Properties

Label 1183.2.c.i
Level $1183$
Weight $2$
Character orbit 1183.c
Analytic conductor $9.446$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.c (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.44630255912\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: 12.0.58891012706304.1
Defining polynomial: \(x^{12} - 5 x^{10} - 2 x^{9} + 15 x^{8} + 2 x^{7} - 30 x^{6} + 4 x^{5} + 60 x^{4} - 16 x^{3} - 80 x^{2} + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of a basis \(1,\beta_1,\ldots,\beta_{11}\) for the coefficient ring described below. We also show the integral \(q\)-expansion of the trace form.

\(f(q)\) \(=\) \( q + ( \beta_{1} - \beta_{7} ) q^{2} -\beta_{2} q^{3} + ( -1 - \beta_{4} + \beta_{5} ) q^{4} + ( \beta_{6} - \beta_{7} - \beta_{8} ) q^{5} + ( -\beta_{7} - \beta_{8} + \beta_{10} + \beta_{11} ) q^{6} -\beta_{7} q^{7} + ( 2 \beta_{7} + 2 \beta_{8} + \beta_{10} ) q^{8} + ( -\beta_{2} - \beta_{3} + \beta_{4} + 2 \beta_{5} ) q^{9} +O(q^{10})\) \( q + ( \beta_{1} - \beta_{7} ) q^{2} -\beta_{2} q^{3} + ( -1 - \beta_{4} + \beta_{5} ) q^{4} + ( \beta_{6} - \beta_{7} - \beta_{8} ) q^{5} + ( -\beta_{7} - \beta_{8} + \beta_{10} + \beta_{11} ) q^{6} -\beta_{7} q^{7} + ( 2 \beta_{7} + 2 \beta_{8} + \beta_{10} ) q^{8} + ( -\beta_{2} - \beta_{3} + \beta_{4} + 2 \beta_{5} ) q^{9} + ( -3 - 2 \beta_{4} + 2 \beta_{5} + \beta_{9} ) q^{10} + ( \beta_{1} - \beta_{6} - \beta_{8} + \beta_{11} ) q^{11} + ( -1 + \beta_{3} + \beta_{5} + \beta_{9} ) q^{12} + ( -1 + \beta_{5} ) q^{14} + ( -\beta_{1} + 2 \beta_{6} - 3 \beta_{7} + \beta_{10} ) q^{15} + ( 2 + \beta_{2} + 3 \beta_{3} + \beta_{4} - 2 \beta_{5} ) q^{16} + ( 1 - \beta_{2} - \beta_{9} ) q^{17} + ( \beta_{1} + \beta_{6} + 2 \beta_{7} + \beta_{8} + \beta_{10} + \beta_{11} ) q^{18} + ( 2 \beta_{8} - \beta_{11} ) q^{19} + ( -4 \beta_{1} + \beta_{6} + 6 \beta_{7} + 2 \beta_{8} + \beta_{10} - \beta_{11} ) q^{20} + \beta_{6} q^{21} + ( -1 + \beta_{2} - \beta_{3} - \beta_{4} ) q^{22} + ( 2 + 2 \beta_{4} + 2 \beta_{5} - 2 \beta_{9} ) q^{23} + ( -2 \beta_{6} - 2 \beta_{8} + \beta_{11} ) q^{24} + ( -2 + 2 \beta_{2} - \beta_{4} + \beta_{5} ) q^{25} + ( 1 + \beta_{3} - 2 \beta_{4} - \beta_{5} + \beta_{9} ) q^{27} + ( -\beta_{1} + \beta_{7} + \beta_{8} ) q^{28} + ( \beta_{2} + \beta_{3} - \beta_{4} - 