Properties

Label 4030.2.a.r
Level 4030
Weight 2
Character orbit 4030.a
Self dual Yes
Analytic conductor 32.180
Analytic rank 0
Dimension 9
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4030.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1797120146\)
Analytic rank: \(0\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
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.

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

Basis of coefficient ring in terms of a root \(\nu\) of \(x^{9}\mathstrut -\mathstrut \) \(4\) \(x^{8}\mathstrut -\mathstrut \) \(8\) \(x^{7}\mathstrut +\mathstrut \) \(39\) \(x^{6}\mathstrut +\mathstrut \) \(13\) \(x^{5}\mathstrut -\mathstrut \) \(106\) \(x^{4}\mathstrut +\mathstrut \) \(9\) \(x^{3}\mathstrut +\mathstrut \) \(74\) \(x^{2}\mathstrut -\mathstrut \) \(3\) \(x\mathstrut -\mathstrut \) \(7\):

\(\beta_{0}\)\(=\)\( 1 \)
\(\beta_{1}\)\(=\)\( \nu^{2} - \nu - 3 \)
\(\beta_{2}\)\(=\)\((\)\( -5 \nu^{8} + 45 \nu^{7} - 39 \nu^{6} - 438 \nu^{5} + 665 \nu^{4} + 1147 \nu^{3} - 1692 \nu^{2} - 524 \nu + 445 \)\()/146\)
\(\beta_{3}\)\(=\)\((\)\( 13 \nu^{8} - 44 \nu^{7} - 103 \nu^{6} + 365 \nu^{5} + 96 \nu^{4} - 617 \nu^{3} + 647 \nu^{2} - 229 \nu - 500 \)\()/146\)
\(\beta_{4}\)\(=\)\((\)\( 12 \nu^{8} - 35 \nu^{7} - 140 \nu^{6} + 365 \nu^{5} + 521 \nu^{4} - 1030 \nu^{3} - 655 \nu^{2} + 659 \nu + 173 \)\()/146\)
\(\beta_{5}\)\(=\)\((\)\( 17 \nu^{8} - 80 \nu^{7} - 101 \nu^{6} + 803 \nu^{5} - 144 \nu^{4} - 2177 \nu^{3} + 1037 \nu^{2} + 745 \nu - 126 \)\()/146\)
\(\beta_{6}\)\(=\)\((\)\( 17 \nu^{8} - 80 \nu^{7} - 101 \nu^{6} + 803 \nu^{5} - 144 \nu^{4} - 2323 \nu^{3} + 1183 \nu^{2} + 1767 \nu - 418 \)\()/146\)
\(\beta_{7}\)\(=\)\((\)\( 49 \nu^{8} - 149 \nu^{7} - 523 \nu^{6} + 1314 \nu^{5} + 1951 \nu^{4} - 2685 \nu^{3} - 2778 \nu^{2} + 580 \nu + 749 \)\()/292\)
\(\beta_{8}\)\(=\)\((\)\( -95 \nu^{8} + 417 \nu^{7} + 573 \nu^{6} - 3796 \nu^{5} + 225 \nu^{4} + 9091 \nu^{3} - 3240 \nu^{2} - 4554 \nu + 279 \)\()/292\)
\(1\)\(=\)\(\beta_0\)
\(\nu\)\(=\)\((\)\(-\)\(\beta_{5}\mathstrut +\mathstrut \) \(\beta_{4}\mathstrut -\mathstrut \) \(\beta_{2}\mathstrut +\mathstrut \) \(1\)\()/3\)
\(\nu^{2}\)\(=\)\((\)\(-\)\(\beta_{5}\mathstrut +\mathstrut \) \(\beta_{4}\mathstrut -\mathstrut \) \(\beta_{2}\mathstrut +\mathstrut \) \(3\) \(\beta_{1}\mathstrut +\mathstrut \) \(10\)\()/3\)
\(\nu^{3}\)\(=\)\((\)\(-\)\(3\) \(\beta_{6}\mathstrut -\mathstrut \) \(5\) \(\beta_{5}\mathstrut +\mathstrut \) \(8\) \(\beta_{4}\mathstrut -\mathstrut \) \(8\) \(\beta_{2}\mathstrut +\mathstrut \) \(3\) \(\beta_{1}\mathstrut +\mathstrut \) \(11\)\()/3\)
\(\nu^{4}\)\(=\)\(-\)\(\beta_{8}\mathstrut -\mathstrut \) \(\beta_{7}\mathstrut -\mathstrut \) \(2\) \(\beta_{6}\mathstrut -\mathstrut \) \(3\) \(\beta_{5}\mathstrut +\mathstrut \) \(5\) \(\beta_{4}\mathstrut -\mathstrut \) \(\beta_{3}\mathstrut -\mathstrut \) \(3\) \(\beta_{2}\mathstrut +\mathstrut \) \(9\) \(\beta_{1}\mathstrut +\mathstrut \) \(22\)
\(\nu^{5}\)\(=\)\((\)\(-\)\(6\) \(\beta_{8}\mathstrut -\mathstrut \) \(12\) \(\beta_{7}\mathstrut -\mathstrut \) \(33\) \(\beta_{6}\mathstrut -\mathstrut \) \(35\) \(\beta_{5}\mathstrut +\mathstrut \) \(77\) \(\beta_{4}\mathstrut -\mathstrut \) \(3\) \(\beta_{3}\mathstrut -\mathstrut \) \(56\) \(\beta_{2}\mathstrut +\mathstrut \) \(45\) \(\beta_{1}\mathstrut +\mathstrut \) \(116\)\()/3\)
\(\nu^{6}\)\(=\)\((\)\(-\)\(48\) \(\beta_{8}\mathstrut -\mathstrut \) \(66\) \(\beta_{7}\mathstrut -\mathstrut \) \(93\) \(\beta_{6}\mathstrut -\mathstrut \) \(86\) \(\beta_{5}\mathstrut +\mathstrut \) \(191\) \(\beta_{4}\mathstrut -\mathstrut \) \(24\) \(\beta_{3}\mathstrut -\mathstrut \) \(80\) \(\beta_{2}\mathstrut +\mathstrut \) \(240\) \(\beta_{1}\mathstrut +\mathstrut \) \(530\)\()/3\)
\(\nu^{7}\)\(=\)\((\)\(-\)\(123\) \(\beta_{8}\mathstrut -\mathstrut \) \(237\) \(\beta_{7}\mathstrut -\mathstrut \) \(363\) \(\beta_{6}\mathstrut -\mathstrut \) \(298\) \(\beta_{5}\mathstrut +\mathstrut \) \(790\) \(\beta_{4}\mathstrut -\mathstrut \) \(18\) \(\beta_{3}\mathstrut -\mathstrut \) \(391\) \(\beta_{2}\mathstrut +\mathstrut \) \(531\) \(\beta_{1}\mathstrut +\mathstrut \) \(1216\)\()/3\)
\(\nu^{8}\)\(=\)\(-\)\(202\) \(\beta_{8}\mathstrut -\mathstrut \) \(322\) \(\beta_{7}\mathstrut -\mathstrut \) \(379\) \(\beta_{6}\mathstrut -\mathstrut \) \(282\) \(\beta_{5}\mathstrut +\mathstrut \) \(754\) \(\beta_{4}\mathstrut -\mathstrut \) \(37\) \(\beta_{3}\mathstrut -\mathstrut \) \(222\) \(\beta_{2}\mathstrut +\mathstrut \) \(743\) \(\beta_{1}\mathstrut +\mathstrut \) \(1576\)

