Properties

Label 4026.2.a.bc
Level 4026
Weight 2
Character orbit 4026.a
Self dual Yes
Analytic conductor 32.148
Analytic rank 0
Dimension 9
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1477718538\)
Analytic rank: \(0\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of a basis \(1,\beta_1,\ldots,\beta_{8}\) for the coefficient ring described below. We also show the integral \(q\)-expansion of the trace form.

\(f(q)\)  \(=\)  \( q\) \(+ q^{2}\) \(+ q^{3}\) \(+ q^{4}\) \( + ( 1 - \beta_{1} ) q^{5} \) \(+ q^{6}\) \( + ( 1 - \beta_{5} ) q^{7} \) \(+ q^{8}\) \(+ q^{9}\) \(+O(q^{10})\) \( q\) \(+ q^{2}\) \(+ q^{3}\) \(+ q^{4}\) \( + ( 1 - \beta_{1} ) q^{5} \) \(+ q^{6}\) \( + ( 1 - \beta_{5} ) q^{7} \) \(+ q^{8}\) \(+ q^{9}\) \( + ( 1 - \beta_{1} ) q^{10} \) \(+ q^{11}\) \(+ q^{12}\) \( + ( 1 + \beta_{2} ) q^{13} \) \( + ( 1 - \beta_{5} ) q^{14} \) \( + ( 1 - \beta_{1} ) q^{15} \) \(+ q^{16}\) \( + ( \beta_{4} - \beta_{5} + \beta_{6} ) q^{17} \) \(+ q^{18}\) \( + ( \beta_{1} - \beta_{2} - \beta_{3} - 2 \beta_{4} + \beta_{5} - \beta_{6} - \beta_{8} ) q^{19} \) \( + ( 1 - \beta_{1} ) q^{20} \) \( + ( 1 - \beta_{5} ) q^{21} \) \(+ q^{22}\) \( + ( \beta_{1} + \beta_{3} + \beta_{5} ) q^{23} \) \(+ q^{24}\) \( + ( 3 - \beta_{1} + \beta_{4} + \beta_{7} + \beta_{8} ) q^{25} \) \( + ( 1 + \beta_{2} ) q^{26} \) \(+ q^{27}\) \( + ( 1 - \beta_{5} ) q^{28} \) \( + ( -2 + \beta_{1} - \beta_{2} - \beta_{3} - 2 \beta_{4} + \beta_{5} - \beta_{8} ) q^{29} \) \( + ( 1 - \beta_{1} ) q^{30} \) \( + ( 3 + \beta_{3} + \beta_{5} ) q^{31} \) \(+ q^{32}\) \(+ q^{33}\) \( + ( \beta_{4} - \beta_{5} + \beta_{6} ) q^{34} \) \( + ( 1 - 3 \beta_{1} + \beta_{2} + 2 \beta_{3} + 4 \beta_{4} - 3 \beta_{5} + \beta_{6} - \beta_{7} + \beta_{8} ) q^{35} \) \(+ q^{36}\) \( + ( 2 + \beta_{1} - \beta_{3} - \beta_{4} + \beta_{5} - \beta_{6} + \beta_{8} ) q^{37} \) \( + ( \beta_{1} - \beta_{2} - \beta_{3} - 2 \beta_{4} + \beta_{5} - \beta_{6} - \beta_{8} ) q^{38} \) \( + ( 1 + \beta_{2} ) q^{39} \) \( + ( 1 - \beta_{1} ) q^{40} \) \( + ( -2 \beta_{2} - \beta_{3} - \beta_{4} + \beta_{6} - \beta_{8} ) q^{41} \) \( + ( 1 - \beta_{5} ) q^{42} \) \( + ( 1 - \beta_{1} + 2 \beta_{2} + \beta_{3} + \beta_{4} - \beta_{6} - 2 \beta_{7} + \beta_{8} ) q^{43} \) \(+ q^{44}\) \( + ( 1 - \beta_{1} ) q^{45} \) \( + ( \beta_{1} + \beta_{3} + \beta_{5} ) q^{46} \) \( + ( 1 + \beta_{1} - \beta_{3} + \beta_{5} + \beta_{8} ) q^{47} \) \(+ q^{48}\) \( + ( 3 - \beta_{2} - \beta_{3} - \beta_{6} + \beta_{7} ) q^{49} \) \( + ( 3 - \beta_{1} + \beta_{4} + \beta_{7} + \beta_{8} ) q^{50} \) \( + ( \beta_{4} - \beta_{5} + \beta_{6} ) q^{51} \) \( + ( 1 + \beta_{2} ) q^{52} \) \( + ( -2 \beta_{1} + \beta_{2} + \beta_{3} + 2 \beta_{4} - \beta_{6} - \beta_{7} ) q^{53} \) \(+ q^{54}\) \( + ( 1 - \beta_{1} ) q^{55} \) \( + ( 1 - \beta_{5} ) q^{56} \) \( + ( \beta_{1} - \beta_{2} - \beta_{3} - 2 \beta_{4} + \beta_{5} - \beta_{6} - \beta_{8} ) q^{57} \) \( + ( -2 + \beta_{1} - \beta_{2} - \beta_{3} - 2 \beta_{4} + \beta_{5} - \beta_{8} ) q^{58} \) \( + ( 1 + \beta_{3} + \beta_{4} + \beta_{7} + \beta_{8} ) q^{59} \) \( + ( 1 - \beta_{1} ) q^{60} \) \(- q^{61}\) \( + ( 3 + \beta_{3} + \beta_{5} ) q^{62} \) \( + ( 1 - \beta_{5} ) q^{63} \) \(+ q^{64}\) \( + ( -1 + 2 \beta_{2} - 2 \beta_{4} + 2 \beta_{5} - \beta_{7} ) q^{65} \) \(+ q^{66}\) \( + ( -1 + 2 \beta_{1} - \beta_{2} - \beta_{4} - \beta_{8} ) q^{67} \) \( + ( \beta_{4} - \beta_{5} + \beta_{6} ) q^{68} \) \( + ( \beta_{1} + \beta_{3} + \beta_{5} ) q^{69} \) \( + ( 1 - 3 \beta_{1} + \beta_{2} + 2 \beta_{3} + 4 \beta_{4} - 3 \beta_{5} + \beta_{6} - \beta_{7} + \beta_{8} ) q^{70} \) \( + ( 2 + \beta_{1} - 2 \beta_{2} + 2 \beta_{5} + \beta_{7} ) q^{71} \) \(+ q^{72}\) \( + ( 1 + 2 \beta_{1} - \beta_{2} + \beta_{5} + \beta_{6} - \beta_{8} ) q^{73} \) \( + ( 2 + \beta_{1} - \beta_{3} - \beta_{4} + \beta_{5} - \beta_{6} + \beta_{8} ) q^{74} \) \( + ( 3 - \beta_{1} + \beta_{4} + \beta_{7} + \beta_{8} ) q^{75} \) \( + ( \beta_{1} - \beta_{2} - \beta_{3} - 2 \beta_{4} + \beta_{5} - \beta_{6} - \beta_{8} ) q^{76} \) \( + ( 1 - \beta_{5} ) q^{77} \) \( + ( 1 + \beta_{2} ) q^{78} \) \( + ( \beta_{1} + \beta_{3} + \beta_{4} - 2 \beta_{5} + 3 \beta_{6} ) q^{79} \) \( + ( 1 - \beta_{1} ) q^{80} \) \(+ q^{81}\) \( + ( -2 \beta_{2} - \beta_{3} - \beta_{4} + \beta_{6} - \beta_{8} ) q^{82} \) \( + ( 3 + 2 \beta_{1} + \beta_{2} - 2 \beta_{4} + \beta_{5} - \beta_{6} + \beta_{8} ) q^{83} \) \( + ( 1 - \beta_{5} ) q^{84} \) \( + ( -2 - \beta_{2} - \beta_{3} + \beta_{4} - 3 \beta_{5} + 2 \beta_{6} + \beta_{7} ) q^{85} \) \( + ( 1 - \beta_{1} + 2 \beta_{2} + \beta_{3} + \beta_{4} - \beta_{6} - 2 \beta_{7} + \beta_{8} ) q^{86} \) \( + ( -2 + \beta_{1} - \beta_{2} - \beta_{3} - 2 \beta_{4} + \beta_{5} - \beta_{8} ) q^{87} \) \(+ q^{88}\) \( + ( 1 + \beta_{1} - 2 \beta_{2} + \beta_{5} + \beta_{6} + \beta_{7} ) q^{89} \) \( + ( 1 - \beta_{1} ) q^{90} \) \( + ( -3 + 3 \beta_{1} - \beta_{3} - 3 \beta_{4} + \beta_{5} - \beta_{6} - 2 \beta_{8} ) q^{91} \) \( + ( \beta_{1} + \beta_{3} + \beta_{5} ) q^{92} \) \( + ( 3 + \beta_{3} + \beta_{5} ) q^{93} \) \( + ( 1 + \beta_{1} - \beta_{3} + \beta_{5} + \beta_{8} ) q^{94} \) \( + ( -2 + \beta_{1} - \beta_{2} - \beta_{4} + 4 \beta_{5} - 2 \beta_{6} - \beta_{7} - 2 \beta_{8} ) q^{95} \) \(+ q^{96}\) \( + ( 1 + 3 \beta_{2} + \beta_{3} + 2 \beta_{4} + \beta_{7} + \beta_{8} ) q^{97} \) \( + ( 3 - \beta_{2} - \beta_{3} - \beta_{6} + \beta_{7} ) q^{98} \) \(+ q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)  \(=\)  \(9q \) \(\mathstrut +\mathstrut 9q^{2} \) \(\mathstrut +\mathstrut 9q^{3} \) \(\mathstrut +\mathstrut 9q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(9q \) \(\mathstrut +\mathstrut 9q^{2} \) \(\mathstrut +\mathstrut 9q^{3} \) \(\mathstrut +\mathstrut 9q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut 8q^{10} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut +\mathstrut 9q^{12} \) \(\mathstrut +\mathstrut 8q^{13} \) \(\mathstrut +\mathstrut 9q^{14} \) \(\mathstrut +\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 9q^{16} \) \(\mathstrut +\mathstrut q^{17} \) \(\mathstrut +\mathstrut 9q^{18} \) \(\mathstrut +\mathstrut 5q^{19} \) \(\mathstrut +\mathstrut 8q^{20} \) \(\mathstrut +\mathstrut 9q^{21} \) \(\mathstrut +\mathstrut 9q^{22} \) \(\mathstrut -\mathstrut q^{23} \) \(\mathstrut +\mathstrut 9q^{24} \) \(\mathstrut +\mathstrut 23q^{25} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut +\mathstrut 9q^{27} \) \(\mathstrut +\mathstrut 9q^{28} \) \(\mathstrut -\mathstrut 14q^{29} \) \(\mathstrut +\mathstrut 8q^{30} \) \(\mathstrut +\mathstrut 25q^{31} \) \(\mathstrut +\mathstrut 9q^{32} \) \(\mathstrut +\mathstrut 9q^{33} \) \(\mathstrut +\mathstrut q^{34} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 9q^{36} \) \(\mathstrut +\mathstrut 16q^{37} \) \(\mathstrut +\mathstrut 5q^{38} \) \(\mathstrut +\mathstrut 8q^{39} \) \(\mathstrut +\mathstrut 8q^{40} \) \(\mathstrut +\mathstrut 5q^{41} \) \(\mathstrut +\mathstrut 9q^{42} \) \(\mathstrut +\mathstrut 5q^{43} \) \(\mathstrut +\mathstrut 9q^{44} \) \(\mathstrut +\mathstrut 8q^{45} \) \(\mathstrut -\mathstrut q^{46} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 9q^{48} \) \(\mathstrut +\mathstrut 30q^{49} \) \(\mathstrut +\mathstrut 23q^{50} \) \(\mathstrut +\mathstrut q^{51} \) \(\mathstrut +\mathstrut 8q^{52} \) \(\mathstrut +\mathstrut q^{53} \) \(\mathstrut +\mathstrut 9q^{54} \) \(\mathstrut +\mathstrut 8q^{55} \) \(\mathstrut +\mathstrut 9q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 4q^{59} \) \(\mathstrut +\mathstrut 8q^{60} \) \(\mathstrut -\mathstrut 9q^{61} \) \(\mathstrut +\mathstrut 25q^{62} \) \(\mathstrut +\mathstrut 9q^{63} \) \(\mathstrut +\mathstrut 9q^{64} \) \(\mathstrut -\mathstrut 14q^{65} \) \(\mathstrut +\mathstrut 9q^{66} \) \(\mathstrut -\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut q^{68} \) \(\mathstrut -\mathstrut q^{69} \) \(\mathstrut +\mathstrut 5q^{70} \) \(\mathstrut +\mathstrut 20q^{71} \) \(\mathstrut +\mathstrut 9q^{72} \) \(\mathstrut +\mathstrut 15q^{73} \) \(\mathstrut +\mathstrut 16q^{74} \) \(\mathstrut +\mathstrut 23q^{75} \) \(\mathstrut +\mathstrut 5q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 8q^{78} \) \(\mathstrut -\mathstrut 2q^{79} \) \(\mathstrut +\mathstrut 8q^{80} \) \(\mathstrut +\mathstrut 9q^{81} \) \(\mathstrut +\mathstrut 5q^{82} \) \(\mathstrut +\mathstrut 21q^{83} \) \(\mathstrut +\mathstrut 9q^{84} \) \(\mathstrut -\mathstrut 16q^{85} \) \(\mathstrut +\mathstrut 5q^{86} \) \(\mathstrut -\mathstrut 14q^{87} \) \(\mathstrut +\mathstrut 9q^{88} \) \(\mathstrut +\mathstrut 10q^{89} \) \(\mathstrut +\mathstrut 8q^{90} \) \(\mathstrut -\mathstrut 19q^{91} \) \(\mathstrut -\mathstrut q^{92} \) \(\mathstrut +\mathstrut 25q^{93} \) \(\mathstrut +\mathstrut 8q^{94} \) \(\mathstrut -\mathstrut 7q^{95} \) \(\mathstrut +\mathstrut 9q^{96} \) \(\mathstrut +\mathstrut 3q^{97} \) \(\mathstrut +\mathstrut 30q^{98} \) \(\mathstrut +\mathstrut 9q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Basis of coefficient ring in terms of a root \(\nu\) of \(x^{9}\mathstrut -\mathstrut \) \(x^{8}\mathstrut -\mathstrut \) \(30\) \(x^{7}\mathstrut +\mathstrut \) \(7\) \(x^{6}\mathstrut +\mathstrut \) \(284\) \(x^{5}\mathstrut +\mathstrut \) \(100\) \(x^{4}\mathstrut -\mathstrut \) \(777\) \(x^{3}\mathstrut -\mathstrut \) \(250\) \(x^{2}\mathstrut +\mathstrut \) \(574\) \(x\mathstrut -\mathstrut \) \(68\):

\(\beta_{0}\)\(=\)\( 1 \)
