Properties

Label 11.3.b.a
Level 11
Weight 3
Character orbit 11.b
Self dual Yes
Analytic conductor 0.300
Analytic rank 0
Dimension 1
CM disc. -11
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 11 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 11.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: Yes
Analytic conductor: \(0.299728290796\)
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

\(f(q)\) \(=\) \(q \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut -\mathstrut 11q^{11} \) \(\mathstrut -\mathstrut 20q^{12} \) \(\mathstrut +\mathstrut 5q^{15} \) \(\mathstrut +\mathstrut 16q^{16} \) \(\mathstrut -\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 35q^{23} \) \(\mathstrut -\mathstrut 24q^{25} \) \(\mathstrut -\mathstrut 35q^{27} \) \(\mathstrut -\mathstrut 37q^{31} \) \(\mathstrut +\mathstrut 55q^{33} \) \(\mathstrut +\mathstrut 64q^{36} \) \(\mathstrut -\mathstrut 25q^{37} \) \(\mathstrut -\mathstrut 44q^{44} \) \(\mathstrut -\mathstrut 16q^{45} \) \(\mathstrut +\mathstrut 50q^{47} \) \(\mathstrut -\mathstrut 80q^{48} \) \(\mathstrut +\mathstrut 49q^{49} \) \(\mathstrut -\mathstrut 70q^{53} \) \(\mathstrut +\mathstrut 11q^{55} \) \(\mathstrut +\mathstrut 107q^{59} \) \(\mathstrut +\mathstrut 20q^{60} \) \(\mathstrut +\mathstrut 64q^{64} \) \(\mathstrut +\mathstrut 35q^{67} \) \(\mathstrut -\mathstrut 175q^{69} \) \(\mathstrut -\mathstrut 133q^{71} \) \(\mathstrut +\mathstrut 120q^{75} \) \(\mathstrut -\mathstrut 16q^{80} \) \(\mathstrut +\mathstrut 31q^{81} \) \(\mathstrut -\mathstrut 97q^{89} \) \(\mathstrut +\mathstrut 140q^{92} \) \(\mathstrut +\mathstrut 185q^{93} \) \(\mathstrut +\mathstrut 95q^{97} \) \(\mathstrut -\mathstrut 176q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −5.00000 4.00000 −1.00000 0 0 0 16.0000 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

There are no other newforms in \(S_{3}^{\mathrm{new}}(11, [\chi])\).