Properties

Label 23.1.b.a
Level 23
Weight 1
Character orbit 23.b
Self dual yes
Analytic conductor 0.011
Analytic rank 0
Dimension 1
Projective image \(D_{3}\)
CM discriminant -23
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 23 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 23.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(0.0114784952906\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image \(D_{3}\)
Projective field Galois closure of 3.1.23.1
Artin image $S_3$
Artin field Galois closure of 3.1.23.1

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} - q^{3} + q^{6} + q^{8} + O(q^{10}) \) \( q - q^{2} - q^{3} + q^{6} + q^{8} - q^{13} - q^{16} + q^{23} - q^{24} + q^{25} + q^{26} + q^{27} - q^{29} - q^{31} + q^{39} - q^{41} - q^{46} - q^{47} + q^{48} + q^{49} - q^{50} - q^{54} + q^{58} + 2q^{59} + q^{62} + q^{64} - q^{69} - q^{71} - q^{73} - q^{75} - q^{78} - q^{81} + q^{82} + q^{87} + q^{93} + q^{94} - q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/23\mathbb{Z}\right)^\times\).

\(n\) \(5\)
\(\chi(n)\) \(-1\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
22.1
0
−1.00000 −1.00000 0 0 1.00000 0 1.00000 0 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
23.b odd 2 1 CM by \(\Q(\sqrt{-23}) \)

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 23.1.b.a 1
3.b odd 2 1 207.1.d.a 1
4.b odd 2 1 368.1.f.a 1
5.b even 2 1 575.1.d.a 1
5.c odd 4 2 575.1.c.a 2
7.b odd 2 1 1127.1.d.b 1
7.c even 3 2 1127.1.f.b 2
7.d odd 6 2 1127.1.f.a 2
8.b even 2 1 1472.1.f.b 1
8.d odd 2 1 1472.1.f.a 1
9.c even 3 2 1863.1.f.b 2
9.d odd 6 2 1863.1.f.a 2
11.b odd 2 1 2783.1.d.b 1
11.c even 5 4 2783.1.f.c 4
11.d odd 10 4 2783.1.f.a 4
12.b even 2 1 3312.1.c.a 1
13.b even 2 1 3887.1.d.b 1
13.c even 3 2 3887.1.h.c 2
13.d odd 4 2 3887.1.c.a 2
13.e even 6 2 3887.1.h.a 2
13.f odd 12 4 3887.1.j.e 4
23.b odd 2 1 CM 23.1.b.a 1
23.c even 11 10 529.1.d.a 10
23.d odd 22 10 529.1.d.a 10
69.c even 2 1 207.1.d.a 1
92.b even 2 1 368.1.f.a 1
115.c odd 2 1 575.1.d.a 1
115.e even 4 2 575.1.c.a 2
161.c even 2 1 1127.1.d.b 1
161.f odd 6 2 1127.1.f.b 2
161.g even 6 2 1127.1.f.a 2
184.e odd 2 1 1472.1.f.b 1
184.h even 2 1 1472.1.f.a 1
207.f odd 6 2 1863.1.f.b 2
207.g even 6 2 1863.1.f.a 2
253.b even 2 1 2783.1.d.b 1
253.f odd 10 4 2783.1.f.c 4
253.h even 10 4 2783.1.f.a 4
276.h odd 2 1 3312.1.c.a 1
299.c odd 2 1 3887.1.d.b 1
299.g even 4 2 3887.1.c.a 2
299.h odd 6 2 3887.1.h.c 2
299.j odd 6 2 3887.1.h.a 2
299.l even 12 4 3887.1.j.e 4
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
23.1.b.a 1 1.a even 1 1 trivial
23.1.b.a 1 23.b odd 2 1 CM
207.1.d.a 1 3.b odd 2 1
207.1.d.a 1 69.c even 2 1
368.1.f.a 1 4.b odd 2 1
368.1.f.a 1 92.b even 2 1
529.1.d.a 10 23.c even 11 10
529.1.d.a 10 23.d odd 22 10
575.1.c.a 2 5.c odd 4 2
575.1.c.a 2 115.e even 4 2
575.1.d.a 1 5.b even 2 1
575.1.d.a 1 115.c odd 2 1
1127.1.d.b 1 7.b odd 2 1
1127.1.d.b 1 161.c even 2 1
1127.1.f.a 2 7.d odd 6 2
1127.1.f.a 2 161.g even 6 2
1127.1.f.b 2 7.c even 3 2
1127.1.f.b 2 161.f odd 6 2
1472.1.f.a 1 8.d odd 2 1
1472.1.f.a 1 184.h even 2 1
1472.1.f.b 1 8.b even 2 1
1472.1.f.b 1 184.e odd 2 1
1863.1.f.a 2 9.d odd 6 2
1863.1.f.a 2 207.g even 6 2
1863.1.f.b 2 9.c even 3 2
1863.1.f.b 2 207.f odd 6 2
2783.1.d.b 1 11.b odd 2 1
2783.1.d.b 1 253.b even 2 1
2783.1.f.a 4 11.d odd 10 4
2783.1.f.a 4 253.h even 10 4
2783.1.f.c 4 11.c even 5 4
2783.1.f.c 4 253.f odd 10 4
3312.1.c.a 1 12.b even 2 1
3312.1.c.a 1 276.h odd 2 1
3887.1.c.a 2 13.d odd 4 2
3887.1.c.a 2 299.g even 4 2
3887.1.d.b 1 13.b even 2 1
3887.1.d.b 1 299.c odd 2 1
3887.1.h.a 2 13.e even 6 2
3887.1.h.a 2 299.j odd 6 2
3887.1.h.c 2 13.c even 3 2
3887.1.h.c 2 299.h odd 6 2
3887.1.j.e 4 13.f odd 12 4
3887.1.j.e 4 299.l even 12 4

Hecke kernels

This newform subspace is the entire newspace \(S_{1}^{\mathrm{new}}(23, [\chi])\).

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 + T + T^{2} \)
$3$ \( 1 + T + T^{2} \)
$5$ \( ( 1 - T )( 1 + T ) \)
$7$ \( ( 1 - T )( 1 + T ) \)
$11$ \( ( 1 - T )( 1 + T ) \)
$13$ \( 1 + T + T^{2} \)
$17$ \( ( 1 - T )( 1 + T ) \)
$19$ \( ( 1 - T )( 1 + T ) \)
$23$ \( 1 - T \)
$29$ \( 1 + T + T^{2} \)
$31$ \( 1 + T + T^{2} \)
$37$ \( ( 1 - T )( 1 + T ) \)
$41$ \( 1 + T + T^{2} \)
$43$ \( ( 1 - T )( 1 + T ) \)
$47$ \( 1 + T + T^{2} \)
$53$ \( ( 1 - T )( 1 + T ) \)
$59$ \( ( 1 - T )^{2} \)
$61$ \( ( 1 - T )( 1 + T ) \)
$67$ \( ( 1 - T )( 1 + T ) \)
$71$ \( 1 + T + T^{2} \)
$73$ \( 1 + T + T^{2} \)
$79$ \( ( 1 - T )( 1 + T ) \)
$83$ \( ( 1 - T )( 1 + T ) \)
$89$ \( ( 1 - T )( 1 + T ) \)
$97$ \( ( 1 - T )( 1 + T ) \)
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