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Properties

Label 230.2.g.b
Level $230$
Weight $2$
Character orbit 230.g
Analytic conductor $1.837$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 230.g (of order \(11\), degree \(10\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.83655924649\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(2\) over \(\Q(\zeta_{11})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Defining polynomial: \( x^{20} - 5 x^{19} + 12 x^{18} + 16 x^{17} - 49 x^{16} + 59 x^{15} - 197 x^{14} + 42 x^{13} + 1625 x^{12} - 5910 x^{11} + 14651 x^{10} - 22501 x^{9} + 26003 x^{8} - 19607 x^{7} + \cdots + 529 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

$q$-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.

\(f(q)\) \(=\) \( q + \beta_{6} q^{2} + (\beta_{18} - \beta_{13} + \beta_{5} - \beta_{2} + \beta_1) q^{3} + \beta_{3} q^{4} + \beta_{4} q^{5} + (\beta_{19} - \beta_{17} + \beta_{4} + \beta_{3} - \beta_1 + 1) q^{6} + ( - \beta_{19} - \beta_{15} - \beta_{14} - \beta_{11} + \beta_{10} - \beta_{8} + \beta_{6} - \beta_{4} - \beta_{3} - \beta_{2}) q^{7} - \beta_{8} q^{8} + ( - \beta_{17} + \beta_{15} - \beta_{14} + \beta_{13} + \beta_{12} - 2 \beta_{11} + \beta_{9} - 2 \beta_{8} + \cdots - 1) q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + \beta_{6} q^{2} + (\beta_{18} - \beta_{13} + \beta_{5} - \beta_{2} + \beta_1) q^{3} + \beta_{3} q^{4} + \beta_{4} q^{5} + (\beta_{19} - \beta_{17} + \beta_{4} + \beta_{3} - \beta_1 + 1) q^{6} + ( - \beta_{19} - \beta_{15} - \beta_{14} - \beta_{11} + \beta_{10} - \beta_{8} + \beta_{6} - \beta_{4} - \beta_{3} - \beta_{2}) q^{7} - \beta_{8} q^{8} + ( - \beta_{17} + \beta_{15} - \beta_{14} + \beta_{13} + \beta_{12} - 2 \beta_{11} + \beta_{9} - 2 \beta_{8} + \cdots - 1) q^{9}+ \cdots + (3 \beta_{19} - 3 \beta_{17} + 5 \beta_{16} - 4 \beta_{14} + 6 \beta_{13} - 2 \beta_{12} + \cdots - 2) q^{99}+O(q^{100}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 2 q^{2} - 3 q^{3} - 2 q^{4} - 2 q^{5} + 3 q^{6} + 19 q^{7} + 2 q^{8} - 27 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 2 q^{2} - 3 q^{3} - 2 q^{4} - 2 q^{5} + 3 q^{6} + 19 q^{7} + 2 q^{8} - 27 q^{9} + 2 q^{10} + 7 q^{11} + 8 q^{12} + 8 q^{13} + 3 q^{14} - 3 q^{15} - 2 q^{16} + 8 q^{17} + 27 q^{18} - q^{19} - 2 q^{20} - 31 q^{21} - 18 q^{22} - 9 q^{23} - 8 q^{24} - 2 q^{25} - 8 q^{26} - 18 q^{27} - 3 q^{28} + 20 q^{29} + 3 q^{30} - 17 q^{31} + 2 q^{32} + 17 q^{33} + 3 q^{34} - 3 q^{35} + 17 q^{36} + 6 q^{37} - 21 q^{38} - 75 q^{39} + 2 q^{40} - 2 q^{41} + 42 q^{42} - 18 q^{43} + 7 q^{44} + 28 q^{45} - 2 q^{46} + 42 q^{47} + 8 q^{48} - 19 q^{49} + 2 q^{50} + 