T^{16} + 24 T^{14} - 24 T^{13} + 423 T^{12} + \cdots + 81 \) Copy content Toggle raw display
$7$ \( T^{16} \) 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
$17$ \( (T^{8} - 18 T^{7} + 93 T^{6} + 60 T^{5} + \cdots + 7488)^{2} \) Copy content Toggle raw display
$19$ \( T^{16} + 144 T^{14} + 7218 T^{12} + \cdots + 9199089 \) 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
$31$ \( T^{16} + 6 T^{15} - 84 T^{14} + \cdots + 65610000 \) Copy content Toggle raw display
$37$ \( (T^{8} - 2 T^{7} - 176 T^{6} + \cdots - 180959)^{2} \) 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
$47$ \( T^{16} - 18 T^{15} + \cdots + 588203099136 \) Copy content Toggle raw display
$53$ \( T^{16} + 612 T^{14} + \cdots + 36759242529 \) Copy content Toggle raw display
$59$ \( T^{16} + 30 T^{15} + \cdots + 216504090000 \) Copy content Toggle raw display
$61$ \( T^{16} - 60 T^{15} + \cdots + 547560000 \) Copy content Toggle raw display
$67$ \( T^{16} - 14 T^{15} + \cdots + 2603856784 \) Copy content Toggle raw display
$71$ \( T^{16} + 486 T^{14} + \cdots + 65610000 \) Copy content Toggle raw display
$73$ \( T^{16} + 300 T^{14} + \cdots + 71115489 \) Copy content Toggle raw display
$79$ \( T^{16} + 16 T^{15} + \cdots + 970422010000 \) Copy content Toggle raw display
$83$ \( T^{16} + 177 T^{14} + \cdots + 953512641 \) Copy content Toggle raw display
$89$ \( (T^{8} - 24 T^{7} - 126 T^{6} + \cdots + 11451861)^{2} \) Copy content Toggle raw display
$97$ \( T^{16} + 6 T^{15} + \cdots + 9120206721024 \) Copy content Toggle raw display
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