Properties

Label 5290.2.a.bj
Level $5290$
Weight $2$
Character orbit 5290.a
Self dual yes
Analytic conductor $42.241$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5290 = 2 \cdot 5 \cdot 23^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5290.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(42.2408626693\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Defining polynomial: \(x^{10} - 3 x^{9} - 15 x^{8} + 35 x^{7} + 78 x^{6} - 123 x^{5} - 185 x^{4} + 140 x^{3} + 177 x^{2} - 15 x - 23\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 230)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of a basis \(1,\beta_1,\ldots,\beta_{9}\) for the coefficient ring described below. We also show the integral \(q\)-expansion of the trace form.

\(f(q)\) \(=\) \( q - q^{2} + ( 1 + \beta_{7} + \beta_{9} ) q^{3} + q^{4} + q^{5} + ( -1 - \beta_{7} - \beta_{9} ) q^{6} + ( -1 - \beta_{3} + \beta_{4} - \beta_{5} - \beta_{6} - \beta_{7} + \beta_{8} ) q^{7} - q^{8} + ( 1 - \beta_{1} - \beta_{4} - \beta_{5} - \beta_{7} + 2 \beta_{8} + \beta_{9} ) q^{9} +O(q^{10})\) \( q - q^{2} + ( 1 + \beta_{7} + \beta_{9} ) q^{3} + q^{4} + q^{5} + ( -1 - \beta_{7} - \beta_{9} ) q^{6} + ( -1 - \beta_{3} + \beta_{4} - \beta_{5} - \beta_{6} - \beta_{7} + \beta_{8} ) q^{7} - q^{8} + ( 1 - \beta_{1} - \beta_{4} - \beta_{5} - \beta_{7} + 2 \beta_{8} + \beta_{9} ) q^{9} - q^{10} + ( 1 - \beta_{3} + \beta_{4} - \beta_{6} + \beta_{8} ) q^{11} + ( 1 + \beta_{7} + \beta_{9} ) q^{12} + ( -1 - \beta_{1} - \beta_{3} + \beta_{6} - \beta_{7} + 2 \beta_{8} + \beta_{9} ) q^{13} + ( 1 + \beta_{3} - \beta_{4} + \beta_{5} + \beta_{6} + \beta_{7} - \beta_{8} ) q^{14} + ( 1 + \beta_{7} + \beta_{9} ) q^{15} + q^{16} + ( -1 + \beta_{2} + \beta_{3} + \beta_{4} + \beta_{5} - \beta_{6} - \beta_{8} ) q^{17} + ( -1 + \beta_{1} + \beta_{4} + \beta_{5} + \beta_{7} - 2 \beta_{8} - \beta_{9} ) q^{18} + ( 1 + 2 \beta_{2} + \beta_{3} - \beta_{7} + 2 \beta_{8} + \beta_{9} ) q^{19} + q^{20} + ( \beta_{1} + \beta_{4} - 3 \beta_{5} - 2 \beta_{6} - 3 \beta_{7} - \beta_{9} ) q^{21} + ( -1 + \beta_{3} - \beta_{4} + \beta_{6} - \beta_{8} ) q^{22} + ( -1 - \beta_{7} - \beta_{9} ) q^{24} + q^{25} + ( 1 + \beta_{1} + \beta_{3} - \beta_{6} + \beta_{7} - 2 \beta_{8} - \beta_{9} ) q^{26} + ( 2 - \beta_{2} + 2 \beta_{3} - 2 \beta_{4} - \beta_{6} + \beta_{7} + \beta_{8} + \beta_{9} ) q^{27} + ( -1 - \beta_{3} + \beta_{4} - \beta_{5} - \beta_{6} - \beta_{7} + \beta_{8} ) q^{28} + ( \beta_{1} + \beta_{2} - \beta_{3} + 