Properties

Label 2835.1.e.d
Level $2835$
Weight $1$
Character orbit 2835.e
Self dual yes
Analytic conductor $1.415$
Analytic rank $0$
Dimension $1$
Projective image $D_{3}$
CM discriminant -35
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2835 = 3^{4} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2835.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(1.41484931081\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 315)
Projective image \(D_{3}\)
Projective field Galois closure of 3.1.2835.1
Artin image $S_3$
Artin field Galois closure of 3.1.2835.1

$q$-expansion

\(f(q)\) \(=\) \( q + q^{4} + q^{5} + q^{7} + O(q^{10}) \) \( q + q^{4} + q^{5} + q^{7} - q^{11} - q^{13} + q^{16} - q^{17} + q^{20} + q^{25} + q^{28} + 2q^{29} + q^{35} - q^{44} - q^{47} + q^{49} - q^{52} - q^{55} + q^{64} - q^{65} - q^{68} - q^{71} - q^{73} - q^{77} - q^{79} + q^{80} - q^{83} - q^{85} - q^{91} - q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2835\mathbb{Z}\right)^\times\).

\(n\) \(1541\) \(1702\) \(2026\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
244.1
0
0 0 1.00000 1.00000 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
35.c odd 2 1 CM by \(\Q(\sqrt{-35}) \)

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2835.1.e.d 1
3.b odd 2 1 2835.1.e.b 1
5.b even 2 1 2835.1.e.a 1
7.b odd 2 1 2835.1.e.a 1
9.c even 3 2 315.1.bg.b yes 2
9.d odd 6 2 945.1.bg.b 2
15.d odd 2 1 2835.1.e.c 1
21.c even 2 1 2835.1.e.c 1
35.c odd 2 1 CM 2835.1.e.d 1
45.h odd 6 2 945.1.bg.a 2
45.j even 6 2 315.1.bg.a 2
45.k odd 12 4 1575.1.y.a 4
63.g even 3 2 2205.1.bn.a 2
63.h even 3 2 2205.1.q.a 2
63.k odd 6 2 2205.1.bn.b 2
63.l odd 6 2 315.1.bg.a 2
63.o even 6 2 945.1.bg.a 2
63.t odd 6 2 2205.1.q.b 2
105.g even 2 1 2835.1.e.b 1
315.q odd 6 2 2205.1.q.a 2
315.r even 6 2 2205.1.q.b 2
315.z even 6 2 945.1.bg.b 2
315.bg odd 6 2 315.1.bg.b yes 2
315.bn odd 6 2 2205.1.bn.a 2
315.bo even 6 2 2205.1.bn.b 2
315.cb even 12 4 1575.1.y.a 4
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
315.1.bg.a 2 45.j even 6 2
315.1.bg.a 2 63.l odd 6 2
315.1.bg.b yes 2 9.c even 3 2
315.1.bg.b yes 2 315.bg odd 6 2
945.1.bg.a 2 45.h odd 6 2
945.1.bg.a 2 63.o even 6 2
945.1.bg.b 2 9.d odd 6 2
945.1.bg.b 2 315.z even 6 2
1575.1.y.a 4 45.k odd 12 4
1575.1.y.a 4 315.cb even 12 4
2205.1.q.a 2 63.h even 3 2
2205.1.q.a 2 315.q odd 6 2
2205.1.q.b 2 63.t odd 6 2
2205.1.q.b 2 315.r even 6 2
2205.1.bn.a 2 63.g even 3 2
2205.1.bn.a 2 315.bn odd 6 2
2205.1.bn.b 2 63.k odd 6 2
2205.1.bn.b 2 315.bo even 6 2
2835.1.e.a 1 5.b even 2 1
2835.1.e.a 1 7.b odd 2 1
2835.1.e.b 1 3.b odd 2 1
2835.1.e.b 1 105.g even 2 1
2835.1.e.c 1 15.d odd 2 1
2835.1.e.c 1 21.c even 2 1
2835.1.e.d 1 1.a even 1 1 trivial
2835.1.e.d 1 35.c odd 2 1 CM

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{1}^{\mathrm{new}}(2835, [\chi])\):

\( T_{11} + 1 \)
\( T_{13} + 1 \)