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Properties

Label 36.2.h.a
Level 36
Weight 2
Character orbit 36.h
Analytic conductor 0.287
Analytic rank 0
Dimension 8
CM No
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 36 = 2^{2} \cdot 3^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 36.h (of order \(6\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(0.287461447277\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.170772624.1
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

$q$-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.

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

Display 100 coefficients 10 coefficients

Basis of coefficient ring in terms of a root \(\nu\) of \(x^{8} - 3 x^{7} + 5 x^{6} - 6 x^{5} + 6 x^{4} - 12 x^{3} + 20 x^{2} - 24 x + 16\):

\(\beta_{0}\)\(=\)\( 1 \)
\(\beta_{1}\)\(=\)\( \nu \)
\(\beta_{2}\)\(=\)\((\)\( \nu^{7} - \nu^{6} - \nu^{5} - 2 \nu^{3} - 4 \nu^{2} + 4 \nu + 8 \)\()/8\)
\(\beta_{3}\)\(=\)\((\)\( -\nu^{6} + \nu^{5} - \nu^{4} + 2 \nu^{3} + 4 \nu - 4 \)\()/4\)
\(\beta_{4}\)\(=\)\((\)\( \nu^{7} - 3 \nu^{6} + 5 \nu^{5} - 2 \nu^{4} + 2 \nu^{3} - 8 \nu^{2} + 20 \nu - 24 \)\()/8\)
\(\beta_{5}\)\(=\)\((\)\( -3 \nu^{7} + 3 \nu^{6} - 5 \nu^{5} + 4 \nu^{4} - 6 \nu^{3} + 16 \nu^{2} - 12 \nu + 16 \)\()/8\)
\(\beta_{6}\)\(=\)\((\)\( \nu^{7} - 3 \nu^{6} + 5 \nu^{5} - 6 \nu^{4} + 6 \nu^{3} - 12 \nu^{2} + 20 \nu - 24 \)\()/8\)
\(\beta_{7}\)\(=\)\((\)\( 3 \nu^{7} - 5 \nu^{6} + 7 \nu^{5} - 6 \nu^{4} + 10 \nu^{3} - 24 \nu^{2} + 28 \nu - 32 \)\()/8\)
Display \(\nu^j\) in terms of \(\beta_i\)
\(1\)\(=\)\(\beta_0\)
\(\nu\)\(=\)\(\beta_{1}\)
\(\nu^{2}\)\(=\)\(-\beta_{7} - \beta_{5} + \beta_{3} + \beta_{1} - 1\)
\(\nu^{3}\)\(=\)\(\beta_{7} - \beta_{6} - \beta_{4} + \beta_{3} - \beta_{2} + \beta_{1}\)
\(\nu^{4}\)\(=\)\(2 \beta_{7} - 3 \beta_{6} + \beta_{5} + \beta_{4} - \beta_{2} + 1\)
\(\nu^{5}\)\(=\)\(-\beta_{7} - \beta_{5} + 2 \beta_{4} - \beta_{3} - 2 \beta_{2} - \beta_{1} + 5\)
\(\nu^{6}\)\(=\)\(-\beta_{7} + \beta_{6} - 2 \beta_{5} - \beta_{4} - 3 \beta_{3} - 3 \beta_{2} + 5 \beta_{1}\)
\(\nu^{7}\)\(=\)\(-4 \beta_{7} - \beta_{6} - 7 \beta_{5} - \beta_{4} + 2 \beta_{3} + \beta_{2} + 6 \beta_{1} - 7\)
Display \(\beta_i\) in terms of \(\nu^j\)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/36\mathbb{Z}\right)^\times\).

\(n\) \(19\) \(29\)
\(\chi(n)\) \(-1\) \(-\beta_{7}\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
11.1
0.774115 − 1.18353i
1.41203 − 0.0786378i
−1.02187 − 0.977642i
0.335728 + 1.37379i
0.774115 + 1.18353i
1.41203 + 0.0786378i
−1.02187 + 0.977642i
0.335728 − 1.37379i
−1.41203 − 0.0786378i 0.637910 + 1.61030i 1.98763 + 0.222077i 0.686141 − 0.396143i −0.774115 − 2.32395i −2.35143 − 1.35760i −2.78912 − 0.469882i −2.18614 + 2.05446i −1.00000 + 0.505408i
11.2 −0.774115 − 1.18353i −0.637910 − 1.61030i −0.801492 + 1.83238i 0.686141 − 0.396143i −1.41203 + 2.00155i 2.35143 + 1.35760i 2.78912 − 0.469882i −2.18614 + 2.05446i −1.00000 − 0.505408i
11.3 −0.335728 + 1.37379i 1.35760 − 1.07561i −1.77457 − 0.922437i −2.18614 + 1.26217i 1.02187 + 2.22616i −1.10489 − 0.637910i 1.86301 − 2.12819i 0.686141 − 2.92048i −1.00000 − 3.42703i
11.4 1.02187 − 0.977642i −1.35760 + 1.07561i 0.0884324 − 1.99804i −2.18614 + 1.26217i −0.335728 + 2.42637i 1.10489 + 0.637910i −1.86301 − 2.12819i 0.686141 − 2.92048i −1.00000 + 3.42703i
23.1 −1.41203 + 0.0786378i 0.637910 − 1.61030i 1.98763 − 0.222077i 0.686141 + 0.396143i −0.774115 + 2.32395i −2.35143 + 1.35760i −2.78912 + 0.469882i −2.18614 − 2.05446i −1.00000 − 0.505408i
23.2 −0.774115 + 1.18353i −0.637910 + 1.61030i −0.801492 − 1.83238i 0.686141 + 0.396143i −1.41203 − 2.00155i 2.35143 − 1.35760i 2.78912 + 0.469882i −2.18614 − 2.05446i −1.00000 + 0.505408i
23.3 −0.335728 − 1.37379i 1.35760 + 1.07561i −1.77457 + 0.922437i −2.18614 − 1.26217i 1.02187 − 2.22616i −1.10489 + 0.637910i 1.86301 + 2.12819i 0.686141 + 2.92048i −1.00000 + 3.42703i
23.4 1.02187 + 0.977642i −1.35760 − 1.07561i 0.0884324 + 1.99804i −2.18614 − 1.26217i −0.335728 − 2.42637i 1.10489 − 0.637910i −1.86301 + 2.12819i 0.686141 + 2.92048i −1.00000 − 3.42703i
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 23.4
Significant digits:
Format:

Inner twists

Char. orbit Parity Mult. Self Twist Proved
1.a Even 1 trivial yes
4.b Odd 1 yes
9.d Odd 1 yes
36.h Even 1 yes

Hecke kernels

There are no other newforms in \(S_{2}^{\mathrm{new}}(36, [\chi])\).