2 \beta_{6} + \beta_{7} + 2 \beta_{8} + \beta_{9} ) q^{29} + ( -1 - \beta_{7} - \beta_{9} ) q^{30} + ( -2 - 3 \beta_{3} + \beta_{4} - 3 \beta_{5} - 2 \beta_{7} + 2 \beta_{8} ) q^{31} - q^{32} + ( 2 + \beta_{2} - 2 \beta_{5} - \beta_{6} - \beta_{7} + \beta_{8} + \beta_{9} ) q^{33} + ( 1 - \beta_{2} - \beta_{3} - \beta_{4} - \beta_{5} + \beta_{6} + \beta_{8} ) q^{34} + ( -1 - \beta_{3} + \beta_{4} - \beta_{5} - \beta_{6} - \beta_{7} + \beta_{8} ) q^{35} + ( 1 - \beta_{1} - \beta_{4} - \beta_{5} - \beta_{7} + 2 \beta_{8} + \beta_{9} ) q^{36} + ( 2 \beta_{1} - \beta_{2} + 3 \beta_{4} + 2 \beta_{7} - \beta_{8} - \beta_{9} ) q^{37} + ( -1 - 2 \beta_{2} - \beta_{3} + \beta_{7} - 2 \beta_{8} - \beta_{9} ) q^{38} + ( 4 + \beta_{2} + 5 \beta_{3} - \beta_{4} + 5 \beta_{5} + \beta_{6} + 3 \beta_{7} - 3 \beta_{8} + \beta_{9} ) q^{39} - q^{40} + ( 3 - 2 \beta_{1} - \beta_{2} + \beta_{4} + \beta_{5} - 2 \beta_{6} - \beta_{7} + \beta_{9} ) q^{41} + ( -\beta_{1} - \beta_{4} + 3 \beta_{5} + 2 \beta_{6} + 3 \beta_{7} + \beta_{9} ) q^{42} + ( 2 - 2 \beta_{1} + \beta_{3} - \beta_{4} + 5 \beta_{5} - \beta_{6} + 3 \beta_{7} - \beta_{8} + \beta_{9} ) q^{43} + ( 1 - \beta_{3} + \beta_{4} - \beta_{6} + \beta_{8} ) q^{44} + ( 1 - \beta_{1} - \beta_{4} - \beta_{5} - \beta_{7} + 2 \beta_{8} + \beta_{9} ) q^{45} + ( 1 - 3 \beta_{1} - 4 \beta_{3} - 3 \beta_{5} + 2 \beta_{6} - 2 \beta_{7} + \beta_{8} + \beta_{9} ) q^{47} + ( 1 + \beta_{7} + \beta_{9} ) q^{48} + ( 2 + \beta_{3} - 3 \beta_{4} + \beta_{6} + 4 \beta_{7} - 3 \beta_{8} + 2 \beta_{9} ) q^{49} - q^{50} + ( -4 - \beta_{1} - 5 \beta_{3} + 2 \beta_{4} - 2 \beta_{5} - 5 \beta_{7} + 2 \beta_{8} - 3 \beta_{9} ) q^{51} + ( -1 - \beta_{1} - \beta_{3} + \beta_{6} - \beta_{7} + 2 \beta_{8} + \beta_{9} ) q^{52} + ( -5 - 2 \beta_{3} + \beta_{6} + 2 \beta_{8} ) q^{53} + ( -2 + \beta_{2} - 2 \beta_{3} + 2 \beta_{4} + \beta_{6} - \beta_{7} - \beta_{8} - \beta_{9} ) q^{54} + ( 1 - \beta_{3} + \beta_{4} - \beta_{6} + \beta_{8} ) q^{55} + ( 1 + \beta_{3} - \beta_{4} + \beta_{5} + \beta_{6} + \beta_{7} - \beta_{8} ) q^{56} + ( 2 - \beta_{1} - \beta_{2} - 4 \beta_{3} - \beta_{4} + 3 \beta_{5} + \beta_{7} + 2 \beta_{8} + 3 \beta_{9} ) q^{57} + ( -\beta_{1} - \beta_{2} + \beta_{3} - 2 \beta_{6} - \beta_{7} - 2 \beta_{8} - \beta_{9} ) q^{58} + ( 2 - \beta_{1} - \beta_{2} + \beta_{3} - \beta_{4} - 2 \beta_{5} + \beta_{6} - 2 \beta_{7} + 4 \beta_{8} + \beta_{9} ) q^{59} + ( 1 + \beta_{7} + \beta_{9} ) q^{60} + ( 5 - 2 \beta_{1} - \beta_{2} + 