Properties

Label 23.7.b.a
Level $23$
Weight $7$
Character orbit 23.b
Self dual yes
Analytic conductor $5.291$
Analytic rank $0$
Dimension $1$
CM discriminant -23
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 23 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 23.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(5.29124392326\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

$q$-expansion

\(f(q)\) \(=\) \( q - 7 q^{2} - 38 q^{3} - 15 q^{4} + 266 q^{6} + 553 q^{8} + 715 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - 7 q^{2} - 38 q^{3} - 15 q^{4} + 266 q^{6} + 553 q^{8} + 715 q^{9} + 570 q^{12} + 1082 q^{13} - 2911 q^{16} - 5005 q^{18} - 12167 q^{23} - 21014 q^{24} + 15625 q^{25} - 7574 q^{26} + 532 q^{27} + 30746 q^{29} + 58754 q^{31} - 15015 q^{32} - 10725 q^{36} - 41116 q^{39} + 43634 q^{41} + 85169 q^{46} - 205342 q^{47} + 110618 q^{48} + 117649 q^{49} - 109375 q^{50} - 16230 q^{52} - 3724 q^{54} - 215222 q^{58} - 253942 q^{59} - 411278 q^{62} + 291409 q^{64} + 462346 q^{69} + 667154 q^{71} + 395395 q^{72} + 725042 q^{73} - 593750 q^{75} + 287812 q^{78} - 541451 q^{81} - 305438 q^{82} - 1168348 q^{87} + 182505 q^{92} - 2232652 q^{93} + 1437394 q^{94} + 570570 q^{96} - 823543 q^{98}+O(q^{100}) \) Copy content Toggle raw display

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
−7.00000 −38.0000 −15.0000 0 266.000 0 553.000 715.000 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 23.7.b.a 1
3.b odd 2 1 207.7.d.a 1
4.b odd 2 1 368.7.f.a 1
23.b odd 2 1 CM 23.7.b.a 1
69.c even 2 1 207.7.d.a 1
92.b even 2 1 368.7.f.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
23.7.b.a 1 1.a even 1 1 trivial
23.7.b.a 1 23.b odd 2 1 CM
207.7.d.a 1 3.b odd 2 1
207.7.d.a 1 69.c even 2 1
368.7.f.a 1 4.b odd 2 1
368.7.f.a 1 92.b even 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} + 7 \) acting on \(S_{7}^{\mathrm{new}}(23, [\chi])\). Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T + 7 \) Copy content Toggle raw display
$3$ \( T + 38 \) Copy content Toggle raw display
$5$ \( T \) Copy content Toggle raw display
$7$ \( T \) Copy content Toggle raw display
$11$ \( T \) Copy content Toggle raw display
$13$ \( T - 1082 \) Copy content Toggle raw display
$17$ \( T \) Copy content Toggle raw display
$19$ \( T \) Copy content Toggle raw display
$23$ \( T + 12167 \) Copy content Toggle raw display
$29$ \( T - 30746 \) Copy content Toggle raw display
$31$ \( T - 58754 \) Copy content Toggle raw display
$37$ \( T \) Copy content Toggle raw display
$41$ \( T - 43634 \) Copy content Toggle raw display
$43$ \( T \) Copy content Toggle raw display
$47$ \( T + 205342 \) Copy content Toggle raw display
$53$ \( T \) Copy content Toggle raw display
$59$ \( T + 253942 \) Copy content Toggle raw display
$61$ \( T \) Copy content Toggle raw display
$67$ \( T \) Copy content Toggle raw display
$71$ \( T - 667154 \) Copy content Toggle raw display
$73$ \( T - 725042 \) Copy content Toggle raw display
$79$ \( T \) Copy content Toggle raw display
$83$ \( T \) Copy content Toggle raw display
$89$ \( T \) Copy content Toggle raw display
$97$ \( T \) Copy content Toggle raw display
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