Properties

Label 6018.2.a.x
Level 6018
Weight 2
Character orbit 6018.a
Self dual Yes
Analytic conductor 48.054
Analytic rank 0
Dimension 10
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0539719364\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
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.

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

Basis of coefficient ring in terms of a root \(\nu\) of \(x^{10}\mathstrut -\mathstrut \) \(x^{9}\mathstrut -\mathstrut \) \(34\) \(x^{8}\mathstrut +\mathstrut \) \(30\) \(x^{7}\mathstrut +\mathstrut \) \(341\) \(x^{6}\mathstrut -\mathstrut \) \(276\) \(x^{5}\mathstrut -\mathstrut \) \(1032\) \(x^{4}\mathstrut +\mathstrut \) \(1176\) \(x^{3}\mathstrut +\mathstrut \) \(416\) \(x^{2}\mathstrut -\mathstrut \) \(896\) \(x\mathstrut +\mathstrut \) \(272\):

\(\beta_{0}\)\(=\)\( 1 \)
\(\beta_{1}\)\(=\)\( \nu \)
\(\beta_{2}\)\(=\)\((\)\( 158 \nu^{9} + 225 \nu^{8} - 4779 \nu^{7} - 5750 \nu^{6} + 32040 \nu^{5} + 12263 \nu^{4} + 67732 \nu^{3} + 300692 \nu^{2} - 399092 \nu - 66416 \)\()/120304\)
\(\beta_{3}\)\(=\)\((\)\( 1042 \nu^{9} - 3275 \nu^{8} - 35705 \nu^{7} + 105416 \nu^{6} + 375768 \nu^{5} - 987205 \nu^{4} - 1375194 \nu^{3} + 2975172 \nu^{2} + 843124 \nu - 1593080 \)\()/120304\)
\(\beta_{4}\)\(=\)\((\)\( 5903 \nu^{9} - 5918 \nu^{8} - 207243 \nu^{7} + 177972 \nu^{6} + 2223525 \nu^{5} - 1593723 \nu^{4} - 7953632 \nu^{3} + 6020464 \nu^{2} + 6322324 \nu - 4079568 \)\()/120304\)
\(\beta_{5}\)\(=\)\((\)\( 11493 \nu^{9} - 1955 \nu^{8} - 393074 \nu^{7} + 21556 \nu^{6} + 3954805 \nu^{5} + 26618 \nu^{4} - 11927502 \nu^{3} + 4205884 \nu^{2} + 8148160 \nu - 4432912 \)\()/60152\)
\(\beta_{6}\)\(=\)\((\)\( -24821 \nu^{9} + 10767 \nu^{8} + 848932 \nu^{7} - 255106 \nu^{6} - 8588857 \nu^{5} + 1739438 \nu^{4} + 26641132 \nu^{3} - 12453916 \nu^{2} - 18090136 \nu + 10265344 \)\()/120304\)
\(\beta_{7}\)\(=\)\((\)\( 20873 \nu^{9} - 4492 \nu^{8} - 711529 \nu^{7} + 62998 \nu^{6} + 7121451 \nu^{5} - 52371 \nu^{4} - 21305118 \nu^{3} + 7212112 \nu^{2} + 14231612 \nu - 7071528 \)\()/60152\)
\(\beta_{8}\)\(=\)\((\)\( -73925 \nu^{9} + 15269 \nu^{8} + 2527192 \nu^{7} - 221448 \nu^{6} - 25415913 \nu^{5} + 470848 \nu^{4} + 76622382 \nu^{3} - 27434996 \nu^{2} - 51134312 \nu + 26070664 \)\()/120304\)
\(\beta_{9}\)\(=\)\((\)\( 89793 \nu^{9} - 16752 \nu^{8} - 3064731 \nu^{7} + 197524 \nu^{6} + 30729695 \nu^{5} + 289317 \nu^{4} - 92137756 \nu^{3} + 30417112 \nu^{2} + 62114404 \nu - 30442128 \)\()/120304\)
\(1\)\(=\)\(\beta_0\)
\(\nu\)\(=\)\(\beta_{1}\)
\(\nu^{2}\)\(=\)\(-\)\(\beta_{7}\mathstrut -\mathstrut \) \(\beta_{6}\mathstrut +\mathstrut \) \(\beta_{5}\mathstrut -\mathstrut \) \(\beta_{4}\mathstrut -\mathstrut \) \(\beta_{2}\mathstrut +\mathstrut \) \(7\)
\(\nu^{3}\)\(=\)\(-\)\(2\) \(\beta_{9}\mathstrut -\mathstrut \) \(\beta_{8}\mathstrut +\mathstrut \) \(\beta_{7}\mathstrut -\mathstrut \) \(2\) \(\beta_{6}\mathstrut +\mathstrut \) \(\beta_{5}\mathstrut -\mathstrut \) \(\beta_{4}\mathstrut -\mathstrut \) \(3\) \(\beta_{3}\mathstrut +\mathstrut \) \(2\) \(\beta_{2}\mathstrut +\mathstrut \) \(15\) \(\beta_{1}\)
\(\nu^{4}\)\(=\)\(6\) \(\beta_{9}\mathstrut -\mathstrut \) \(30\) \(\beta_{7}\mathstrut -\mathstrut \) \(22\) \(\beta_{6}\mathstrut +\mathstrut \) \(13\) \(\beta_{5}\mathstrut -\mathstrut \) \(22\) \(\beta_{4}\mathstrut +\mathstrut \) \(2\) \(\beta_{3}\mathstrut -\mathstrut \) \(22\) \(\beta_{2}\mathstrut +\mathstrut \) \(95\)
\(\nu^{5}\)\(=\)\(-\)\(38\) \(\beta_{9}\mathstrut -\mathstrut \) \(12\) \(\beta_{8}\mathstrut +\mathstrut \) \(26\) \(\beta_{7}\mathstrut -\mathstrut \) \(41\) \(\beta_{6}\mathstrut +\mathstrut \) \(24\) \(\beta_{5}\mathstrut -\mathstrut \) \(11\) \(\beta_{4}\mathstrut -\mathstrut \) \(72\) \(\beta_{3}\mathstrut +\mathstrut \) \(65\) \(\beta_{2}\mathstrut +\mathstrut \) \(250\) \(\beta_{1}\mathstrut +\mathstrut \) \(18\)
\(\nu^{6}\)\(=\)\(177\) \(\beta_{9}\mathstrut +\mathstrut \) \(11\) \(\beta_{8}\mathstrut -\mathstrut \) \(659\) \(\beta_{7}\mathstrut -\mathstrut \) \(426\) \(\beta_{6}\mathstrut +\mathstrut \) \(189\) \(\beta_{5}\mathstrut -\mathstrut \) \(422\) \(\beta_{4}\mathstrut +\mathstrut \) \(63\) \(\beta_{3}\mathstrut -\mathstrut \) \(394\) \(\beta_{2}\mathstrut -\mathstrut \) \(27\) \(\beta_{1}\mathstrut +\mathstrut \) \(1517\)
\(\nu^{7}\)\(=\)\(-\)\(625\) \(\beta_{9}\mathstrut -\mathstrut \) \(112\) \(\beta_{8}\mathstrut +\mathstrut \) \(472\) \(\beta_{7}\mathstrut -\mathstrut \) \(790\) \(\beta_{6}\mathstrut +\mathstrut \) \(458\) \(\beta_{5}\mathstrut -\mathstrut \) \(127\) \(\beta_{4}\mathstrut -\mathstrut \) \(1430\) \(\beta_{3}\mathstrut +\mathstrut \) \(1522\) \(\beta_{2}\mathstrut +\mathstrut \) \(4330\) \(\beta_{1}\mathstrut +\mathstrut \) \(367\)
\(\nu^{8}\)\(=\)\(3987\) \(\beta_{9}\mathstrut +\mathstrut \) \(398\) \(\beta_{8}\mathstrut -\mathstrut \) \(13224\) \(\beta_{7}\mathstrut -\mathstrut \) \(8058\) \(\beta_{6}\mathstrut +\mathstrut \) \(3027\) \(\beta_{5}\mathstrut -\mathstrut \) \(7867\) \(\beta_{4}\mathstrut +\mathstrut \) \(1342\) \(\beta_{3}\mathstrut -\mathstrut \) \(6830\) \(\beta_{2}\mathstrut -\mathstrut \) \(996\) \(\beta_{1}\mathstrut +\mathstrut \) \(25886\)
\(\nu^{9}\)\(=\)\(-\)\(10043\) \(\beta_{9}\mathstrut -\mathstrut \) \(692\) \(\beta_{8}\mathstrut +\mathstrut \) \(7656\) \(\beta_{7}\mathstrut -\mathstrut \) \(15141\) \(\beta_{6}\mathstrut +\mathstrut \) \(8213\) \(\beta_{5}\mathstrut -\mathstrut \) \(1726\) \(\beta_{4}\mathstrut -\mathstrut \) \(27140\) \(\beta_{3}\mathstrut +\mathstrut \) \(31757\) \(\beta_{2}\mathstrut +\mathstrut \) \(76804\) \(\beta_{1}\mathstrut +\mathstrut \) \(5520\)