4 \beta_{5} - \beta_{6} + 4 \beta_{7} - 3 \beta_{8} - 2 \beta_{9} ) q^{61} + ( 2 + 3 \beta_{3} - \beta_{4} + 3 \beta_{5} + 2 \beta_{7} - 2 \beta_{8} ) q^{62} + ( -1 + 4 \beta_{1} - 3 \beta_{2} - \beta_{3} + \beta_{4} - 7 \beta_{5} - 2 \beta_{6} - 2 \beta_{7} - 2 \beta_{8} - \beta_{9} ) q^{63} + q^{64} + ( -1 - \beta_{1} - \beta_{3} + \beta_{6} - \beta_{7} + 2 \beta_{8} + \beta_{9} ) q^{65} + ( -2 - \beta_{2} + 2 \beta_{5} + \beta_{6} + \beta_{7} - \beta_{8} - \beta_{9} ) q^{66} + ( -1 - \beta_{3} - \beta_{4} - \beta_{5} + 3 \beta_{6} + 2 \beta_{7} + \beta_{8} + 2 \beta_{9} ) q^{67} + ( -1 + \beta_{2} + \beta_{3} + \beta_{4} + \beta_{5} - \beta_{6} - \beta_{8} ) q^{68} + ( 1 + \beta_{3} - \beta_{4} + \beta_{5} + \beta_{6} + \beta_{7} - \beta_{8} ) q^{70} + ( 5 + \beta_{2} - 3 \beta_{3} - \beta_{4} - \beta_{5} + \beta_{6} + 3 \beta_{8} + 2 \beta_{9} ) q^{71} + ( -1 + \beta_{1} + \beta_{4} + \beta_{5} + \beta_{7} - 2 \beta_{8} - \beta_{9} ) q^{72} + ( 1 + \beta_{2} + 3 \beta_{3} + 3 \beta_{4} + \beta_{5} - 3 \beta_{6} + 2 \beta_{7} - \beta_{8} ) q^{73} + ( -2 \beta_{1} + \beta_{2} - 3 \beta_{4} - 2 \beta_{7} + \beta_{8} + \beta_{9} ) q^{74} + ( 1 + \beta_{7} + \beta_{9} ) q^{75} + ( 1 + 2 \beta_{2} + \beta_{3} - \beta_{7} + 2 \beta_{8} + \beta_{9} ) q^{76} + ( 6 + \beta_{1} - 2 \beta_{5} - \beta_{6} + \beta_{7} - 3 \beta_{8} ) q^{77} + ( -4 - \beta_{2} - 5 \beta_{3} + \beta_{4} - 5 \beta_{5} - \beta_{6} - 3 \beta_{7} + 3 \beta_{8} - \beta_{9} ) q^{78} + ( 5 - 2 \beta_{2} + 2 \beta_{3} + 2 \beta_{4} - 2 \beta_{6} - \beta_{7} - 4 \beta_{8} - 5 \beta_{9} ) q^{79} + q^{80} + ( 1 + 3 \beta_{1} - 2 \beta_{2} - \beta_{4} - 5 \beta_{5} - \beta_{6} + 4 \beta_{7} + 3 \beta_{8} + 2 \beta_{9} ) q^{81} + ( -3 + 2 \beta_{1} + \beta_{2} - \beta_{4} - \beta_{5} + 2 \beta_{6} + \beta_{7} - \beta_{9} ) q^{82} + ( -2 - \beta_{1} + 4 \beta_{3} + \beta_{4} - \beta_{5} + \beta_{7} + 2 \beta_{8} - \beta_{9} ) q^{83} + ( \beta_{1} + \beta_{4} - 3 \beta_{5} - 2 \beta_{6} - 3 \beta_{7} - \beta_{9} ) q^{84} + ( -1 + \beta_{2} + \beta_{3} + \beta_{4} + \beta_{5} - \beta_{6} - \beta_{8} ) q^{85} + ( -2 + 2 \beta_{1} - \beta_{3} + \beta_{4} - 5 \beta_{5} + \beta_{6} - 3 \beta_{7} + \beta_{8} - \beta_{9} ) q^{86} + ( 5 - \beta_{1} + \beta_{2} + 2 \beta_{3} - 3 \beta_{4} + 9 \beta_{5} + 2 \beta_{6} + 2 \beta_{7} - 2 \beta_{8} + 2 \beta_{9} ) q^{87} + ( -1 + \beta_{3} - \beta_{4} + \beta_{6} - \beta_{8} ) q^{88} + ( \beta_{1} - \beta_{2} + \beta_{3} + \beta_{4} - 2 \beta_{5} + \beta_{7} + 