26 q^{51} + 19 q^{52} + 19 q^{53} - 26 q^{54} - 15 q^{55} - 19 q^{56} + 7 q^{57} - 9 q^{58} + 25 q^{59} - 3 q^{60} - 49 q^{61} - 38 q^{62} - 87 q^{63} - 2 q^{64} + 19 q^{65} - 6 q^{66} + 19 q^{67} - 36 q^{68} + 36 q^{69} + 14 q^{70} + 7 q^{71} - 17 q^{72} - 10 q^{73} - 6 q^{74} - 3 q^{75} - q^{76} - 29 q^{77} - 2 q^{78} - 33 q^{79} - 2 q^{80} + 72 q^{81} + 2 q^{82} - 41 q^{83} + 13 q^{84} - 14 q^{85} - 48 q^{86} - 16 q^{87} - 7 q^{88} + 55 q^{89} + 5 q^{90} + 13 q^{92} + 10 q^{93} + 13 q^{94} + 21 q^{95} + 3 q^{96} - 9 q^{97} + 41 q^{98} + 59 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

Basis of coefficient ring in terms of a root \(\nu\) of \( x^{20} - 5 x^{19} + 12 x^{18} + 16 x^{17} - 49 x^{16} + 59 x^{15} - 197 x^{14} + 42 x^{13} + 1625 x^{12} - 5910 x^{11} + 14651 x^{10} - 22501 x^{9} + 26003 x^{8} - 19607 x^{7} + \cdots + 529 \) : Copy content Toggle raw display

\(\beta_{1}\)\(=\) \( \nu \) Copy content Toggle raw display
\(\beta_{2}\)\(=\) \( ( 25\!\cdots\!20 \nu^{19} + \cdots + 57\!\cdots\!44 ) / 14\!\cdots\!87 \) Copy content Toggle raw display
\(\beta_{3}\)\(=\) \( ( - 68\!\cdots\!51 \nu^{19} + \cdots - 28\!\cdots\!27 ) / 14\!\cdots\!87 \) Copy content Toggle raw display
\(\beta_{4}\)\(=\) \( ( 10\!\cdots\!36 \nu^{19} + \cdots - 61\!\cdots\!32 ) / 14\!\cdots\!87 \) Copy content Toggle raw display
\(\beta_{5}\)\(=\) \( ( 64\!\cdots\!88 \nu^{19} + \cdots - 88\!\cdots\!56 ) / 14\!\cdots\!87 \) Copy content Toggle raw display
\(\beta_{6}\)\(=\) \( ( 87\!\cdots\!15 \nu^{19} + \cdots + 23\!\cdots\!08 ) / 14\!\cdots\!87 \) Copy content Toggle raw display
\(\beta_{7}\)\(=\) \( ( 16\!\cdots\!91 \nu^{19} + \cdots + 24\!\cdots\!54 ) / 14\!\cdots\!87 \) Copy content Toggle raw display
\(\beta_{8}\)\(=\) \( ( 16\!\cdots\!64 \nu^{19} + \cdots + 56\!\cdots\!03 ) / 14\!\cdots\!87 \) Copy content Toggle raw display
\(\beta_{9}\)\(=\) \( ( - 76\!\cdots\!98 \nu^{19} + \cdots - 94\!\cdots\!93 ) / 61\!\cdots\!69 \) Copy content Toggle raw display
\(\beta_{10}\)\(=\) \( ( - 21\!\cdots\!27 \nu^{19} + \cdots - 39\!\cdots\!82 ) / 14\!\cdots\!87 \) Copy content Toggle raw display
\(\beta_{11}\)\(=\) \( ( 22\!\cdots\!84 \nu^{19} + \cdots - 32\!\cdots\!98 ) / 14\!\cdots\!87 \) Copy content Toggle raw display
\(\beta_{12}\)\(=\) \( ( - 22\!\cdots\!71 \nu^{19} + \cdots - 58\!\cdots\!01 ) / 14\!\cdots\!87 \) Copy content Toggle raw display
\(\beta_{13}\)\(=\) \( ( 28\!\cdots\!65 \nu^{19} + \cdots + 30\!\cdots\!95 ) / 14\!\cdots\!87 \) Copy content Toggle raw display
\(\beta_{14}\)\(=\) \( ( - 29\!\cdots\!15 \nu^{19} + \cdots - 61\!\cdots\!61 ) / 14\!\cdots\!87 \) Copy content Toggle raw display