2 \beta_{5} - 2 \beta_{9} ) q^{29} + ( -3 + \beta_{2} + 3 \beta_{3} + 3 \beta_{5} + 2 \beta_{9} ) q^{30} + ( 3 \beta_{7} + \beta_{8} - \beta_{10} - 2 \beta_{11} ) q^{31} + ( 3 \beta_{1} - 3 \beta_{6} - 2 \beta_{7} - \beta_{8} - 3 \beta_{10} - \beta_{11} ) q^{32} + ( 4 \beta_{1} - 2 \beta_{6} + \beta_{7} + \beta_{8} + \beta_{10} + \beta_{11} ) q^{33} + ( \beta_{6} - \beta_{7} - \beta_{8} + 2 \beta_{10} + 2 \beta_{11} ) q^{34} + ( -1 + \beta_{2} - \beta_{4} ) q^{35} + ( 1 + 2 \beta_{3} + 2 \beta_{4} + 2 \beta_{9} ) q^{36} + ( \beta_{6} + 3 \beta_{7} + \beta_{8} - 2 \beta_{10} - 3 \beta_{11} ) q^{37} + ( 1 - \beta_{2} + \beta_{3} + 2 \beta_{4} - \beta_{5} - \beta_{9} ) q^{38} + ( 8 + 3 \beta_{3} + 2 \beta_{4} - 3 \beta_{5} + 2 \beta_{9} ) q^{40} + ( \beta_{6} - 5 \beta_{7} + \beta_{8} + 2 \beta_{10} + \beta_{11} ) q^{41} + ( -1 + \beta_{3} - \beta_{4} + \beta_{9} ) q^{42} + ( 1 + \beta_{2} + \beta_{3} + 3 \beta_{4} - 2 \beta_{5} - 2 \beta_{9} ) q^{43} + ( -\beta_{6} + 3 \beta_{7} + \beta_{8} + \beta_{10} + \beta_{11} ) q^{44} + ( -2 \beta_{1} + 3 \beta_{6} - 2 \beta_{7} + 2 \beta_{8} + \beta_{10} ) q^{45} + ( 2 \beta_{1} + 2 \beta_{6} + 2 \beta_{7} + 2 \beta_{11} ) q^{46} + ( 2 \beta_{6} + 3 \beta_{7} + \beta_{8} + 3 \beta_{10} - 2 \beta_{11} ) q^{47} + ( -1 + \beta_{2} - \beta_{3} + 3 \beta_{5} + \beta_{9} ) q^{48} - q^{49} + ( -3 \beta_{1} + 7 \beta_{7} + 4 \beta_{8} - \beta_{10} - 2 \beta_{11} ) q^{50} + ( 4 - 2 \beta_{2} - 2 \beta_{3} + \beta_{4} + \beta_{5} ) q^{51} + ( -3 - 2 \beta_{2} - 2 \beta_{9} ) q^{53} + ( -2 \beta_{6} - 2 \beta_{7} - \beta_{11} ) q^{54} + ( -1 - 3 \beta_{2} + \beta_{3} + 5 \beta_{5} + \beta_{9} ) q^{55} + ( 2 + \beta_{3} + 2 \beta_{4} ) q^{56} + ( -3 \beta_{1} + \beta_{7} - 2 \beta_{8} - \beta_{10} ) q^{57} + ( -3 \beta_{1} + \beta_{6} - \beta_{8} + \beta_{10} + \beta_{11} ) q^{58} + ( -2 \beta_{1} + \beta_{7} - 3 \beta_{8} - \beta_{10} - 2 \beta_{11} ) q^{59} + ( -3 \beta_{1} - \beta_{6} + 2 \beta_{7} + \beta_{8} - 4 \beta_{10} - 3 \beta_{11} ) q^{60} + ( -2 - \beta_{2} + \beta_{3} - 3 \beta_{5} + 2 \beta_{9} ) q^{61} + ( 2 - 3 \beta_{2} - 2 \beta_{3} - 2 \beta_{5} - 2 \beta_{9} ) q^{62} + ( -2 \beta_{1} + \beta_{6} - \beta_{8} + \beta_{10} ) q^{63} + ( -3 - 2 \beta_{2} - 2 \beta_{3} - 2 \beta_{4} - 4 \beta_{9} ) q^{64} + ( -3 + 2 \beta_{2} + \beta_{3} - 3 \beta_{5} - \beta_{9} ) q^{66} + ( 2 \beta_{1} + \beta_{6} - 5 \beta_{7} + 3 \beta_{8} - \beta_{10} + \beta_{11} ) q^{67} + ( 1 + 2 \beta_{2} + 4 \beta_{3} + \beta_{9} ) q^{68} + ( -4 \beta_{2} - 4 \beta_{4} - 4 \beta_{5} + 2 \beta_{9} ) q^{69} + ( -2 \beta_{1} + 3 \beta_{7} + 2 \beta_{8} - \beta_{11} ) q^{70} + ( -2 \beta_{1} + 2 \beta_{6} - 2 \beta_{8} + 2 \beta_{10} ) q^{71} + ( 7 \beta_{1} - 2 \beta_{6} - \beta_{7} - 2 \beta_{8} - 4 \beta_{10} ) q^{72} + ( 2 \beta_{1} - \beta_{6} + 5 \beta_{7} + \beta_{8} - 2 \beta_{10} + \beta_{11} ) q^{73} + ( -5 \beta_{2} - 3 \beta_{3} - 2 \beta_{4} - \beta_{5} - 2 \beta_{9} ) q^{74} + ( -7 + 3 \beta_{2} + 3 \beta_{3} - 2 \beta_{4} - 3 \beta_{5} + \beta_{9} ) q^{75} + ( 2 \beta_{1} - 5 \beta_{7} - \beta_{8} - \beta_{10} ) q^{76} + ( -\beta_{2} - \beta_{4} + \beta_{5} + \beta_{9} ) q^{77} + ( -4 + 4 \beta_{4} - 2 \beta_{9} ) q^{79} + ( 4 \beta_{1} - 3 \beta_{6} - 6 \beta_{7} - 4 \beta_{8} - 5 \beta_{10} - 4 \beta_{11} ) q^{80} + ( 3 \beta_{2} + 3 \beta_{3} - \beta_{5} ) q^{81} + ( -4 + 3 \beta_{2} + 5 \beta_{3} + 2 \beta_{4} + 3 \beta_{5} + 2 \beta_{9} ) q^{82} + ( 2 \beta_{1} - 2 \beta_{6} - 5 \beta_{7} - \beta_{8} + \beta_{10} ) q^{83} + ( -\beta_{1} + \beta_{7} - \beta_{10} - \beta_{11} ) q^{84} + ( -\beta_{1} + 4 \beta_{6} - 3 \beta_{7} + 4 \beta_{10} ) q^{85} + ( 2 \beta_{1} + \beta_{6} - 5 \beta_{7} - 5 \beta_{8} - 3 \beta_{10} + \beta_{11} ) q^{86} + ( 1 + 3 \beta_{2} - 3 \beta_{3} + 2 \beta_{4} - \beta_{5} - \beta_{9} ) q^{87} + ( 4 + 4 \beta_{2} + \beta_{4} - 5 \beta_{5} ) q^{88} + ( 2 \beta_{6} + 6 \beta_{7} + 3 \beta_{11} ) q^{89} + ( 1 + \beta_{2} + 6 \beta_{3} + 2 \beta_{4} + 3 \beta_{9} ) q^{90} + ( 2 + 2 \beta_{2} + 4 \beta_{3} ) q^{92} + ( -5 \beta_{1} - 3 \beta_{6} + 2 \beta_{7} - \beta_{8} - 2 \beta_{10} - \beta_{11} ) q^{93} + ( \beta_{2} + 4 \beta_{3} + 2 \beta_{4} - 2 \beta_{5} ) q^{94} + ( 5 + \beta_{2} - \beta_{3} - \beta_{4} - 4 \beta_{5} ) q^{95} + ( -4 \beta_{6} + 7 \beta_{7} + \beta_{8} - \beta_{10} ) q^{96} + ( 4 \beta_{1} - 2 \beta_{6} - 5 \beta_{7} + 3 \beta_{8} - \beta_{10} - \beta_{11} ) q^{97} + ( -\beta_{1} + \beta_{7} ) q^{98} + ( 3 \beta_{1} - 4 \beta_{6} + \beta_{7} + 3 \beta_{10} + 2 \beta_{11} ) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 8q^{4} + 8q^{9} + O(q^{10}) \) \( 12q - 8q^{4} + 8q^{9} - 24q^{10} - 4q^{12} - 8q^{14} + 16q^{16} + 8q^{17} - 12q^{22} + 24q^{23} - 20q^{25} + 12q^{27} - 16q^{29} - 16q^{30} - 12q^{35} + 20q^{36} + 4q^{38} + 92q^{40} - 8q^{42} - 4q^{43} + 4q^{48} - 12q^{49} + 52q^{51} - 44q^{53} + 12q^{55} + 24q^{56} - 28q^{61} + 8q^{62} - 52q^{64} - 52q^{66} + 16q^{68} - 8q^{69} - 12q^{74} - 92q^{75} + 8q^{77} - 56q^{79} - 4q^{81} - 28q^{82} + 4q^{87} + 28q^{88} + 24q^{90} + 24q^{92} - 8q^{94} + 44q^{95} + O(q^{100}) \)

Basis of coefficient ring in terms of a root \(\nu\) of \(x^{12} - 5 x^{10} - 2 x^{9} + 15 x^{8} + 2 x^{7} - 30 x^{6} + 4 x^{5} + 60 x^{4} - 16 x^{3} - 80 x^{2} + 64\):

\(\beta_{0}\)\(=\)\( 1 \)
\(\beta_{1}\)\(=\)\((\)\( \nu^{11} - 5 \nu^{9} - 2 \nu^{8} + 15 \nu^{7} + 2 \nu^{6} - 30 \nu^{5} + 4 \nu^{4} + 60 \nu^{3} - 16 \nu^{2} - 48 \nu \)\()/32\)
\(\beta_{2}\)\(=\)\((\)\( \nu^{10} - 3 \nu^{9} - \nu^{8} + 9 \nu^{7} + \nu^{6} - 23 \nu^{5} + 16 \nu^{4} + 26 \nu^{3} - 32 \nu^{2} - 28 \nu + 48 \)\()/8\)
\(\beta_{3}\)\(=\)\((\)\( \nu^{11} + 6 \nu^{10} - 5 \nu^{9} - 24 \nu^{8} + 3 \nu^{7} + 52 \nu^{6} - 34 \nu^{5} - 88 \nu^{4} + 100 \nu^{3} + 168 \nu^{2} - 112 \nu - 160 \)\()/32\)
\(\beta_{4}\)\(=\)\((\)\( \nu^{11} + 4 \nu^{10} - 17 \nu^{9} - 6 \nu^{8} + 51 \nu^{7} + 6 \nu^{6} - 122 \nu^{5} + 68 \nu^{4} + 164 \nu^{3} - 144 \nu^{2} - 224 \nu + 192 \)\()/32\)
\(\beta_{5}\)\(=\)\((\)\( -\nu^{11} - 2 \nu^{10} + 17 \nu^{9} - 4 \nu^{8} - 55 \nu^{7} + 24 \nu^{6} + 126 \nu^{5} - 128 \nu^{4} - 156 \nu^{3} + 232 \nu^{2} + 192 \nu - 288 \)\()/32\)
\(\beta_{6}\)\(=\)\((\)\( \nu^{11} - 8 \nu^{10} - 5 \nu^{9} + 30 \nu^{8} + 15 \nu^{7} - 78 \nu^{6} + 18 \nu^{5} + 124 \nu^{4} - 68 \nu^{3} - 192 \nu^{2} + 112 \nu + 96 \)\()/32\)
\(\beta_{7}\)\(=\)\((\)\( -5 \nu^{11} + 2 \nu^{10} + 17 \nu^{9} - 8 \nu^{8} - 39 \nu^{7} + 44 \nu^{6} + 50 \nu^{5} - 88 \nu^{4} - 68 \nu^{3} + 120 \nu^{2} + 16 \nu - 32 \)\()/32\)
\(\beta_{8}\)\(=\)\((\)\( -\nu^{11} + 5 \nu^{10} + 7 \nu^{9} - 19 \nu^{8} - 19 \nu^{7} + 49 \nu^{6} + 14 \nu^{5} - 106 \nu^{4} + 4 \nu^{3} + 172 \nu^{2} - 8 \nu - 128 \)\()/16\)
