Properties

Label 11.5.b.a
Level 11
Weight 5
Character orbit 11.b
Self dual Yes
Analytic conductor 1.137
Analytic rank 0
Dimension 1
CM disc. -11
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 11 \)
Weight: \( k \) = \( 5 \)
Character orbit: \([\chi]\) = 11.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: Yes
Analytic conductor: \(1.13706959392\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

$q$-expansion

\(f(q)\) \(=\) \( q + 7q^{3} + 16q^{4} - 49q^{5} - 32q^{9} + O(q^{10}) \) \( q + 7q^{3} + 16q^{4} - 49q^{5} - 32q^{9} + 121q^{11} + 112q^{12} - 343q^{15} + 256q^{16} - 784q^{20} + 167q^{23} + 1776q^{25} - 791q^{27} - 553q^{31} + 847q^{33} - 512q^{36} - 2113q^{37} + 1936q^{44} + 1568q^{45} - 1918q^{47} + 1792q^{48} + 2401q^{49} - 718q^{53} - 5929q^{55} + 4487q^{59} - 5488q^{60} + 4096q^{64} - 7753q^{67} + 1169q^{69} + 7607q^{71} + 12432q^{75} - 12544q^{80} - 2945q^{81} - 6433q^{89} + 2672q^{92} - 3871q^{93} - 9793q^{97} - 3872q^{99} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/11\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(-1\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
10.1
0
0 7.00000 16.0000 −49.0000 0 0 0 −32.0000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

Char. orbit Parity Mult. Self Twist Proved
1.a Even 1 trivial yes
11.b Odd 1 CM by \(\Q(\sqrt{-11}) \) yes

Hecke kernels

This newform can be constructed as the kernel of the linear operator \( T_{2} \) acting on \(S_{5}^{\mathrm{new}}(11, [\chi])\).