Properties

Label 1008.2.ca.c
Level $1008$
Weight $2$
Character orbit 1008.ca
Analytic conductor $8.049$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1008,2,Mod(257,1008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 5, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1008.257");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.ca (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(8.04892052375\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
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

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 

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.

\(f(q)\) \(=\) \( q + (\beta_{9} - \beta_{3}) q^{3} + (\beta_{14} - \beta_{13} - \beta_{9}) q^{5} + (\beta_{14} + \beta_{11} - \beta_{3} + \beta_{2}) q^{7} + (\beta_{14} + \beta_{11} + \beta_{5} + \beta_{4} + \beta_{2} + \beta_1) q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + (\beta_{9} - \beta_{3}) q^{3} + (\beta_{14} - \beta_{13} - \beta_{9}) q^{5} + (\beta_{14} + \beta_{11} - \beta_{3} + \beta_{2}) q^{7} + (\beta_{14} + \beta_{11} + \beta_{5} + \beta_{4} + \beta_{2} + \beta_1) q^{9} + ( - \beta_{12} + \beta_{10} + \beta_{9} - \beta_{8}) q^{11} + ( - \beta_{15} - \beta_{14} + 2 \beta_{9} + \beta_{6} - \beta_{5} - \beta_{3} - \beta_{2}) q^{13} + (\beta_{15} + \beta_{10} + \beta_{8} + \beta_{6} - \beta_{4} - 2 \beta_{2} + \beta_1) q^{15} + (\beta_{15} + \beta_{14} - \beta_{9} - \beta_{8} - \beta_{7} - \beta_{4} - \beta_1 - 1) q^{17} + ( - \beta_{15} - \beta_{13} + \beta_{12} - 2 \beta_{10} + \beta_{8} - 2 \beta_{7} + 2 \beta_{4} + \cdots - 2) q^{19}+ \cdots + (\beta_{15} - 3 \beta_{14} + 2 \beta_{13} - 2 \beta_{12} - 4 \beta_{11} - 2 \beta_{10} - \beta_{9} + \cdots - 2) q^{99}+O(q^{100}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 2 q^{7} - 12 q^{11} + 6 q^{13} + 18 q^{15} - 18 q^{17} - 12 q^{21} + 6 q^{23} - 8 q^{25} - 36 q^{27} + 6 q^{29} - 30 q^{35} - 2 q^{37} + 12 q^{39} - 6 q^{41} + 2 q^{43} - 30 q^{45} + 36 q^{47} - 8 q^{49} - 6 q^{51} - 36 q^{53} + 6 q^{57} - 60 q^{59} - 36 q^{63} + 28 q^{67} - 42 q^{69} - 60 q^{75} - 42 q^{77} - 32 q^{79} - 36 q^{81} - 12 q^{85} + 24 q^{87} - 24 q^{89} + 12 q^{91} - 42 q^{93} + 6 q^{97} - 18 q^{99}+O(q^{100}) \) 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

\(\beta_{1}\)\(=\) \( ( - 154 \nu^{15} + 1325 \nu^{14} - 3608 \nu^{13} + 224 \nu^{12} + 22478 \nu^{11} - 55022 \nu^{10} + 23518 \nu^{9} + 159688 \nu^{8} - 382978 \nu^{7} + 226785 \nu^{6} + \cdots + 1285227 ) / 47385 \) Copy content Toggle raw display
\(\beta_{2}\)\(=\) \( ( 1342 \nu^{15} - 9134 \nu^{14} + 18833 \nu^{13} + 17821 \nu^{12} - 164858 \nu^{11} + 301448 \nu^{10} + 55817 \nu^{9} - 1253167 \nu^{8} + 2222275 \nu^{7} - 414219 \nu^{6} + \cdots - 6445089 ) / 142155 \) 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