\(\beta_{9}\)\(=\)\((\)\( -5 \nu^{11} + 9 \nu^{9} + 18 \nu^{8} - 11 \nu^{7} - 18 \nu^{6} + 6 \nu^{5} + 68 \nu^{4} - 76 \nu^{3} - 160 \nu^{2} + 16 \nu + 288 \)\()/32\)
\(\beta_{10}\)\(=\)\((\)\( -\nu^{11} + 3 \nu^{10} + 5 \nu^{9} - 13 \nu^{8} - 13 \nu^{7} + 35 \nu^{6} + 12 \nu^{5} - 70 \nu^{4} + 8 \nu^{3} + 108 \nu^{2} - 16 \nu - 88 \)\()/8\)
\(\beta_{11}\)\(=\)\((\)\( -3 \nu^{11} + \nu^{10} + 12 \nu^{9} - 3 \nu^{8} - 28 \nu^{7} + 19 \nu^{6} + 43 \nu^{5} - 52 \nu^{4} - 66 \nu^{3} + 64 \nu^{2} + 52 \nu - 16 \)\()/8\)
\(1\)\(=\)\(\beta_0\)
\(\nu\)\(=\)\((\)\(-\beta_{4} + \beta_{2} + \beta_{1}\)\()/2\)
\(\nu^{2}\)\(=\)\((\)\(-\beta_{11} + \beta_{8} + 2 \beta_{7} + \beta_{6} - \beta_{5} - \beta_{4} - \beta_{1} + 2\)\()/2\)
\(\nu^{3}\)\(=\)\((\)\(\beta_{10} + \beta_{9} - \beta_{8} - \beta_{7} - \beta_{5} - 2 \beta_{4} + \beta_{3} + 2 \beta_{1} + 1\)\()/2\)
\(\nu^{4}\)\(=\)\((\)\(-2 \beta_{11} + \beta_{10} + 3 \beta_{7} - 2 \beta_{5} - 3 \beta_{4} - \beta_{3} + \beta_{2} - 3 \beta_{1} - 1\)\()/2\)
\(\nu^{5}\)\(=\)\((\)\(-\beta_{11} + 4 \beta_{10} + 2 \beta_{9} - 2 \beta_{8} - 2 \beta_{7} + 2 \beta_{6} - \beta_{2} - 2 \beta_{1} + 6\)\()/2\)
\(\nu^{6}\)\(=\)\((\)\(-3 \beta_{11} + \beta_{10} + 2 \beta_{9} - \beta_{8} + 3 \beta_{7} - 3 \beta_{6} + 3 \beta_{5} - 2 \beta_{4} - 3 \beta_{3} + 3 \beta_{2} + 2 \beta_{1} - 3\)\()/2\)
\(\nu^{7}\)\(=\)\((\)\(-5 \beta_{11} + 5 \beta_{10} + \beta_{9} + 5 \beta_{8} + 5 \beta_{7} + 8 \beta_{6} - \beta_{5} + 2 \beta_{4} - 7 \beta_{3} - \beta_{2} - 4 \beta_{1} + 7\)\()/2\)
\(\nu^{8}\)\(=\)\((\)\(-5 \beta_{11} + 12 \beta_{9} + 3 \beta_{8} - \beta_{6} + 5 \beta_{5} - 3 \beta_{4} + 2 \beta_{3} - 2 \beta_{2} + 13 \beta_{1} - 6\)\()/2\)
\(\nu^{9}\)\(=\)\((\)\(-8 \beta_{11} + 3 \beta_{10} + \beta_{9} + 11 \beta_{8} + 9 \beta_{7} - 13 \beta_{5} - 8 \beta_{4} - 17 \beta_{3} - 6 \beta_{2} - 13\)\()/2\)
\(\nu^{10}\)\(=\)\((\)\(-4 \beta_{11} + 13 \beta_{10} + 24 \beta_{9} + 4 \beta_{8} - 25 \beta_{7} + 8 \beta_{6} - 2 \beta_{5} - 3 \beta_{4} + 7 \beta_{3} - 9 \beta_{2} - 7 \beta_{1} - 9\)\()/2\)
\(\nu^{11}\)\(=\)\((\)\(-7 \beta_{11} - 6 \beta_{10} + 10 \beta_{9} + 4 \beta_{8} - 16 \beta_{7} - 40 \beta_{6} + 6 \beta_{5} - 4 \beta_{4} - 26 \beta_{3} - 11 \beta_{2} + 10 \beta_{1} - 20\)\()/2\)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).

