Properties

Label 44.1.d.a
Level 44
Weight 1
Character orbit 44.d
Self dual Yes
Analytic conductor 0.022
Analytic rank 0
Dimension 1
Projective image \(D_{3}\)
CM disc. -11
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 44 = 2^{2} \cdot 11 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 44.d (of order \(2\) and degree \(1\))

Newform invariants

Self dual: Yes
Analytic conductor: \(0.0219588605559\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Projective image \(D_{3}\)
Projective field Galois closure of 3.1.44.1
Artin image size \(6\)
Artin image $S_3$
Artin field Galois closure of 3.1.44.1

$q$-expansion

\(f(q)\) \(=\) \(q \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut q^{11} \) \(\mathstrut +\mathstrut q^{15} \) \(\mathstrut -\mathstrut q^{23} \) \(\mathstrut +\mathstrut q^{27} \) \(\mathstrut -\mathstrut q^{31} \) \(\mathstrut -\mathstrut q^{33} \) \(\mathstrut -\mathstrut q^{37} \) \(\mathstrut +\mathstrut 2q^{47} \) \(\mathstrut +\mathstrut q^{49} \) \(\mathstrut +\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut q^{55} \) \(\mathstrut -\mathstrut q^{59} \) \(\mathstrut -\mathstrut q^{67} \) \(\mathstrut +\mathstrut q^{69} \) \(\mathstrut -\mathstrut q^{71} \) \(\mathstrut -\mathstrut q^{81} \) \(\mathstrut -\mathstrut q^{89} \) \(\mathstrut +\mathstrut q^{93} \) \(\mathstrut -\mathstrut q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/44\mathbb{Z}\right)^\times\).

\(n\) \(13\) \(23\)
\(\chi(n)\) \(-1\) \(1\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
21.1
0
0 −1.00000 0 −1.00000 0 0 0 0 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 \(S_{1}^{\mathrm{new}}(44, [\chi])\).