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
−0.316108
−2.32727
1.72735
0.351548
3.27701
−1.78896
1.19574
2.70656
−0.825879
1.00000 −2.83087 1.00000 1.00000 −2.83087 3.35447 1.00000 5.01385 1.00000
1.2 1.00000 −2.15121 1.00000 1.00000 −2.15121 −1.07964 1.00000 1.62769 1.00000
1.3 1.00000 −1.50823 1.00000 1.00000 −1.50823 −3.09594 1.00000 −0.725248 1.00000
1.4 1.00000 −0.748457 1.00000 1.00000 −0.748457 4.59004 1.00000 −2.43981 1.00000
1.5 1.00000 0.574493 1.00000 1.00000 0.574493 2.65097 1.00000 −2.66996 1.00000
1.6 1.00000 1.40140 1.00000 1.00000 1.40140 −1.57433 1.00000 −1.03607 1.00000
1.7 1.00000 2.25079 1.00000 1.00000 2.25079 2.47698 1.00000 2.06607 1.00000
1.8 1.00000 2.79279 1.00000 1.00000 2.79279 3.17111 1.00000 4.79966 1.00000
1.9 1.00000 3.21929 1.00000 1.00000 3.21929 −1.49366 1.00000 7.36381 1.00000
\(n\): 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
\(2\) \(-1\)
\(5\) \(-1\)
\(13\) \(-1\)
\(31\) \(1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{3}^{9} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4030))\).