\(\beta_{15}\)\(=\) \( ( 40\!\cdots\!38 \nu^{19} + \cdots + 34\!\cdots\!17 ) / 14\!\cdots\!87 \) Copy content Toggle raw display
\(\beta_{16}\)\(=\) \( ( 17\!\cdots\!17 \nu^{19} + \cdots + 94\!\cdots\!20 ) / 61\!\cdots\!69 \) Copy content Toggle raw display
\(\beta_{17}\)\(=\) \( ( - 56\!\cdots\!79 \nu^{19} + \cdots - 13\!\cdots\!22 ) / 14\!\cdots\!87 \) Copy content Toggle raw display
\(\beta_{18}\)\(=\) \( ( - 72\!\cdots\!74 \nu^{19} + \cdots - 38\!\cdots\!34 ) / 14\!\cdots\!87 \) Copy content Toggle raw display
\(\beta_{19}\)\(=\) \( ( - 14\!\cdots\!30 \nu^{19} + \cdots - 16\!\cdots\!18 ) / 14\!\cdots\!87 \) Copy content Toggle raw display

Display \(\nu^j\) in terms of \(\beta_i\)

\(\nu\)\(=\) \( \beta_1 \) Copy content Toggle raw display
\(\nu^{2}\)\(=\) \( \beta_{18} - \beta_{17} + \beta_{16} + \beta_{15} - \beta_{13} + \beta_{12} + \beta_{11} - \beta_{9} - \beta_{8} - \beta_{7} - 2 \beta_{6} - \beta_{5} + 3 \beta_{4} + \beta_{3} - \beta_{2} + \beta _1 + 2 \) Copy content Toggle raw display
\(\nu^{3}\)\(=\) \( 3 \beta_{19} + \beta_{18} - 3 \beta_{17} + 6 \beta_{16} + 3 \beta_{15} - 3 \beta_{14} + 5 \beta_{13} + 5 \beta_{10} + 2 \beta_{9} - 3 \beta_{8} - 3 \beta_{7} + \beta_{6} - 2 \beta_{5} - \beta_{4} - 2 \beta_{3} - 5 \beta_{2} - 2 \) Copy content Toggle raw display
\(\nu^{4}\)\(=\) \( 18 \beta_{19} - 2 \beta_{18} + 25 \beta_{16} + 12 \beta_{15} - 27 \beta_{14} + 18 \beta_{13} - 15 \beta_{12} - 4 \beta_{11} + 15 \beta_{9} - 4 \beta_{8} - 15 \beta_{7} - 4 \beta_{6} + 13 \beta_{5} - 4 \beta_{3} - 5 \beta _1 - 19 \) Copy content Toggle raw display
\(\nu^{5}\)\(=\) \( 29 \beta_{19} - 79 \beta_{18} + 52 \beta_{17} - 70 \beta_{16} - 27 \beta_{15} - 32 \beta_{14} + 15 \beta_{13} - 62 \beta_{12} + 20 \beta_{11} - 80 \beta_{10} + 79 \beta_{9} + 80 \beta_{8} + 42 \beta_{6} + 39 \beta_{5} - 5 \beta_{4} - 5 \beta_{3} + 52 \beta_{2} + \cdots - 62 \) Copy content Toggle raw display
\(\nu^{6}\)\(=\) \( - 56 \beta_{19} - 239 \beta_{18} + 282 \beta_{17} - 369 \beta_{16} - 239 \beta_{15} + 37 \beta_{14} - 210 \beta_{13} - 166 \beta_{12} - 19 \beta_{11} - 356 \beta_{10} + 56 \beta_{9} + 359 \beta_{8} + 221 \beta_{7} + 123 \beta_{6} + \cdots - 89 \) Copy content Toggle raw display
\(\nu^{7}\)\(=\) \( - 1081 \beta_{19} - 361 \beta_{18} + 535 \beta_{17} - 1933 \beta_{16} - 1081 \beta_{15} + 1400 \beta_{14} - 1420 \beta_{13} + 361 \beta_{12} + 14 \beta_{11} - 854 \beta_{10} - 535 \beta_{9} + 640 \beta_{8} + 1038 \beta_{7} + \cdots + 852 \) Copy content Toggle raw display
\(\nu^{8}\)\(=\) \( - 3798 \beta_{19} + 2438 \beta_{18} - 1058 \beta_{17} - 1773 \beta_{16} - 1058 \beta_{15} + 4464 \beta_{14} - 3798 \beta_{13} + 3798 \beta_{12} - 810 \beta_{11} + 1868 \beta_{10} - 4325 \beta_{9} - 1922 \beta_{8} + \cdots + 4464 \) Copy content Toggle raw display
