Properties

Label 1475.1.c.b
Level $1475$
Weight $1$
Character orbit 1475.c
Self dual yes
Analytic conductor $0.736$
Analytic rank $0$
Dimension $1$
Projective image $D_{3}$
CM discriminant -59
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 1475 = 5^{2} \cdot 59 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1475.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(0.736120893634\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 59)
Projective image \(D_{3}\)
Projective field Galois closure of 3.1.59.1
Artin image $D_6$
Artin field Galois closure of 6.2.435125.1

$q$-expansion

\(f(q)\) \(=\) \( q + q^{3} + q^{4} + q^{7} + O(q^{10}) \) \( q + q^{3} + q^{4} + q^{7} + q^{12} + q^{16} - 2q^{17} - q^{19} + q^{21} - q^{27} + q^{28} - q^{29} - q^{41} + q^{48} - 2q^{51} + q^{53} - q^{57} + q^{59} + q^{64} - 2q^{68} + 2q^{71} - q^{76} - q^{79} - q^{81} + q^{84} - q^{87} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1475\mathbb{Z}\right)^\times\).

\(n\) \(651\) \(827\)
\(\chi(n)\) \(-1\) \(1\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
176.1
0
0 1.00000 1.00000 0 0 1.00000 0 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
59.b odd 2 1 CM by \(\Q(\sqrt{-59}) \)

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1475.1.c.b 1
5.b even 2 1 59.1.b.a 1
5.c odd 4 2 1475.1.d.a 2
15.d odd 2 1 531.1.c.a 1
20.d odd 2 1 944.1.h.a 1
35.c odd 2 1 2891.1.c.e 1
35.i odd 6 2 2891.1.g.b 2
35.j even 6 2 2891.1.g.d 2
40.e odd 2 1 3776.1.h.a 1
40.f even 2 1 3776.1.h.b 1
59.b odd 2 1 CM 1475.1.c.b 1
295.d odd 2 1 59.1.b.a 1
295.e even 4 2 1475.1.d.a 2
295.h odd 58 28 3481.1.d.a 28
295.j even 58 28 3481.1.d.a 28
885.c even 2 1 531.1.c.a 1
1180.h even 2 1 944.1.h.a 1
2065.h even 2 1 2891.1.c.e 1
2065.n even 6 2 2891.1.g.b 2
2065.p odd 6 2 2891.1.g.d 2
2360.f even 2 1 3776.1.h.a 1
2360.l odd 2 1 3776.1.h.b 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
59.1.b.a 1 5.b even 2 1
59.1.b.a 1 295.d odd 2 1
531.1.c.a 1 15.d odd 2 1
531.1.c.a 1 885.c even 2 1
944.1.h.a 1 20.d odd 2 1
944.1.h.a 1 1180.h even 2 1
1475.1.c.b 1 1.a even 1 1 trivial
1475.1.c.b 1 59.b odd 2 1 CM
1475.1.d.a 2 5.c odd 4 2
1475.1.d.a 2 295.e even 4 2
2891.1.c.e 1 35.c odd 2 1
2891.1.c.e 1 2065.h even 2 1
2891.1.g.b 2 35.i odd 6 2
2891.1.g.b 2 2065.n even 6 2
2891.1.g.d 2 35.j even 6 2
2891.1.g.d 2 2065.p odd 6 2
3481.1.d.a 28 295.h odd 58 28
3481.1.d.a 28 295.j even 58 28
3776.1.h.a 1 40.e odd 2 1
3776.1.h.a 1 2360.f even 2 1
3776.1.h.b 1 40.f even 2 1
3776.1.h.b 1 2360.l odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{1}^{\mathrm{new}}(1475, [\chi])\):

\( T_{2} \)
\( T_{3} - 1 \)

Hecke characteristic polynomials

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