7 \beta_{8} ) q^{89} + ( -1 + \beta_{1} + \beta_{4} + \beta_{5} + \beta_{7} - 2 \beta_{8} - \beta_{9} ) q^{90} + ( -1 + 4 \beta_{1} + 3 \beta_{3} - 2 \beta_{4} + \beta_{5} + \beta_{6} - 7 \beta_{8} - 3 \beta_{9} ) q^{91} + ( 2 + 2 \beta_{1} + 3 \beta_{3} + \beta_{4} + \beta_{5} - 3 \beta_{6} - \beta_{7} - 5 \beta_{8} - \beta_{9} ) q^{93} + ( -1 + 3 \beta_{1} + 4 \beta_{3} + 3 \beta_{5} - 2 \beta_{6} + 2 \beta_{7} - \beta_{8} - \beta_{9} ) q^{94} + ( 1 + 2 \beta_{2} + \beta_{3} - \beta_{7} + 2 \beta_{8} + \beta_{9} ) q^{95} + ( -1 - \beta_{7} - \beta_{9} ) q^{96} + ( -5 - 3 \beta_{1} + \beta_{2} - 7 \beta_{3} - 4 \beta_{5} + 2 \beta_{6} - 4 \beta_{7} + 6 \beta_{8} ) q^{97} + ( -2 - \beta_{3} + 3 \beta_{4} - \beta_{6} - 4 \beta_{7} + 3 \beta_{8} - 2 \beta_{9} ) q^{98} + ( 1 - 2 \beta_{2} - \beta_{3} - 3 \beta_{4} - 4 \beta_{5} - \beta_{7} + 3 \beta_{9} ) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 10q^{2} + 4q^{3} + 10q^{4} + 10q^{5} - 4q^{6} - 7q^{7} - 10q^{8} + 14q^{9} + O(q^{10}) \) \( 10q - 10q^{2} + 4q^{3} + 10q^{4} + 10q^{5} - 4q^{6} - 7q^{7} - 10q^{8} + 14q^{9} - 10q^{10} + 9q^{11} + 4q^{12} - 7q^{13} + 7q^{14} + 4q^{15} + 10q^{16} - 18q^{17} - 14q^{18} + 16q^{19} + 10q^{20} + 12q^{21} - 9q^{22} - 4q^{24} + 10q^{25} + 7q^{26} + 13q^{27} - 7q^{28} + 10q^{29} - 4q^{30} - 3q^{31} - 10q^{32} + 25q^{33} + 18q^{34} - 7q^{35} + 14q^{36} - 8q^{37} - 16q^{38} + 12q^{39} - 10q^{40} + 10q^{41} - 12q^{42} - 9q^{43} + 9q^{44} + 14q^{45} + 21q^{47} + 4q^{48} + 7q^{49} - 10q^{50} - 9q^{51} - 7q^{52} - 40q^{53} - 13q^{54} + 9q^{55} + 7q^{56} + 9q^{57} - 10q^{58} + 29q^{59} + 4q^{60} + 25q^{61} + 3q^{62} + 6q^{63} + 10q^{64} - 7q^{65} - 25q^{66} - 7q^{67} - 18q^{68} + 7q^{70} + 64q^{71} - 14q^{72} - 16q^{73} + 8q^{74} + 4q^{75} + 16q^{76} + 57q^{77} - 12q^{78} + 44q^{79} + 10q^{80} + 14q^{81} - 10q^{82} - 26q^{83} + 12q^{84} - 18q^{85} + 9q^{86} + 25q^{87} - 9q^{88} + 11q^{89} - 14q^{90} + 5q^{93} - 21q^{94} + 16q^{95} - 4q^{96} - 10q^{97} - 7q^{98} + 13q^{99} + O(q^{100}) \)

Basis of coefficient ring in terms of a root \(\nu\) of \(x^{10} - 3 x^{9} - 15 x^{8} + 35 x^{7} + 78 x^{6} - 123 x^{5} - 185 x^{4} + 140 x^{3} + 177 x^{2} - 15 x - 23\):

\(\beta_{0}\)\(=\)\( 1 \)
\(\beta_{1}\)\(=\)\( \nu \)
\(\beta_{2}\)\(=\)\((\)\( -2208 \nu^{9} + 55689 \nu^{8} - 154322 \nu^{7} - 545688 \nu^{6} + 1652926 \nu^{5} + 1112130 \nu^{4} - 4082687 \nu^{3} - 414919 \nu^{2} + 2607844 \nu + 112859 \)\()/249061\)