\(\nu^{9}\)\(=\) \( - 5135 \beta_{19} + 16473 \beta_{18} - 15916 \beta_{17} + 15193 \beta_{16} + 8789 \beta_{15} + 6870 \beta_{14} + 420 \beta_{13} + 15916 \beta_{12} - 1210 \beta_{11} + 21605 \beta_{10} - 12724 \beta_{9} + \cdots + 14706 \) Copy content Toggle raw display
\(\nu^{10}\)\(=\) \( 36734 \beta_{19} + 50703 \beta_{18} - 59591 \beta_{17} + 118069 \beta_{16} + 66327 \beta_{15} - 47053 \beta_{14} + 67366 \beta_{13} + 17683 \beta_{12} - 4813 \beta_{11} + 87212 \beta_{10} - 77404 \beta_{8} + \cdots - 9938 \) Copy content Toggle raw display
\(\nu^{11}\)\(=\) \( 256857 \beta_{19} - 76135 \beta_{17} + 344581 \beta_{16} + 196934 \beta_{15} - 318507 \beta_{14} + 318507 \beta_{13} - 138918 \beta_{12} + 22073 \beta_{11} + 101338 \beta_{10} + 196934 \beta_{9} + \cdots - 232313 \) Copy content Toggle raw display
\(\nu^{12}\)\(=\) \( 778490 \beta_{19} - 778490 \beta_{18} + 560354 \beta_{17} - 972564 \beta_{14} + 654831 \beta_{13} - 1019617 \beta_{12} + 123659 \beta_{11} - 777936 \beta_{10} + 1019617 \beta_{9} + \cdots - 1153146 \) Copy content Toggle raw display
\(\nu^{13}\)\(=\) \( - 3979257 \beta_{18} + 3979257 \beta_{17} - 5344858 \beta_{16} - 3042920 \beta_{15} - 1672508 \beta_{13} - 3042920 \beta_{12} + 397588 \beta_{11} - 5651765 \beta_{10} + 2164279 \beta_{9} + \cdots - 2111735 \) Copy content Toggle raw display
\(\nu^{14}\)\(=\) \( - 11985926 \beta_{19} - 8599271 \beta_{18} + 11985926 \beta_{17} - 27688350 \beta_{16} - 15700939 \beta_{15} + 14954050 \beta_{14} - 18419890 \beta_{13} - 16918620 \beta_{10} + \cdots + 6433964 \) Copy content Toggle raw display
\(\nu^{15}\)\(=\) \( - 61492387 \beta_{19} + 17642007 \beta_{18} - 58907654 \beta_{16} - 33525393 \beta_{15} + 76549661 \beta_{14} - 69535225 \beta_{13} + 46978173 \beta_{12} - 6084356 \beta_{11} + \cdots + 66536352 \) Copy content Toggle raw display
\(\nu^{16}\)\(=\) \( - 132340428 \beta_{19} + 221906105 \beta_{18} - 184749586 \beta_{17} + 120271015 \beta_{16} + 68506823 \beta_{15} + 165278556 \beta_{14} - 72491788 \beta_{13} + \cdots + 242001342 \) Copy content Toggle raw display
\(\nu^{17}\)\(=\) \( 271144644 \beta_{19} + 873784229 \beta_{18} - 949293604 \beta_{17} + 1539365880 \beta_{16} + 873784229 \beta_{15} - 338975821 \beta_{14} + 698859189 \beta_{13} + \cdots + 217095417 \) Copy content Toggle raw display
\(\nu^{18}\)\(=\) \( 3426020339 \beta_{19} + 1059630164 \beta_{18} - 2039347103 \beta_{17} + 6028541248 \beta_{16} + 3426020339 \beta_{15} - 4266560602 \beta_{14} + 4710719625 \beta_{13} + \cdots - 2602520909 \) Copy content Toggle raw display
