Properties

Label 6027.2.a.bc
Level 6027
Weight 2
Character orbit 6027.a
Self dual Yes
Analytic conductor 48.126
Analytic rank 0
Dimension 8
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1258372982\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.8.7457527933.1
Coefficient ring: \(\Z[a_1, a_2]\)
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 \(1,\beta_1,\ldots,\beta_{7}\) for the coefficient ring described below. We also show the integral \(q\)-expansion of the trace form.

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

Basis of coefficient ring in terms of a root \(\nu\) of \(x^{8}\mathstrut -\mathstrut \) \(3\) \(x^{7}\mathstrut -\mathstrut \) \(6\) \(x^{6}\mathstrut +\mathstrut \) \(23\) \(x^{5}\mathstrut -\mathstrut \) \(4\) \(x^{4}\mathstrut -\mathstrut \) \(27\) \(x^{3}\mathstrut +\mathstrut \) \(8\) \(x^{2}\mathstrut +\mathstrut \) \(8\) \(x\mathstrut +\mathstrut \) \(1\):

\(\beta_{0}\)\(=\)\( 1 \)
\(\beta_{1}\)\(=\)\( \nu \)
\(\beta_{2}\)\(=\)\( \nu^{7} - 2 \nu^{6} - 7 \nu^{5} + 14 \nu^{4} + 3 \nu^{3} - 10 \nu^{2} + \nu \)
\(\beta_{3}\)\(=\)\( -\nu^{6} + 2 \nu^{5} + 8 \nu^{4} - 15 \nu^{3} - 10 \nu^{2} + 16 \nu + 3 \)
\(\beta_{4}\)\(=\)\( \nu^{6} - 2 \nu^{5} - 8 \nu^{4} + 15 \nu^{3} + 11 \nu^{2} - 16 \nu - 6 \)
\(\beta_{5}\)\(=\)\( -\nu^{7} + 2 \nu^{6} + 8 \nu^{5} - 15 \nu^{4} - 11 \nu^{3} + 16 \nu^{2} + 7 \nu - 1 \)
\(\beta_{6}\)\(=\)\( 2 \nu^{6} - 4 \nu^{5} - 15 \nu^{4} + 29 \nu^{3} + 14 \nu^{2} - 26 \nu - 6 \)
\(\beta_{7}\)\(=\)\( -3 \nu^{7} + 6 \nu^{6} + 23 \nu^{5} - 44 \nu^{4} - 24 \nu^{3} + 42 \nu^{2} + 8 \nu \)
\(1\)\(=\)\(\beta_0\)
\(\nu\)\(=\)\(\beta_{1}\)
\(\nu^{2}\)\(=\)\(\beta_{4}\mathstrut +\mathstrut \) \(\beta_{3}\mathstrut +\mathstrut \) \(3\)
\(\nu^{3}\)\(=\)\(\beta_{7}\mathstrut -\mathstrut \) \(2\) \(\beta_{5}\mathstrut +\mathstrut \) \(\beta_{2}\mathstrut +\mathstrut \) \(5\) \(\beta_{1}\mathstrut -\mathstrut \) \(2\)
\(\nu^{4}\)\(=\)\(\beta_{7}\mathstrut +\mathstrut \) \(\beta_{6}\mathstrut -\mathstrut \) \(2\) \(\beta_{5}\mathstrut +\mathstrut \) \(6\) \(\beta_{4}\mathstrut +\mathstrut \) \(8\) \(\beta_{3}\mathstrut +\mathstrut \) \(\beta_{2}\mathstrut -\mathstrut \) \(\beta_{1}\mathstrut +\mathstrut \) \(16\)
\(\nu^{5}\)\(=\)\(9\) \(\beta_{7}\mathstrut +\mathstrut \) \(\beta_{6}\mathstrut -\mathstrut \) \(17\) \(\beta_{5}\mathstrut +\mathstrut \) \(2\) \(\beta_{3}\mathstrut +\mathstrut \) \(10\) \(\beta_{2}\mathstrut +\mathstrut \) \(31\) \(\beta_{1}\mathstrut -\mathstrut \) \(17\)
\(\nu^{6}\)\(=\)\(11\) \(\beta_{7}\mathstrut +\mathstrut \) \(10\) \(\beta_{6}\mathstrut -\mathstrut \) \(20\) \(\beta_{5}\mathstrut +\mathstrut \) \(38\) \(\beta_{4}\mathstrut +\mathstrut \) \(57\) \(\beta_{3}\mathstrut +\mathstrut \) \(13\) \(\beta_{2}\mathstrut -\mathstrut \) \(5\) \(\beta_{1}\mathstrut +\mathstrut \) \(97\)
\(\nu^{7}\)\(=\)\(68\) \(\beta_{7}\mathstrut +\mathstrut \) \(13\) \(\beta_{6}\mathstrut -\mathstrut \) \(125\) \(\beta_{5}\mathstrut +\mathstrut \) \(2\) \(\beta_{4}\mathstrut +\mathstrut \) \(26\) \(\beta_{3}\mathstrut +\mathstrut \) \(80\) \(\beta_{2}\mathstrut +\mathstrut \) \(205\) \(\beta_{1}\mathstrut -\mathstrut \) \(113\)

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
2.70360
1.35554
1.21768
−0.978012
−0.169079
1.70821
−2.52358
−0.314356
−2.23115 1.00000 2.97801 −0.893036 −2.23115 0 −2.18209 1.00000 1.99249
1.2 −2.04183 1.00000 2.16908 3.68950 −2.04183 0 −0.345232 1.00000 −7.53333
1.3 −1.51387 1.00000 0.291794 −3.80505 −1.51387 0 2.58600 1.00000 5.76034
1.4 −1.13860 1.00000 −0.703600 2.27123 −1.13860 0 3.07831 1.00000 −2.58601
1.5 1.62618 1.00000 0.644462 1.67363 1.62618 0 −2.20435 1.00000 2.72162
1.6 1.66803 1.00000 0.782321 4.32429 1.66803 0 −2.03112 1.00000 7.21304
1.7 2.07710 1.00000 2.31436 −2.30039 2.07710 0 0.652949 1.00000 −4.77814
1.8 2.55413 1.00000 4.52358 2.03983 2.55413 0 6.44554 1.00000 5.20999
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.8
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(3\) \(-1\)
\(7\) \(-1\)
\(41\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6027))\):

\(T_{2}^{8} - \cdots\)
\(T_{5}^{8} - \cdots\)
\(T_{13}^{4} \) \(\mathstrut -\mathstrut 5 T_{13}^{3} \) \(\mathstrut -\mathstrut 10 T_{13}^{2} \) \(\mathstrut +\mathstrut 44 T_{13} \) \(\mathstrut +\mathstrut 49 \)