\(\beta_{5}\)\(=\) \( ( - 5666 \nu^{15} + 35256 \nu^{14} - 67793 \nu^{13} - 74626 \nu^{12} + 609708 \nu^{11} - 1074116 \nu^{10} - 260022 \nu^{9} + 4521984 \nu^{8} - 7792711 \nu^{7} + \cdots + 21264930 ) / 47385 \) Copy content Toggle raw display
\(\beta_{6}\)\(=\) \( ( - 432 \nu^{15} + 2816 \nu^{14} - 5740 \nu^{13} - 5150 \nu^{12} + 49010 \nu^{11} - 90874 \nu^{10} - 11735 \nu^{9} + 363706 \nu^{8} - 657698 \nu^{7} + 149366 \nu^{6} + \cdots + 1853118 ) / 3645 \) Copy content Toggle raw display
\(\beta_{7}\)\(=\) \( ( 4120 \nu^{15} - 25571 \nu^{14} + 48788 \nu^{13} + 55006 \nu^{12} - 441224 \nu^{11} + 771188 \nu^{10} + 200900 \nu^{9} - 3269857 \nu^{8} + 5585140 \nu^{7} + \cdots - 14963454 ) / 28431 \) Copy content Toggle raw display
\(\beta_{8}\)\(=\) \( ( 20555 \nu^{15} - 129232 \nu^{14} + 250807 \nu^{13} + 267434 \nu^{12} - 2233957 \nu^{11} + 3963841 \nu^{10} + 897553 \nu^{9} - 16558319 \nu^{8} + 28688468 \nu^{7} + \cdots - 77795964 ) / 142155 \) Copy content Toggle raw display
\(\beta_{9}\)\(=\) \( ( - 21860 \nu^{15} + 133486 \nu^{14} - 249901 \nu^{13} - 298607 \nu^{12} + 2298061 \nu^{11} - 3952333 \nu^{10} - 1174129 \nu^{9} + 17020292 \nu^{8} + \cdots + 75541167 ) / 142155 \) Copy content Toggle raw display
\(\beta_{10}\)\(=\) \( ( 2015 \nu^{15} - 12538 \nu^{14} + 24088 \nu^{13} + 26576 \nu^{12} - 216643 \nu^{11} + 381184 \nu^{10} + 93322 \nu^{9} - 1605386 \nu^{8} + 2760692 \nu^{7} - 423483 \nu^{6} + \cdots - 7453296 ) / 10935 \) Copy content Toggle raw display
\(\beta_{11}\)\(=\) \( ( 29357 \nu^{15} - 190006 \nu^{14} + 382390 \nu^{13} + 360905 \nu^{12} - 3304405 \nu^{11} + 6053149 \nu^{10} + 947140 \nu^{9} - 24541961 \nu^{8} + 43845563 \nu^{7} + \cdots - 122535423 ) / 142155 \) Copy content Toggle raw display
\(\beta_{12}\)\(=\) \( ( - 11745 \nu^{15} + 73063 \nu^{14} - 139508 \nu^{13} - 157621 \nu^{12} + 1262908 \nu^{11} - 2204834 \nu^{10} - 583027 \nu^{9} + 9367136 \nu^{8} - 15968257 \nu^{7} + \cdots + 42448941 ) / 47385 \) Copy content Toggle raw display
\(\beta_{13}\)\(=\) \( ( - 45758 \nu^{15} + 290392 \nu^{14} - 571483 \nu^{13} - 583571 \nu^{12} + 5039353 \nu^{11} - 9054625 \nu^{10} - 1803427 \nu^{9} + 37411250 \nu^{8} + \cdots + 181431333 ) / 142155 \) Copy content Toggle raw display
\(\beta_{14}\)\(=\) \( ( - 17267 \nu^{15} + 108242 \nu^{14} - 209241 \nu^{13} - 227007 \nu^{12} + 1874096 \nu^{11} - 3311892 \nu^{10} - 782399 \nu^{9} + 13905028 \nu^{8} + \cdots + 65023155 ) / 47385 \) Copy content Toggle raw display
\(\beta_{15}\)\(=\) \( ( - 56402 \nu^{15} + 348301 \nu^{14} - 661000 \nu^{13} - 757115 \nu^{12} + 6004885 \nu^{11} - 10449439 \nu^{10} - 2822275 \nu^{9} + 44476256 \nu^{8} + \cdots + 200862828 ) / 142155 \) Copy content Toggle raw display
\(\nu\)\(=\) \( ( -\beta_{14} - \beta_{10} + \beta_{9} - \beta_{7} + 2\beta_{4} + \beta_{3} - 2\beta_{2} + 1 ) / 3 \) Copy content Toggle raw display
