Properties

Label 152.1.g.a
Level 152
Weight 1
Character orbit 152.g
Self dual Yes
Analytic conductor 0.076
Analytic rank 0
Dimension 1
Projective image \(D_{3}\)
CM disc. -152
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 152 = 2^{3} \cdot 19 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 152.g (of order \(2\) and degree \(1\))

Newform invariants

Self dual: Yes
Analytic conductor: \(0.0758578819202\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Projective image \(D_{3}\)
Projective field Galois closure of 3.1.152.1
Artin image size \(12\)
Artin image $D_6$
Artin field Galois closure of 6.2.184832.1

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} + q^{3} + q^{4} - q^{6} - q^{7} - q^{8} + O(q^{10}) \) \( q - q^{2} + q^{3} + q^{4} - q^{6} - q^{7} - q^{8} + q^{12} + q^{13} + q^{14} + q^{16} - q^{17} - q^{19} - q^{21} - q^{23} - q^{24} + q^{25} - q^{26} - q^{27} - q^{28} + q^{29} - q^{32} + q^{34} - 2q^{37} + q^{38} + q^{39} + q^{42} + q^{46} + 2q^{47} + q^{48} - q^{50} - q^{51} + q^{52} + q^{53} + q^{54} + q^{56} - q^{57} - q^{58} + q^{59} + q^{64} + q^{67} - q^{68} - q^{69} - q^{73} + 2q^{74} + q^{75} - q^{76} - q^{78} - q^{81} - q^{84} + q^{87} - q^{91} - q^{92} - 2q^{94} - q^{96} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/152\mathbb{Z}\right)^\times\).

\(n\) \(39\) \(77\) \(97\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
37.1
0
−1.00000 1.00000 1.00000 0 −1.00000 −1.00000 −1.00000 0 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

Char. orbit Parity Mult. Self Twist Proved
1.a Even 1 trivial yes
152.g Odd 1 CM by \(\Q(\sqrt{-38}) \) yes

Hecke kernels

This newform can be constructed as the kernel of the linear operator \( T_{3} - 1 \) acting on \(S_{1}^{\mathrm{new}}(152, [\chi])\).