\(\beta_{3}\)\(=\)\((\)\( 2856 \nu^{9} - 20596 \nu^{8} - 22377 \nu^{7} + 272686 \nu^{6} + 130597 \nu^{5} - 1043267 \nu^{4} - 753448 \nu^{3} + 1302822 \nu^{2} + 1088251 \nu - 121616 \)\()/249061\)
\(\beta_{4}\)\(=\)\((\)\( 5316 \nu^{9} - 48801 \nu^{8} + 49392 \nu^{7} + 490819 \nu^{6} - 814900 \nu^{5} - 1229230 \nu^{4} + 1739091 \nu^{3} + 1246670 \nu^{2} - 566508 \nu - 611472 \)\()/249061\)
\(\beta_{5}\)\(=\)\((\)\( 10640 \nu^{9} - 57196 \nu^{8} - 54064 \nu^{7} + 615438 \nu^{6} - 294830 \nu^{5} - 1796522 \nu^{4} + 1241499 \nu^{3} + 1557255 \nu^{2} - 770678 \nu - 33094 \)\()/249061\)
\(\beta_{6}\)\(=\)\((\)\( 12028 \nu^{9} - 20463 \nu^{8} - 172726 \nu^{7} + 92171 \nu^{6} + 691979 \nu^{5} + 225088 \nu^{4} - 902982 \nu^{3} - 582739 \nu^{2} - 170285 \nu - 65688 \)\()/249061\)
\(\beta_{7}\)\(=\)\((\)\( 12627 \nu^{9} - 46061 \nu^{8} - 160414 \nu^{7} + 567778 \nu^{6} + 587601 \nu^{5} - 2203788 \nu^{4} - 725436 \nu^{3} + 3018820 \nu^{2} + 372511 \nu - 824425 \)\()/249061\)
\(\beta_{8}\)\(=\)\((\)\( -12901 \nu^{9} + 31991 \nu^{8} + 165177 \nu^{7} - 229417 \nu^{6} - 607630 \nu^{5} + 79944 \nu^{4} + 932367 \nu^{3} + 835933 \nu^{2} - 454068 \nu - 202708 \)\()/249061\)
\(\beta_{9}\)\(=\)\((\)\( 38772 \nu^{9} - 183328 \nu^{8} - 319479 \nu^{7} + 2012874 \nu^{6} + 323569 \nu^{5} - 6049688 \nu^{4} + 420396 \nu^{3} + 5763096 \nu^{2} - 57994 \nu - 1146613 \)\()/249061\)
\(1\)\(=\)\(\beta_0\)
\(\nu\)\(=\)\(\beta_{1}\)
\(\nu^{2}\)\(=\)\(\beta_{9} + \beta_{8} - \beta_{7} - \beta_{5} + \beta_{4} - 2 \beta_{3} + \beta_{2} + \beta_{1} + 3\)
\(\nu^{3}\)\(=\)\(3 \beta_{9} + 5 \beta_{8} - 5 \beta_{7} + 2 \beta_{6} + \beta_{4} - 4 \beta_{3} + 3 \beta_{2} + 7 \beta_{1} + 1\)
\(\nu^{4}\)\(=\)\(15 \beta_{9} + 18 \beta_{8} - 22 \beta_{7} + 2 \beta_{6} - 4 \beta_{5} + 12 \beta_{4} - 27 \beta_{3} + 18 \beta_{2} + 15 \beta_{1} + 19\)
\(\nu^{5}\)\(=\)\(52 \beta_{9} + 82 \beta_{8} - 90 \beta_{7} + 27 \beta_{6} + 5 \beta_{5} + 29 \beta_{4} - 76 \beta_{3} + 62 \beta_{2} + 79 \beta_{1} + 22\)
\(\nu^{6}\)\(=\)\(221 \beta_{9} + 299 \beta_{8} - 359 \beta_{7} + 56 \beta_{6} - 3 \beta_{5} + 166 \beta_{4} - 378 \beta_{3} + 282 \beta_{2} + 239 \beta_{1} + 182\)
\(\nu^{7}\)\(=\)\(819 \beta_{9} + 1252 \beta_{8} - 1424 \beta_{7} + 361 \beta_{6} + 105 \beta_{5} + 535 \beta_{4} - 1272 \beta_{3} + 1038 \beta_{2} + 1081 \beta_{1} + 407\)
\(\nu^{8}\)\(=\)\(3324 \beta_{9} + 4738 \beta_{8} - 5602 \beta_{7} + 1058 \beta_{6} + 253 \beta_{5} + 2438 \beta_{4} - 5548 \beta_{3} + 4325 \beta_{2} + 3798 \beta_{1} + 2245\)