\(n\) \(339\) \(1016\)
\(\chi(n)\) \(1\) \(-1\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
337.1
−1.12906 0.851598i
−1.30089 0.554694i
0.759479 1.19298i
1.40744 0.138282i
−1.08105 0.911778i
1.34408 + 0.439820i
1.34408 0.439820i
−1.08105 + 0.911778i
1.40744 + 0.138282i
0.759479 + 1.19298i
−1.30089 + 0.554694i
−1.12906 + 0.851598i
2.70320i −0.345949 −5.30727 3.25812i 0.935168i 1.00000i 8.94020i −2.88032 −8.80735
337.2 2.10939i 2.26165 −2.44952 3.60178i 4.77070i 1.00000i 0.948212i 2.11505 −7.59755
337.3 1.38595i −2.82577 0.0791355 0.518957i 3.91639i 1.00000i 2.88158i 4.98500 −0.719250
337.4 1.27656i −1.16793 0.370384 1.81487i 1.49093i 1.00000i 3.02595i −1.63595 2.31680
337.5 0.823556i 2.66029 1.32176 3.16209i 2.19090i 1.00000i 2.73565i 4.07715 2.60416
337.6 0.120360i −0.582292 1.98551 1.68817i 0.0700846i 1.00000i 0.479696i −2.66094 0.203187
337.7 0.120360i −0.582292 1.98551 1.68817i 0.0700846i 1.00000i 0.479696i −2.66094 0.203187
337.8 0.823556i 2.66029 1.32176 3.16209i 2.19090i 1.00000i 2.73565i 4.07715 2.60416
337.9 1.27656i −1.16793 0.370384 1.81487i 1.49093i 1.00000i 3.02595i −1.63595 2.31680
337.10 1.38595i −2.82577 0.0791355 0.518957i 3.91639i 1.00000i 2.88158i 4.98500 −0.719250
337.11 2.10939i 2.26165 −2.44952 3.60178i 4.77070i 1.00000i 0.948212i 2.11505 −7.59755
337.12 2.70320i −0.345949 −5.30727 3.25812i 0.935168i 1.00000i 8.94020i −2.88032 −8.80735
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 337.12
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
13.b even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1183.2.c.i 12
13.b even 2 1 inner 1183.2.c.i 12
13.c even 3 1 91.2.q.a 12
13.d odd 4 1 1183.2.a.m 6
13.d odd 4 1 1183.2.a.p 6
13.e even 6 1 91.2.q.a 12
39.h odd 6 1 819.2.ct.a 12
39.i odd 6 1 819.2.ct.a 12
52.i odd 6 1 1456.2.cc.c 12
52.j odd 6 1 1456.2.cc.c 12
91.g even 3 1 637.2.u.h 12
91.h even 3 1 637.2.k.h 12
91.i even 4 1 8281.2.a.by 6
91.i even 4 1 8281.2.a.ch 6
91.k even 6 1 637.2.k.h 12
91.l odd 6 1 637.2.k.g 12
91.m odd 6 1 637.2.u.i 12
91.n odd 6 1 637.2.q.h 12
91.p odd 6 1 637.2.u.i 12
91.t odd 6 1 637.2.q.h 12
91.u even 6 1 637.2.u.h 12
91.v odd 6 1 637.2.k.g 12
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
91.2.q.a 12 13.c even 3 1
91.2.q.a 12 13.e even 6 1
637.2.k.g 12 91.l odd 6 1
637.2.k.g 12 91.v odd 6 1
637.2.k.h 12 91.h even 3 1
637.2.k.h 12 91.k even 6 1
637.2.q.h 12 91.n odd 6 1
637.2.q.h 12 91.t odd 6 1
637.2.u.h 12 91.g even 3 1
637.2.u.h 12 91.u even 6 1
637.2.u.i 12 91.m odd 6 1
637.2.u.i 12 91.p odd 6 1
819.2.ct.a 12 39.h odd 6 1
819.2.ct.a 12 39.i odd 6 1
1183.2.a.m 6 13.d odd 4 1
1183.2.a.p 6 13.d odd 4 1
1183.2.c.i 12 1.a even 1 1 trivial
1183.2.c.i 12 13.b even 2 1 inner
1456.2.cc.c 12 52.i odd 6 1
1456.2.cc.c 12 52.j odd 6 1
8281.2.a.by 6 91.i even 4 1
8281.2.a.ch 6 91.i even 4 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{12} + 16 T_{2}^{10} + 88 T_{2}^{8} + 206 T_{2}^{6} + 208 T_{2}^{4} + 72 T_{2}^{2} + 1 \) acting on \(S_{2}^{\mathrm{new}}(1183, [\chi])\).