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
−4.29748
−2.78078
−2.54849
−0.976160
0.580342
0.780661
0.931948
1.39621
3.58712
4.32662
−1.00000 −1.00000 1.00000 −4.29748 1.00000 0.914984 −1.00000 1.00000 4.29748
1.2 −1.00000 −1.00000 1.00000 −2.78078 1.00000 3.42043 −1.00000 1.00000 2.78078
1.3 −1.00000 −1.00000 1.00000 −2.54849 1.00000 4.63796 −1.00000 1.00000 2.54849
1.4 −1.00000 −1.00000 1.00000 −0.976160 1.00000 −3.87477 −1.00000 1.00000 0.976160
1.5 −1.00000 −1.00000 1.00000 0.580342 1.00000 4.77865 −1.00000 1.00000 −0.580342
1.6 −1.00000 −1.00000 1.00000 0.780661 1.00000 1.13694 −1.00000 1.00000 −0.780661
1.7 −1.00000 −1.00000 1.00000 0.931948 1.00000 −0.903548 −1.00000 1.00000 −0.931948
1.8 −1.00000 −1.00000 1.00000 1.39621 1.00000 −1.23174 −1.00000 1.00000 −1.39621
1.9 −1.00000 −1.00000 1.00000 3.58712 1.00000 −2.07087 −1.00000 1.00000 −3.58712
1.10 −1.00000 −1.00000 1.00000 4.32662 1.00000 3.19198 −1.00000 1.00000 −4.32662
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.10
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(3\) \(1\)
\(17\) \(-1\)
\(59\) \(1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6018))\):

\(T_{5}^{10} - \cdots\)
\(T_{7}^{10} - \cdots\)