\(\nu^{9}\)\(=\)\(12724 \beta_{9} + 19118 \beta_{8} - 22063 \beta_{7} + 5135 \beta_{6} + 1700 \beta_{5} + 8789 \beta_{4} - 20328 \beta_{3} + 16473 \beta_{2} + 15916 \beta_{1} + 6874\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1
−1.41654
−0.414299
0.380178
1.49412
2.00869
3.92764
−2.60304
−1.58379
−0.973013
2.18006
−1.00000 −2.66797 1.00000 1.00000 2.66797 −1.17277 −1.00000 4.11808 −1.00000
1.2 −1.00000 −2.26320 1.00000 1.00000 2.26320 −0.287092 −1.00000 2.12206 −1.00000
1.3 −1.00000 −2.03928 1.00000 1.00000 2.03928 −3.23485 −1.00000 1.15865 −1.00000
1.4 −1.00000 −0.274376 1.00000 1.00000 0.274376 0.557477 −1.00000 −2.92472 −1.00000
1.5 −1.00000 0.259097 1.00000 1.00000 −0.259097 −4.66427 −1.00000 −2.93287 −1.00000
1.6 −1.00000 1.34421 1.00000 1.00000 −1.34421 0.948752 −1.00000 −1.19309 −1.00000
1.7 −1.00000 1.57173 1.00000 1.00000 −1.57173 3.09501 −1.00000 −0.529655 −1.00000
1.8 −1.00000 1.72956 1.00000 1.00000 −1.72956 −1.60312 −1.00000 −0.00863819 −1.00000
1.9 −1.00000 2.95688 1.00000 1.00000 −2.95688 −4.17692 −1.00000 5.74316 −1.00000
1.10 −1.00000 3.38334 1.00000 1.00000 −3.38334 3.53778 −1.00000 8.44702 −1.00000
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.10
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(5\) \(-1\)
\(23\) \(1\)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 5290.2.a.bj 10
23.b odd 2 1 5290.2.a.bi 10
23.c even 11 2 230.2.g.b 20
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
230.2.g.b 20 23.c even 11 2
5290.2.a.bi 10 23.b odd 2 1
5290.2.a.bj 10 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(5290))\):

\(T_{3}^{10} - \cdots\)
\(T_{7}^{10} + \cdots\)
\(T_{11}^{10} - \cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( ( 1 + T )^{10} \)
$3$ \( 32 - 48 T - 448 T^{2} + 604 T^{3} + 86 T^{4} - 343 T^{5} + 46 T^{6} + 65 T^{7} - 14 T^{8} - 4 T^{9} + T^{10} \)
$5$ \( ( -1 + T )^{10} \)
$7$ \( 197 + 447 T - 1262 T^{2} - 1255 T^{3} + 1142 T^{4} + 1076 T^{5} - 64 T^{6} - 166 T^{7} - 14 T^{8} + 7 T^{9} + T^{10} \)
$11$ \( 1541 - 3851 T - 3708 T^{2} + 4119 T^{3} + 1876 T^{4} - 1496 T^{5} - 212 T^{6} + 202 T^{7} - 4 T^{8} - 9 T^{9} + T^{10} \)
$13$ \( -115831 + 89393 T + 45059 T^{2} - 37797 T^{3} - 7614 T^{4} + 5619 T^{5} + 805 T^{6} - 342 T^{7} - 47 T^{8} + 7 T^{9} + T^{10} \)
$17$ \( -24608 - 47072 T + 15624 T^{2} + 51856 T^{3} + 16664 T^{4} - 4259 T^{5} - 2697 T^{6} - 201 T^{7} + 87 T^{8} + 18 T^{9} + T^{10} \)
$19$ \( 19823 + 48957 T - 140904 T^{2} - 4872 T^{3} + 65292 T^{4} - 13332 T^{5} - 3191 T^{6} + 933 T^{7} + 8 T^{8} - 16 T^{9} + T^{10} \)