\(\nu^{2}\)\(=\) \( ( 2 \beta_{15} - \beta_{12} - \beta_{10} - \beta_{9} + 2 \beta_{8} - \beta_{7} - 2 \beta_{6} - \beta_{5} + 2 \beta_{4} - \beta_{3} - 2 \beta_{2} + \beta _1 + 2 ) / 3 \) Copy content Toggle raw display
\(\nu^{3}\)\(=\) \( ( 2 \beta_{15} + 2 \beta_{14} - 2 \beta_{13} - 4 \beta_{12} + \beta_{11} - 2 \beta_{10} - \beta_{9} - 3 \beta_{8} - \beta_{6} - 2 \beta_{5} + \beta_{4} - 2 \beta_{3} - 5 \beta_{2} - 3 ) / 3 \) Copy content Toggle raw display
\(\nu^{4}\)\(=\) \( ( 3 \beta_{15} + 10 \beta_{14} - 4 \beta_{13} - 6 \beta_{12} + 5 \beta_{11} + 4 \beta_{10} - 3 \beta_{9} - \beta_{8} - \beta_{7} + 2 \beta_{6} - 5 \beta_{5} - 2 \beta_{4} - 8 \beta_{3} + 3 \beta_{2} - 2 \beta _1 + 11 ) / 3 \) Copy content Toggle raw display
\(\nu^{5}\)\(=\) \( ( - 3 \beta_{15} - 2 \beta_{14} - 6 \beta_{13} - 6 \beta_{12} + 3 \beta_{11} - 8 \beta_{10} - 4 \beta_{9} - 3 \beta_{8} - 20 \beta_{7} + 15 \beta_{6} - 3 \beta_{5} - 5 \beta_{4} + 2 \beta_{3} - 13 \beta_{2} - 9 \beta _1 - 7 ) / 3 \) Copy content Toggle raw display
\(\nu^{6}\)\(=\) \( ( - 7 \beta_{15} - 3 \beta_{14} + 4 \beta_{13} - 4 \beta_{12} - 2 \beta_{11} - 10 \beta_{10} + 7 \beta_{9} + 33 \beta_{8} - 44 \beta_{7} + 8 \beta_{6} - 20 \beta_{5} - \beta_{4} + 6 \beta_{3} - 12 \beta_{2} + 9 \beta _1 - 31 ) / 3 \) Copy content Toggle raw display
\(\nu^{7}\)\(=\) \( ( - 6 \beta_{15} - 35 \beta_{14} + \beta_{13} - 18 \beta_{12} - 38 \beta_{11} - 59 \beta_{10} + \beta_{9} + 22 \beta_{8} - 36 \beta_{7} + \beta_{6} - 34 \beta_{5} - 35 \beta_{4} + 21 \beta_{3} - 68 \beta_{2} + 11 \beta _1 - 85 ) / 3 \) Copy content Toggle raw display
\(\nu^{8}\)\(=\) \( ( - 10 \beta_{15} + 35 \beta_{14} - 18 \beta_{13} - 40 \beta_{12} - 48 \beta_{11} + 7 \beta_{10} + 84 \beta_{9} + 38 \beta_{8} + 13 \beta_{7} - 17 \beta_{6} - 70 \beta_{5} - 41 \beta_{4} - 21 \beta_{3} - 22 \beta_{2} + 34 \beta _1 - 36 ) / 3 \) Copy content Toggle raw display
\(\nu^{9}\)\(=\) \( ( 32 \beta_{14} - 126 \beta_{13} - 72 \beta_{12} - 90 \beta_{11} - 46 \beta_{10} - 20 \beta_{9} - 12 \beta_{8} + 20 \beta_{7} + 87 \beta_{6} + 48 \beta_{5} - 124 \beta_{4} + 10 \beta_{3} - 98 \beta_{2} - 42 \beta _1 + 64 ) / 3 \) Copy content Toggle raw display
\(\nu^{10}\)\(=\) \( ( - 90 \beta_{15} + 171 \beta_{14} - 167 \beta_{13} - 36 \beta_{12} - 5 \beta_{11} + 153 \beta_{10} + 143 \beta_{9} + 229 \beta_{8} - 220 \beta_{7} + 199 \beta_{6} + 146 \beta_{5} - 15 \beta_{4} + 40 \beta_{3} - 85 \beta_{2} + 170 \beta _1 - 225 ) / 3 \) Copy content Toggle raw display
\(\nu^{11}\)\(=\) \( ( 100 \beta_{15} + 83 \beta_{14} - 141 \beta_{13} - 113 \beta_{12} - 90 \beta_{11} - 27 \beta_{10} - 412 \beta_{9} + 403 \beta_{8} - 42 \beta_{7} + 335 \beta_{6} + 286 \beta_{5} - 360 \beta_{4} + 272 \beta_{3} - 489 \beta_{2} + 383 \beta _1 - 325 ) / 3 \) Copy content Toggle raw display
