Properties

Label 22.10.a.c
Level 22
Weight 10
Character orbit 22.a
Self dual Yes
Analytic conductor 11.331
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 22 = 2 \cdot 11 \)
Weight: \( k \) = \( 10 \)
Character orbit: \([\chi]\) = 22.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(11.3307883956\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 16q^{2} + 201q^{3} + 256q^{4} + 2349q^{5} + 3216q^{6} - 8806q^{7} + 4096q^{8} + 20718q^{9} + O(q^{10}) \) \( q + 16q^{2} + 201q^{3} + 256q^{4} + 2349q^{5} + 3216q^{6} - 8806q^{7} + 4096q^{8} + 20718q^{9} + 37584q^{10} - 14641q^{11} + 51456q^{12} - 131068q^{13} - 140896q^{14} + 472149q^{15} + 65536q^{16} - 55698q^{17} + 331488q^{18} + 1041824q^{19} + 601344q^{20} - 1770006q^{21} - 234256q^{22} - 662139q^{23} + 823296q^{24} + 3564676q^{25} - 2097088q^{26} + 208035q^{27} - 2254336q^{28} - 4819344q^{29} + 7554384q^{30} - 180115q^{31} + 1048576q^{32} - 2942841q^{33} - 891168q^{34} - 20685294q^{35} + 5303808q^{36} - 7803025q^{37} + 16669184q^{38} - 26344668q^{39} + 9621504q^{40} - 5927736q^{41} - 28320096q^{42} - 5929162q^{43} - 3748096q^{44} + 48666582q^{45} - 10594224q^{46} + 61576176q^{47} + 13172736q^{48} + 37192029q^{49} + 57034816q^{50} - 11195298q^{51} - 33553408q^{52} + 7349514q^{53} + 3328560q^{54} - 34391709q^{55} - 36069376q^{56} + 209406624q^{57} - 77109504q^{58} - 113901909q^{59} + 120870144q^{60} - 13814260q^{61} - 2881840q^{62} - 182442708q^{63} + 16777216q^{64} - 307878732q^{65} - 47085456q^{66} + 309980903q^{67} - 14258688q^{68} - 133089939q^{69} - 330964704q^{70} + 42752631q^{71} + 84860928q^{72} + 142018340q^{73} - 124848400q^{74} + 716499876q^{75} + 266706944q^{76} + 128928646q^{77} - 421514688q^{78} - 325376446q^{79} + 153944064q^{80} - 365977359q^{81} - 94843776q^{82} + 253502934q^{83} - 453121536q^{84} - 130834602q^{85} - 94866592q^{86} - 968688144q^{87} - 59969536q^{88} - 994227705q^{89} + 778665312q^{90} + 1154184808q^{91} - 169507584q^{92} - 36203115q^{93} + 985218816q^{94} + 2447244576q^{95} + 210763776q^{96} - 352091047q^{97} + 595072464q^{98} - 303332238q^{99} + O(q^{100}) \)

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
16.0000 201.000 256.000 2349.00 3216.00 −8806.00 4096.00 20718.0 37584.0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

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

Hecke kernels

This newform can be constructed as the kernel of the linear operator \( T_{3} - 201 \) acting on \(S_{10}^{\mathrm{new}}(\Gamma_0(22))\).