\(\nu^{19}\)\(=\) \( 13471243579 \beta_{19} - 7998279224 \beta_{18} + 4175877645 \beta_{17} + 7359415616 \beta_{16} + 4175877645 \beta_{15} - 16796005904 \beta_{14} + 13471243579 \beta_{13} + \cdots - 16796005904 \) Copy content Toggle raw display

Display \(\beta_i\) in terms of \(\nu^j\)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(51\)
\(\chi(n)\) \(1\) \(-\beta_{6}\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
31.1
0.588453 − 1.28853i
−0.905632 + 1.98306i
2.57205 + 2.96831i
−0.271308 − 0.313106i
−0.138474 + 0.963109i
0.212636 − 1.47891i
−0.138474 − 0.963109i
0.212636 + 1.47891i
2.57205 − 2.96831i
−0.271308 + 0.313106i
−2.49760 + 0.733362i
1.92732 − 0.565914i
−0.319826 − 0.205540i
1.33237 + 0.856263i
0.588453 + 1.28853i
−0.905632 − 1.98306i
−0.319826 + 0.205540i
1.33237 − 0.856263i
−2.49760 − 0.733362i
1.92732 + 0.565914i
0.142315 − 0.989821i −1.10832 − 2.42687i −0.959493 − 0.281733i −0.654861 − 0.755750i −2.55990 + 0.751655i −0.986597 − 0.634047i −0.415415 + 0.909632i −2.69677 + 3.11224i −0.841254 + 0.540641i
31.2 0.142315 − 0.989821i 1.40549 + 3.07760i −0.959493 − 0.281733i −0.654861 − 0.755750i 3.24630 − 0.953198i 2.97617 + 1.91267i −0.415415 + 0.909632i −5.53162 + 6.38383i −0.841254 + 0.540641i
41.1 0.959493 + 0.281733i −0.880272 + 1.01589i 0.841254 + 0.540641i −0.142315 + 0.989821i −1.13082 + 0.726736i 0.394126 + 0.863015i 0.654861 + 0.755750i 0.169795 + 1.18095i −0.415415 + 0.909632i
41.2 0.959493 + 0.281733i 1.48208 − 1.71041i 0.841254 + 0.540641i −0.142315 + 0.989821i 1.90392 − 1.22358i −0.119262 − 0.261148i 0.654861 + 0.755750i −0.302001 − 2.10046i −0.415415 + 0.909632i
71.1 −0.841254 − 0.540641i −0.420808 − 2.92679i 0.415415 + 0.909632i −0.959493 − 0.281733i −1.22833 + 2.68968i 2.73530 − 3.15671i 0.142315 − 0.989821i −5.51052 + 1.61803i 0.654861 + 0.755750i
71.2 −0.841254 − 0.540641i 0.0390478 + 0.271583i 0.415415 + 0.909632i −0.959493 − 0.281733i 0.113980 − 0.249581i −0.365070 + 0.421313i 0.142315 − 0.989821i 2.80625 − 0.823988i 0.654861 + 0.755750i
81.1 −0.841254 + 0.540641i −0.420808 + 2.92679i 0.415415 − 0.909632i −0.959493 + 0.281733i −1.22833 − 2.68968i 2.73530 + 3.15671i 0.142315 + 0.989821i −5.51052 − 1.61803i 0.654861 − 0.755750i
81.2 −0.841254 + 0.540641i 0.0390478 − 0.271583i 0.415415 − 0.909632i −0.959493 + 0.281733i 0.113980 + 0.249581i −0.365070 − 0.421313i 0.142315 + 0.989821i 2.80625 + 0.823988i 0.654861 − 0.755750i
101.1 0.959493 − 0.281733i −0.880272 − 1.01589i 0.841254 − 0.540641i −0.142315 − 0.989821i −1.13082 − 0.726736i 0.394126 − 0.863015i 0.654861 − 0.755750i 0.169795 − 1.18095i −0.415415 − 0.909632i