\(\beta_{1}\)\(=\)\( \nu \)
\(\beta_{2}\)\(=\)\((\)\( -99 \nu^{8} + 4436 \nu^{7} - 16215 \nu^{6} - 80028 \nu^{5} + 306876 \nu^{4} + 435761 \nu^{3} - 1379713 \nu^{2} - 800938 \nu + 1137130 \)\()/200458\)
\(\beta_{3}\)\(=\)\((\)\( -2961 \nu^{8} + 23336 \nu^{7} + 52616 \nu^{6} - 580331 \nu^{5} - 270479 \nu^{4} + 4358851 \nu^{3} + 711766 \nu^{2} - 8100922 \nu + 1153636 \)\()/400916\)
\(\beta_{4}\)\(=\)\((\)\( 3436 \nu^{8} - 13235 \nu^{7} - 78083 \nu^{6} + 253589 \nu^{5} + 562732 \nu^{4} - 1261001 \nu^{3} - 1100874 \nu^{2} + 1724498 \nu - 168584 \)\()/200458\)
\(\beta_{5}\)\(=\)\((\)\( 7105 \nu^{8} - 16662 \nu^{7} - 187860 \nu^{6} + 285499 \nu^{5} + 1499665 \nu^{4} - 976049 \nu^{3} - 2600248 \nu^{2} + 1017098 \nu - 403440 \)\()/400916\)
\(\beta_{6}\)\(=\)\((\)\( 8041 \nu^{8} - 3932 \nu^{7} - 253236 \nu^{6} - 14833 \nu^{5} + 2370547 \nu^{4} + 1045333 \nu^{3} - 5282530 \nu^{2} - 1141722 \nu + 1565484 \)\()/400916\)
\(\beta_{7}\)\(=\)\((\)\( 4471 \nu^{8} - 4941 \nu^{7} - 127244 \nu^{6} + 33285 \nu^{5} + 1126738 \nu^{4} + 525078 \nu^{3} - 2603901 \nu^{2} - 1838422 \nu + 663210 \)\()/200458\)
\(\beta_{8}\)\(=\)\((\)\( -7907 \nu^{8} + 18176 \nu^{7} + 205327 \nu^{6} - 286874 \nu^{5} - 1689470 \nu^{4} + 735923 \nu^{3} + 3905233 \nu^{2} - 86534 \nu - 1897832 \)\()/200458\)
\(1\)\(=\)\(\beta_0\)
\(\nu\)\(=\)\(\beta_{1}\)
\(\nu^{2}\)\(=\)\(\beta_{8}\mathstrut +\mathstrut \) \(\beta_{7}\mathstrut +\mathstrut \) \(\beta_{4}\mathstrut +\mathstrut \) \(\beta_{1}\mathstrut +\mathstrut \) \(7\)
\(\nu^{3}\)\(=\)\(\beta_{8}\mathstrut +\mathstrut \) \(2\) \(\beta_{7}\mathstrut -\mathstrut \) \(2\) \(\beta_{6}\mathstrut +\mathstrut \) \(2\) \(\beta_{5}\mathstrut +\mathstrut \) \(\beta_{2}\mathstrut +\mathstrut \) \(12\) \(\beta_{1}\mathstrut +\mathstrut \) \(7\)
\(\nu^{4}\)\(=\)\(14\) \(\beta_{8}\mathstrut +\mathstrut \) \(17\) \(\beta_{7}\mathstrut -\mathstrut \) \(\beta_{6}\mathstrut -\mathstrut \) \(4\) \(\beta_{5}\mathstrut +\mathstrut \) \(15\) \(\beta_{4}\mathstrut -\mathstrut \) \(\beta_{3}\mathstrut +\mathstrut \) \(\beta_{2}\mathstrut +\mathstrut \) \(24\) \(\beta_{1}\mathstrut +\mathstrut \) \(86\)
\(\nu^{5}\)\(=\)\(23\) \(\beta_{8}\mathstrut +\mathstrut \) \(48\) \(\beta_{7}\mathstrut -\mathstrut \) \(36\) \(\beta_{6}\mathstrut +\mathstrut \) \(33\) \(\beta_{5}\mathstrut -\mathstrut \) \(5\) \(\beta_{4}\mathstrut -\mathstrut \) \(9\) \(\beta_{3}\mathstrut +\mathstrut \) \(14\) \(\beta_{2}\mathstrut +\mathstrut \) \(181\) \(\beta_{1}\mathstrut +\mathstrut \) \(175\)