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + 72 T^{2} + 208 T^{4} + 206 T^{6} + 88 T^{8} + 16 T^{10} + T^{12} \)
$3$ \( ( 4 + 20 T + 25 T^{2} - 2 T^{3} - 11 T^{4} + T^{6} )^{2} \)
$5$ \( 3481 + 16148 T^{2} + 13040 T^{4} + 4146 T^{6} + 600 T^{8} + 40 T^{10} + T^{12} \)
$7$ \( ( 1 + T^{2} )^{6} \)
$11$ \( 256 + 2464 T^{2} + 4377 T^{4} + 2538 T^{6} + 587 T^{8} + 50 T^{10} + T^{12} \)
$13$ \( T^{12} \)
$17$ \( ( -491 - 224 T + 167 T^{2} + 60 T^{3} - 21 T^{4} - 4 T^{5} + T^{6} )^{2} \)
$19$ \( 55696 + 71352 T^{2} + 34945 T^{4} + 8390 T^{6} + 1027 T^{8} + 58 T^{10} + T^{12} \)
$23$ \( ( 6208 - 1472 T - 1616 T^{2} + 608 T^{3} - 20 T^{4} - 12 T^{5} + T^{6} )^{2} \)
$29$ \( ( 3169 + 336 T - 1412 T^{2} - 566 T^{3} - 44 T^{4} + 8 T^{5} + T^{6} )^{2} \)
$31$ \( 913936 + 1285560 T^{2} + 568225 T^{4} + 96896 T^{6} + 5854 T^{8} + 136 T^{10} + T^{12} \)
$37$ \( 1755945216 + 749015424 T^{2} + 62699184 T^{4} + 2220264 T^{6} + 38457 T^{8} + 318 T^{10} + T^{12} \)
$41$ \( 884705536 + 216982912 T^{2} + 20856496 T^{4} + 990632 T^{6} + 23977 T^{8} + 270 T^{10} + T^{12} \)
$43$ \( ( 1552 - 3776 T + 2421 T^{2} - 90 T^{3} - 109 T^{4} + 2 T^{5} + T^{6} )^{2} \)
$47$ \( 9461776 + 47561752 T^{2} + 10113609 T^{4} + 722232 T^{6} + 21782 T^{8} + 272 T^{10} + T^{12} \)
$53$ \( ( -2339 + 7302 T - 3353 T^{2} - 700 T^{3} + 91 T^{4} + 22 T^{5} + T^{6} )^{2} \)
$59$ \( 4571923456 + 977387904 T^{2} + 71782249 T^{4} + 2425880 T^{6} + 40774 T^{8} + 328 T^{10} + T^{12} \)
$61$ \( ( 2368 + 1600 T - 1888 T^{2} - 1416 T^{3} - 87 T^{4} + 14 T^{5} + T^{6} )^{2} \)
$67$ \( 613651984 + 958137656 T^{2} + 90973265 T^{4} + 3237372 T^{6} + 52710 T^{8} + 388 T^{10} + T^{12} \)
$71$ \( 46895104 + 20912128 T^{2} + 3358464 T^{4} + 244992 T^{6} + 8816 T^{8} + 152 T^{10} + T^{12} \)
$73$ \( 1386221824 + 513361280 T^{2} + 55965104 T^{4} + 2238456 T^{6} + 40473 T^{8} + 334 T^{10} + T^{12} \)
$79$ \( ( -512 + 1664 T - 1584 T^{2} + 192 T^{3} + 212 T^{4} + 28 T^{5} + T^{6} )^{2} \)
$83$ \( 141324544 + 454322976 T^{2} + 48190849 T^{4} + 1905008 T^{6} + 35086 T^{8} + 304 T^{10} + T^{12} \)
$89$ \( 1834580224 + 1726865504 T^{2} + 256467377 T^{4} + 12139518 T^{6} + 146499 T^{8} + 658 T^{10} + T^{12} \)
$97$ \( 53465344 + 258112736 T^{2} + 42543185 T^{4} + 2280594 T^{6} + 46611 T^{8} + 382 T^{10} + T^{12} \)
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