101.2 0.959493 − 0.281733i 1.48208 + 1.71041i 0.841254 − 0.540641i −0.142315 − 0.989821i 1.90392 + 1.22358i −0.119262 + 0.261148i 0.654861 − 0.755750i −0.302001 + 2.10046i −0.415415 − 0.909632i
121.1 −0.415415 + 0.909632i −1.50807 − 0.442808i −0.654861 − 0.755750i 0.841254 − 0.540641i 1.02927 − 1.18784i −0.440465 + 3.06350i 0.959493 − 0.281733i −0.445574 − 0.286353i 0.142315 + 0.989821i
121.2 −0.415415 + 0.909632i −0.248602 − 0.0729960i −0.654861 − 0.755750i 0.841254 − 0.540641i 0.169672 − 0.195812i 0.663794 − 4.61679i 0.959493 − 0.281733i −2.46729 − 1.58563i 0.142315 + 0.989821i
131.1 0.654861 − 0.755750i −1.71555 + 1.10252i −0.142315 − 0.989821i 0.415415 + 0.909632i −0.290219 + 2.01852i 3.10381 − 0.911362i −0.841254 − 0.540641i 0.481321 − 1.05395i 0.959493 + 0.281733i
131.2 0.654861 − 0.755750i 1.45499 − 0.935068i −0.142315 − 0.989821i 0.415415 + 0.909632i 0.246141 − 1.71195i 1.53819 − 0.451652i −0.841254 − 0.540641i −0.00358844 + 0.00785758i 0.959493 + 0.281733i
141.1 0.142315 + 0.989821i −1.10832 + 2.42687i −0.959493 + 0.281733i −0.654861 + 0.755750i −2.55990 − 0.751655i −0.986597 + 0.634047i −0.415415 − 0.909632i −2.69677 − 3.11224i −0.841254 − 0.540641i
141.2 0.142315 + 0.989821i 1.40549 − 3.07760i −0.959493 + 0.281733i −0.654861 + 0.755750i 3.24630 + 0.953198i 2.97617 − 1.91267i −0.415415 − 0.909632i −5.53162 − 6.38383i −0.841254 − 0.540641i
151.1 0.654861 + 0.755750i −1.71555 − 1.10252i −0.142315 + 0.989821i 0.415415 − 0.909632i −0.290219 − 2.01852i 3.10381 + 0.911362i −0.841254 + 0.540641i 0.481321 + 1.05395i 0.959493 − 0.281733i
151.2 0.654861 + 0.755750i 1.45499 + 0.935068i −0.142315 + 0.989821i 0.415415 − 0.909632i 0.246141 + 1.71195i 1.53819 + 0.451652i −0.841254 + 0.540641i −0.00358844 − 0.00785758i 0.959493 − 0.281733i
211.1 −0.415415 − 0.909632i −1.50807 + 0.442808i −0.654861 + 0.755750i 0.841254 + 0.540641i 1.02927 + 1.18784i −0.440465 − 3.06350i 0.959493 + 0.281733i −0.445574 + 0.286353i 0.142315 − 0.989821i
211.2 −0.415415 − 0.909632i −0.248602 + 0.0729960i −0.654861 + 0.755750i 0.841254 + 0.540641i 0.169672 + 0.195812i 0.663794 + 4.61679i 0.959493 + 0.281733i −2.46729 + 1.58563i 0.142315 − 0.989821i
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 211.2
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
23.c even 11 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 230.2.g.b ✓ 20
23.c even 11 1 inner 230.2.g.b ✓ 20
23.c even 11 1 5290.2.a.bj 10
23.d odd 22 1 5290.2.a.bi 10
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
230.2.g.b ✓ 20 1.a even 1 1 trivial
230.2.g.b ✓ 20 23.c even 11 1 inner
5290.2.a.bi 10 23.d odd 22 1