\(\nu^{6}\)\(=\)\(194\) \(\beta_{8}\mathstrut +\mathstrut \) \(290\) \(\beta_{7}\mathstrut -\mathstrut \) \(47\) \(\beta_{6}\mathstrut -\mathstrut \) \(57\) \(\beta_{5}\mathstrut +\mathstrut \) \(165\) \(\beta_{4}\mathstrut -\mathstrut \) \(42\) \(\beta_{3}\mathstrut +\mathstrut \) \(3\) \(\beta_{2}\mathstrut +\mathstrut \) \(498\) \(\beta_{1}\mathstrut +\mathstrut \) \(1246\)
\(\nu^{7}\)\(=\)\(430\) \(\beta_{8}\mathstrut +\mathstrut \) \(978\) \(\beta_{7}\mathstrut -\mathstrut \) \(583\) \(\beta_{6}\mathstrut +\mathstrut \) \(454\) \(\beta_{5}\mathstrut -\mathstrut \) \(184\) \(\beta_{4}\mathstrut -\mathstrut \) \(273\) \(\beta_{3}\mathstrut +\mathstrut \) \(136\) \(\beta_{2}\mathstrut +\mathstrut \) \(2953\) \(\beta_{1}\mathstrut +\mathstrut \) \(3428\)
\(\nu^{8}\)\(=\)\(2762\) \(\beta_{8}\mathstrut +\mathstrut \) \(5085\) \(\beta_{7}\mathstrut -\mathstrut \) \(1227\) \(\beta_{6}\mathstrut -\mathstrut \) \(593\) \(\beta_{5}\mathstrut +\mathstrut \) \(1332\) \(\beta_{4}\mathstrut -\mathstrut \) \(1178\) \(\beta_{3}\mathstrut -\mathstrut \) \(238\) \(\beta_{2}\mathstrut +\mathstrut \) \(9625\) \(\beta_{1}\mathstrut +\mathstrut \) \(19380\)

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
4.23292
3.88536
1.60053
0.731055
0.128459
−1.48002
−2.09192
−2.63661
−3.36977
1.00000 1.00000 1.00000 −3.23292 1.00000 4.29240 1.00000 1.00000 −3.23292
1.2 1.00000 1.00000 1.00000 −2.88536 1.00000 −2.96592 1.00000 1.00000 −2.88536
1.3 1.00000 1.00000 1.00000 −0.600528 1.00000 0.748033 1.00000 1.00000 −0.600528
1.4 1.00000 1.00000 1.00000 0.268945 1.00000 3.42672 1.00000 1.00000 0.268945
1.5 1.00000 1.00000 1.00000 0.871541 1.00000 1.79155 1.00000 1.00000 0.871541
1.6 1.00000 1.00000 1.00000 2.48002 1.00000 3.05465 1.00000 1.00000 2.48002
1.7 1.00000 1.00000 1.00000 3.09192 1.00000 −4.21340 1.00000 1.00000 3.09192
1.8 1.00000 1.00000 1.00000 3.63661 1.00000 −1.65542 1.00000 1.00000 3.63661
1.9 1.00000 1.00000 1.00000 4.36977 1.00000 4.52139 1.00000 1.00000 4.36977
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.9
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(-1\)
\(11\) \(-1\)
\(61\) \(1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4026))\):

\(T_{5}^{9} - \cdots\)
\(T_{7}^{9} - \cdots\)
\(T_{13}^{9} - \cdots\)