↑

Properties

Label 7.3.b.a
Level 7
Weight 3
Character orbit 7.b
Self dual Yes
Analytic conductor 0.191
Analytic rank 0
Dimension 1
CM disc. -7
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 7 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 7.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: Yes
Analytic conductor: \(0.190736185052\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

$q$-expansion

\(f(q)\) \(=\) \( q - 3q^{2} + 5q^{4} - 7q^{7} - 3q^{8} + 9q^{9} + O(q^{10}) \) \( q - 3q^{2} + 5q^{4} - 7q^{7} - 3q^{8} + 9q^{9} - 6q^{11} + 21q^{14} - 11q^{16} - 27q^{18} + 18q^{22} + 18q^{23} + 25q^{25} - 35q^{28} - 54q^{29} + 45q^{32} + 45q^{36} - 38q^{37} + 58q^{43} - 30q^{44} - 54q^{46} + 49q^{49} - 75q^{50} - 6q^{53} + 21q^{56} + 162q^{58} - 63q^{63} - 91q^{64} - 118q^{67} + 114q^{71} - 27q^{72} + 114q^{74} + 42q^{77} - 94q^{79} + 81q^{81} - 174q^{86} + 18q^{88} + 90q^{92} - 147q^{98} - 54q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/7\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(-1\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
6.1
0
−3.00000 0 5.00000 0 0 −7.00000 −3.00000 9.00000 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
7.b Odd 1 CM by \(\Q(\sqrt{-7}) \) yes

Hecke kernels

There are no other newforms in \(S_{3}^{\mathrm{new}}(7, [\chi])\).