Properties

Label 175.1.d.b
Level $175$
Weight $1$
Character orbit 175.d
Self dual yes
Analytic conductor $0.087$
Analytic rank $0$
Dimension $1$
Projective image $D_{3}$
CM discriminant -7
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 175.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(0.0873363772108\)
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 3.1.175.1
Artin image $D_6$
Artin field Galois closure of 6.2.153125.1

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} - q^{7} - q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} - q^{7} - q^{8} + q^{9} - q^{11} - q^{14} - q^{16} + q^{18} - q^{22} + q^{23} - q^{29} + q^{37} + q^{43} + q^{46} + q^{49} - 2q^{53} + q^{56} - q^{58} - q^{63} + q^{64} + q^{67} - q^{71} - q^{72} + q^{74} + q^{77} - q^{79} + q^{81} + q^{86} + q^{88} + q^{98} - q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/175\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(-1\) \(1\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
76.1
0
1.00000 0 0 0 0 −1.00000 −1.00000 1.00000 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
7.b odd 2 1 CM by \(\Q(\sqrt{-7}) \)

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 175.1.d.b yes 1
3.b odd 2 1 1575.1.h.a 1
4.b odd 2 1 2800.1.f.b 1
5.b even 2 1 175.1.d.a 1
5.c odd 4 2 175.1.c.a 2
7.b odd 2 1 CM 175.1.d.b yes 1
7.c even 3 2 1225.1.i.a 2
7.d odd 6 2 1225.1.i.a 2
15.d odd 2 1 1575.1.h.c 1
15.e even 4 2 1575.1.e.a 2
20.d odd 2 1 2800.1.f.a 1
20.e even 4 2 2800.1.p.a 2
21.c even 2 1 1575.1.h.a 1
28.d even 2 1 2800.1.f.b 1
35.c odd 2 1 175.1.d.a 1
35.f even 4 2 175.1.c.a 2
35.i odd 6 2 1225.1.i.b 2
35.j even 6 2 1225.1.i.b 2
35.k even 12 4 1225.1.j.a 4
35.l odd 12 4 1225.1.j.a 4
105.g even 2 1 1575.1.h.c 1
105.k odd 4 2 1575.1.e.a 2
140.c even 2 1 2800.1.f.a 1
140.j odd 4 2 2800.1.p.a 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
175.1.c.a 2 5.c odd 4 2
175.1.c.a 2 35.f even 4 2
175.1.d.a 1 5.b even 2 1
175.1.d.a 1 35.c odd 2 1
175.1.d.b yes 1 1.a even 1 1 trivial
175.1.d.b yes 1 7.b odd 2 1 CM
1225.1.i.a 2 7.c even 3 2
1225.1.i.a 2 7.d odd 6 2
1225.1.i.b 2 35.i odd 6 2
1225.1.i.b 2 35.j even 6 2
1225.1.j.a 4 35.k even 12 4
1225.1.j.a 4 35.l odd 12 4
1575.1.e.a 2 15.e even 4 2
1575.1.e.a 2 105.k odd 4 2
1575.1.h.a 1 3.b odd 2 1
1575.1.h.a 1 21.c even 2 1
1575.1.h.c 1 15.d odd 2 1
1575.1.h.c 1 105.g even 2 1
2800.1.f.a 1 20.d odd 2 1
2800.1.f.a 1 140.c even 2 1
2800.1.f.b 1 4.b odd 2 1
2800.1.f.b 1 28.d even 2 1
2800.1.p.a 2 20.e even 4 2
2800.1.p.a 2 140.j odd 4 2

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} - 1 \) acting on \(S_{1}^{\mathrm{new}}(175, [\chi])\).

Hecke characteristic polynomials

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