5290.2.a.bj 10 23.c even 11 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{20} + 3 T_{3}^{19} + 21 T_{3}^{18} + 66 T_{3}^{17} + 252 T_{3}^{16} + 701 T_{3}^{15} + 1695 T_{3}^{14} + 3432 T_{3}^{13} + 7173 T_{3}^{12} + 15634 T_{3}^{11} + 34605 T_{3}^{10} + 46692 T_{3}^{9} + 31164 T_{3}^{8} + \cdots + 1024 \) acting on \(S_{2}^{\mathrm{new}}(230, [\chi])\). Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( (T^{10} - T^{9} + T^{8} - T^{7} + T^{6} - T^{5} + T^{4} + \cdots + 1)^{2} \) Copy content Toggle raw display
$3$ \( T^{20} + 3 T^{19} + 21 T^{18} + \cdots + 1024 \) Copy content Toggle raw display
$5$ \( (T^{10} + T^{9} + T^{8} + T^{7} + T^{6} + T^{5} + T^{4} + \cdots + 1)^{2} \) Copy content Toggle raw display
$7$ \( T^{20} - 19 T^{19} + 197 T^{18} + \cdots + 38809 \) Copy content Toggle raw display
$11$ \( T^{20} - 7 T^{19} + 40 T^{18} + \cdots + 2374681 \) Copy content Toggle raw display
$13$ \( T^{20} - 8 T^{19} + \cdots + 13416820561 \) Copy content Toggle raw display
$17$ \( T^{20} - 8 T^{19} + 25 T^{18} + \cdots + 605553664 \) Copy content Toggle raw display
$19$ \( T^{20} + T^{19} + 8 T^{18} + \cdots + 392951329 \) Copy content Toggle raw display
$23$ \( T^{20} + 9 T^{19} + \cdots + 41426511213649 \) Copy content Toggle raw display
$29$ \( T^{20} - 20 T^{19} + \cdots + 3969466491904 \) Copy content Toggle raw display
$31$ \( T^{20} + 17 T^{19} + 158 T^{18} + \cdots + 1024 \) Copy content Toggle raw display
$37$ \( T^{20} - 6 T^{19} + \cdots + 7650363233041 \) Copy content Toggle raw display
$41$ \( T^{20} + 2 T^{19} + \cdots + 1804635361 \) Copy content Toggle raw display
$43$ \( T^{20} + 18 T^{19} + \cdots + 23760372736 \) Copy content Toggle raw display
$47$ \( (T^{10} - 21 T^{9} - 141 T^{8} + \cdots + 130098649)^{2} \) Copy content Toggle raw display
$53$ \( T^{20} - 19 T^{19} + 78 T^{18} + \cdots + 7447441 \) Copy content Toggle raw display
$59$ \( T^{20} - 25 T^{19} + \cdots + 27292338778849 \) Copy content Toggle raw display
$61$ \( T^{20} + 49 T^{19} + \cdots + 22\!\cdots\!04 \) Copy content Toggle raw display
$67$ \( T^{20} + \cdots + 246200702534656 \) Copy content Toggle raw display
$71$ \( T^{20} - 7 T^{19} + \cdots + 95950331339776 \) Copy content Toggle raw display
$73$ \( T^{20} + \cdots + 859836921496576 \) Copy content Toggle raw display
$79$ \( T^{20} + 33 T^{19} + \cdots + 90\!\cdots\!76 \) Copy content Toggle raw display
$83$ \( T^{20} + 41 T^{19} + \cdots + 160435495936 \) Copy content Toggle raw display
$89$ \( T^{20} - 55 T^{19} + \cdots + 20\!\cdots\!09 \) Copy content Toggle raw display
$97$ \( T^{20} + \cdots + 286047133533184 \) Copy content Toggle raw display
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