\(\nu^{12}\)\(=\) \( ( 251 \beta_{15} + 97 \beta_{14} + 298 \beta_{13} - 319 \beta_{12} - 128 \beta_{11} + 867 \beta_{10} + 501 \beta_{9} + 471 \beta_{8} + 395 \beta_{7} + 236 \beta_{6} - 284 \beta_{5} - 510 \beta_{4} + 263 \beta_{3} - 847 \beta_{2} + \cdots - 845 ) / 3 \) Copy content Toggle raw display
\(\nu^{13}\)\(=\) \( ( 1440 \beta_{15} - 170 \beta_{14} + 597 \beta_{13} - 1254 \beta_{12} - 999 \beta_{11} + 1288 \beta_{10} - 721 \beta_{9} - 87 \beta_{8} + 2173 \beta_{7} + 198 \beta_{6} - 549 \beta_{5} - 1706 \beta_{4} + 926 \beta_{3} + \cdots + 1901 ) / 3 \) Copy content Toggle raw display
\(\nu^{14}\)\(=\) \( ( 835 \beta_{15} - 918 \beta_{14} + 882 \beta_{13} - 1877 \beta_{12} - 1842 \beta_{11} + 2872 \beta_{10} + 1198 \beta_{9} - 389 \beta_{8} - 1067 \beta_{7} + 101 \beta_{6} - 881 \beta_{5} - 872 \beta_{4} + 2104 \beta_{3} + \cdots - 1013 ) / 3 \) Copy content Toggle raw display
\(\nu^{15}\)\(=\) \( ( 1012 \beta_{15} + 838 \beta_{14} + 431 \beta_{13} - 2534 \beta_{12} - 3259 \beta_{11} + 1145 \beta_{10} - 5435 \beta_{9} + 951 \beta_{8} - 2874 \beta_{7} - 1079 \beta_{6} - 214 \beta_{5} - 1879 \beta_{4} + 4997 \beta_{3} + \cdots + 561 ) / 3 \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(-\beta_{7}\) \(1\) \(-\beta_{7}\)

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.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
257.1
1.58110 0.707199i
0.765614 + 1.55365i
−1.68301 0.409224i
0.320287 1.70218i
−1.70672 + 0.295146i
1.73109 + 0.0577511i
1.27866 + 1.16834i
1.71298 0.256290i
1.58110 + 0.707199i
0.765614 1.55365i
−1.68301 + 0.409224i
0.320287 + 1.70218i
−1.70672 0.295146i
1.73109 0.0577511i
1.27866 1.16834i
1.71298 + 0.256290i
0 −1.64774 0.533822i 0 −0.450129 0.779646i 0 −1.57151 2.12847i 0 2.43007 + 1.75919i 0
257.2 0 −1.52765 + 0.816261i 0 −1.82207 3.15592i 0 1.58246 2.12034i 0 1.66744 2.49392i 0
257.3 0 −1.38631 1.03834i 0 0.714925 + 1.23829i 0 −0.327442 + 2.62541i 0 0.843698 + 2.87892i 0
257.4 0 0.290993 + 1.70743i 0 −0.0338034 0.0585493i 0 −1.19767 + 2.35915i 0 −2.83065 + 0.993700i 0
257.5 0 0.734581 1.56856i 0 0.483662 + 0.837727i 0 2.16249 1.52435i 0 −1.92078 2.30447i 0
257.6 0 0.890915 1.48535i 0 1.14095 + 1.97618i 0 −1.42337 2.23025i 0 −1.41254 2.64665i 0
257.7 0 1.08509 + 1.35003i 0 1.77612 + 3.07634i 0 −2.63804 + 0.201867i 0 −0.645160 + 2.92981i 0
257.8 0 1.56012 + 0.752355i 0 −1.80966 3.13442i 0 2.41308 + 1.08492i 0 1.86792 + 2.34752i 0
353.1 0 −1.64774 + 0.533822i 0 −0.450129 + 0.779646i 0 −1.57151 + 2.12847i 0 2.43007 1.75919i 0
353.2 0 −1.52765 0.816261i 0 −1.82207 + 3.15592i 0 1.58246 + 2.12034i 0 1.66744 + 2.49392i 0
353.3 0 −1.38631 + 1.03834i 0 0.714925 1.23829i 0 −0.327442 2.62541i 0 0.843698 2.87892i 0
353.4 0 0.290993 1.70743i 0 −0.0338034 + 0.0585493i 0 −1.19767 2.35915i 0 −2.83065 0.993700i 0
