Properties

Label 152.1.k.a
Level 152
Weight 1
Character orbit 152.k
Analytic conductor 0.076
Analytic rank 0
Dimension 2
Projective image \(D_{3}\)
CM disc. -8
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 152 = 2^{3} \cdot 19 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 152.k (of order \(6\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(0.0758578819202\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Projective image \(D_{3}\)
Projective field Galois closure of 3.1.2888.1
Artin image size \(18\)
Artin image $C_3\times S_3$
Artin field Galois closure of 6.0.184832.1

$q$-expansion

The \(q\)-expansion and trace form are shown below.

\(f(q)\) \(=\) \( q + \zeta_{6}^{2} q^{2} -\zeta_{6}^{2} q^{3} -\zeta_{6} q^{4} + \zeta_{6} q^{6} + q^{8} +O(q^{10})\) \( q + \zeta_{6}^{2} q^{2} -\zeta_{6}^{2} q^{3} -\zeta_{6} q^{4} + \zeta_{6} q^{6} + q^{8} - q^{11} - q^{12} + \zeta_{6}^{2} q^{16} + 2 \zeta_{6}^{2} q^{17} -\zeta_{6} q^{19} -\zeta_{6}^{2} q^{22} -\zeta_{6}^{2} q^{24} -\zeta_{6} q^{25} + q^{27} -\zeta_{6} q^{32} + \zeta_{6}^{2} q^{33} -2 \zeta_{6} q^{34} + q^{38} -\zeta_{6}^{2} q^{41} + 2 \zeta_{6}^{2} q^{43} + \zeta_{6} q^{44} + \zeta_{6} q^{48} + q^{49} + q^{50} + 2 \zeta_{6} q^{51} + \zeta_{6}^{2} q^{54} - q^{57} -\zeta_{6}^{2} q^{59} + q^{64} -\zeta_{6} q^{66} + \zeta_{6} q^{67} + 2 q^{68} -\zeta_{6}^{2} q^{73} - q^{75} + \zeta_{6}^{2} q^{76} -\zeta_{6}^{2} q^{81} + \zeta_{6} q^{82} - q^{83} -2 \zeta_{6} q^{86} - q^{88} -2 \zeta_{6} q^{89} - q^{96} -\zeta_{6}^{2} q^{97} + \zeta_{6}^{2} q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} + q^{3} - q^{4} + q^{6} + 2q^{8} + O(q^{10}) \) \( 2q - q^{2} + q^{3} - q^{4} + q^{6} + 2q^{8} - 2q^{11} - 2q^{12} - q^{16} - 2q^{17} - q^{19} + q^{22} + q^{24} - q^{25} + 2q^{27} - q^{32} - q^{33} - 2q^{34} + 2q^{38} + q^{41} - 2q^{43} + q^{44} + q^{48} + 2q^{49} + 2q^{50} + 2q^{51} - q^{54} - 2q^{57} + q^{59} + 2q^{64} - q^{66} + q^{67} + 4q^{68} + q^{73} - 2q^{75} - q^{76} + q^{81} + q^{82} - 2q^{83} - 2q^{86} - 2q^{88} - 2q^{89} - 2q^{96} + q^{97} - q^{98} + O(q^{100}) \)

Character Values

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

\(n\) \(39\) \(77\) \(97\)
\(\chi(n)\) \(-1\) \(-1\) \(-\zeta_{6}\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
11.1
0.500000 + 0.866025i
0.500000 0.866025i
−0.500000 + 0.866025i 0.500000 0.866025i −0.500000 0.866025i 0 0.500000 + 0.866025i 0 1.00000 0 0
83.1 −0.500000 0.866025i 0.500000 + 0.866025i −0.500000 + 0.866025i 0 0.500000 0.866025i 0 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
8.d Odd 1 CM by \(\Q(\sqrt{-2}) \) yes
19.c Even 1 yes
152.k Odd 1 yes

Hecke kernels

There are no other newforms in \(S_{1}^{\mathrm{new}}(152, [\chi])\).