$23$ \( T^{10} \)
$29$ \( 1992352 - 2160080 T + 112264 T^{2} + 409644 T^{3} - 50724 T^{4} - 29159 T^{5} + 3556 T^{6} + 906 T^{7} - 97 T^{8} - 10 T^{9} + T^{10} \)
$31$ \( 32 - 976 T + 5024 T^{2} + 6452 T^{3} - 6114 T^{4} - 941 T^{5} + 1252 T^{6} - 49 T^{7} - 63 T^{8} + 3 T^{9} + T^{10} \)
$37$ \( 2765929 - 330796 T - 2874944 T^{2} - 1013142 T^{3} + 131343 T^{4} + 96711 T^{5} + 6813 T^{6} - 1666 T^{7} - 178 T^{8} + 8 T^{9} + T^{10} \)
$41$ \( 42481 + 1261012 T + 2419465 T^{2} + 1101494 T^{3} - 103659 T^{4} - 95544 T^{5} + 7422 T^{6} + 1996 T^{7} - 181 T^{8} - 10 T^{9} + T^{10} \)
$43$ \( -154144 + 5789360 T - 45920 T^{2} - 1120972 T^{3} - 37394 T^{4} + 75847 T^{5} + 5317 T^{6} - 1913 T^{7} - 190 T^{8} + 9 T^{9} + T^{10} \)
$47$ \( 130098649 - 9202654 T - 38102297 T^{2} + 8039739 T^{3} + 1243129 T^{4} - 360930 T^{5} - 5893 T^{6} + 5031 T^{7} - 141 T^{8} - 21 T^{9} + T^{10} \)
$53$ \( -2729 + 14427 T + 95402 T^{2} + 181592 T^{3} + 171610 T^{4} + 92516 T^{5} + 29847 T^{6} + 5795 T^{7} + 658 T^{8} + 40 T^{9} + T^{10} \)
$59$ \( -5224207 - 13195353 T - 8216365 T^{2} + 528255 T^{3} + 1008138 T^{4} - 82049 T^{5} - 28681 T^{6} + 3574 T^{7} + 105 T^{8} - 29 T^{9} + T^{10} \)
$61$ \( 47470048 + 5616464 T - 35047352 T^{2} + 1382444 T^{3} + 3180740 T^{4} - 440717 T^{5} - 26542 T^{6} + 6613 T^{7} - 103 T^{8} - 25 T^{9} + T^{10} \)
$67$ \( -15690784 + 9010416 T + 2999896 T^{2} - 1533724 T^{3} - 296908 T^{4} + 68903 T^{5} + 11465 T^{6} - 1186 T^{7} - 182 T^{8} + 7 T^{9} + T^{10} \)
$71$ \( 9795424 + 4398096 T - 8103272 T^{2} + 614652 T^{3} + 1881072 T^{4} - 908479 T^{5} + 198591 T^{6} - 24251 T^{7} + 1701 T^{8} - 64 T^{9} + T^{10} \)
$73$ \( -29322976 + 18200736 T + 4409704 T^{2} - 3334252 T^{3} - 265566 T^{4} + 183045 T^{5} + 11969 T^{6} - 3183 T^{7} - 197 T^{8} + 16 T^{9} + T^{10} \)
$79$ \( -3014060576 + 492004656 T + 403907080 T^{2} - 141053000 T^{3} + 13153370 T^{4} + 681197 T^{5} - 193788 T^{6} + 8569 T^{7} + 412 T^{8} - 44 T^{9} + T^{10} \)
$83$ \( -400544 + 5244640 T - 1637120 T^{2} - 3620324 T^{3} + 559800 T^{4} + 217871 T^{5} - 13284 T^{6} - 4453 T^{7} - 24 T^{8} + 26 T^{9} + T^{10} \)
$89$ \( -143444653 - 20757187 T + 137507667 T^{2} + 28294519 T^{3} - 6334834 T^{4} - 648417 T^{5} + 91377 T^{6} + 4796 T^{7} - 517 T^{8} - 11 T^{9} + T^{10} \)
$97$ \( 16912928 + 28870624 T + 5110056 T^{2} - 5572168 T^{3} - 618984 T^{4} + 272619 T^{5} + 24414 T^{6} - 4069 T^{7} - 370 T^{8} + 10 T^{9} + T^{10} \)
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