353.5 0 0.734581 + 1.56856i 0 0.483662 0.837727i 0 2.16249 + 1.52435i 0 −1.92078 + 2.30447i 0
353.6 0 0.890915 + 1.48535i 0 1.14095 1.97618i 0 −1.42337 + 2.23025i 0 −1.41254 + 2.64665i 0
353.7 0 1.08509 1.35003i 0 1.77612 3.07634i 0 −2.63804 0.201867i 0 −0.645160 2.92981i 0
353.8 0 1.56012 0.752355i 0 −1.80966 + 3.13442i 0 2.41308 1.08492i 0 1.86792 2.34752i 0
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 257.8
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 1008.2.ca.c 16
3.b odd 2 1 3024.2.ca.c 16
4.b odd 2 1 126.2.l.a 16
7.d odd 6 1 1008.2.df.c 16
9.c even 3 1 3024.2.df.c 16
9.d odd 6 1 1008.2.df.c 16
12.b even 2 1 378.2.l.a 16
21.g even 6 1 3024.2.df.c 16
28.d even 2 1 882.2.l.b 16
28.f even 6 1 126.2.t.a yes 16
28.f even 6 1 882.2.m.a 16
28.g odd 6 1 882.2.m.b 16
28.g odd 6 1 882.2.t.a 16
36.f odd 6 1 378.2.t.a 16
36.f odd 6 1 1134.2.k.a 16
36.h even 6 1 126.2.t.a yes 16
36.h even 6 1 1134.2.k.b 16
63.i even 6 1 inner 1008.2.ca.c 16
63.t odd 6 1 3024.2.ca.c 16
84.h odd 2 1 2646.2.l.a 16
84.j odd 6 1 378.2.t.a 16
84.j odd 6 1 2646.2.m.a 16
84.n even 6 1 2646.2.m.b 16
84.n even 6 1 2646.2.t.b 16
252.n even 6 1 1134.2.k.b 16
252.n even 6 1 2646.2.m.b 16
252.o even 6 1 882.2.m.a 16
252.r odd 6 1 126.2.l.a 16
252.s odd 6 1 882.2.t.a 16
252.u odd 6 1 2646.2.l.a 16
252.bb even 6 1 882.2.l.b 16
252.bi even 6 1 2646.2.t.b 16
252.bj even 6 1 378.2.l.a 16
252.bl odd 6 1 2646.2.m.a 16
252.bn odd 6 1 882.2.m.b 16
252.bn odd 6 1 1134.2.k.a 16
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
126.2.l.a 16 4.b odd 2 1
126.2.l.a 16 252.r odd 6 1
126.2.t.a yes 16 28.f even 6 1
126.2.t.a yes 16 36.h even 6 1
378.2.l.a 16 12.b even 2 1
378.2.l.a 16 252.bj even 6 1
378.2.t.a 16 36.f odd 6 1
378.2.t.a 16 84.j odd 6 1
882.2.l.b 16 28.d even 2 1
882.2.l.b 16 252.bb even 6 1
882.2.m.a 16 28.f even 6 1
882.2.m.a 16 252.o even 6 1
882.2.m.b 16 28.g odd 6 1
882.2.m.b 16 252.bn odd 6 1
882.2.t.a 16 28.g odd 6 1
882.2.t.a 16 252.s odd 6 1
1008.2.ca.c 16 1.a even 1 1 trivial
1008.2.ca.c 16 63.i even 6 1 inner
1008.2.df.c 16 7.d odd 6 1
1008.2.df.c 16 9.d odd 6 1
1134.2.k.a 16 36.f odd 6 1
1134.2.k.a 16 252.bn odd 6 1
1134.2.k.b 16 36.h even 6 1
1134.2.k.b 16 252.n even 6 1
2646.2.l.a 16 84.h odd 2 1
2646.2.l.a 16 252.u odd 6 1
2646.2.m.a 16 84.j odd 6 1
2646.2.m.a 16 252.bl odd 6 1
2646.2.m.b 16 84.n even 6 1
2646.2.m.b 16 252.n even 6 1
2646.2.t.b 16 84.n even 6 1
2646.2.t.b 16 252.bi even 6 1
3024.2.ca.c 16 3.b odd 2 1
3024.2.ca.c 16 63.t odd 6 1
3024.2.df.c 16 9.c even 3 1
3024.2.df.c 16 21.g even 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 \(S_{2}^{\mathrm{new}}(1008, [\chi])\). Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T^{16} \) 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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