Properties

Label 12.17.c.a
Level 12
Weight 17
Character orbit 12.c
Self dual Yes
Analytic conductor 19.479
Analytic rank 0
Dimension 1
CM disc. -3
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) = \( 17 \)
Character orbit: \([\chi]\) = 12.c (of order \(2\) and degree \(1\))

Newform invariants

Self dual: Yes
Analytic conductor: \(19.4789452628\)
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

\(f(q)\) \(=\) \(q \) \(\mathstrut +\mathstrut 6561q^{3} \) \(\mathstrut +\mathstrut 4743554q^{7} \) \(\mathstrut +\mathstrut 43046721q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut +\mathstrut 6561q^{3} \) \(\mathstrut +\mathstrut 4743554q^{7} \) \(\mathstrut +\mathstrut 43046721q^{9} \) \(\mathstrut -\mathstrut 349391806q^{13} \) \(\mathstrut +\mathstrut 32868566594q^{19} \) \(\mathstrut +\mathstrut 31122457794q^{21} \) \(\mathstrut +\mathstrut 152587890625q^{25} \) \(\mathstrut +\mathstrut 282429536481q^{27} \) \(\mathstrut +\mathstrut 1568167997954q^{31} \) \(\mathstrut -\mathstrut 6771424503358q^{37} \) \(\mathstrut -\mathstrut 2292359639166q^{39} \) \(\mathstrut -\mathstrut 11180981621566q^{43} \) \(\mathstrut -\mathstrut 10731626018685q^{49} \) \(\mathstrut +\mathstrut 215650665423234q^{57} \) \(\mathstrut +\mathstrut 184288715234114q^{61} \) \(\mathstrut +\mathstrut 204194445586434q^{63} \) \(\mathstrut -\mathstrut 782743712096446q^{67} \) \(\mathstrut -\mathstrut 1351474503392638q^{73} \) \(\mathstrut +\mathstrut 1001129150390625q^{75} \) \(\mathstrut -\mathstrut 2677497415399678q^{79} \) \(\mathstrut +\mathstrut 1853020188851841q^{81} \) \(\mathstrut -\mathstrut 1657358898918524q^{91} \) \(\mathstrut +\mathstrut 10288750234576194q^{93} \) \(\mathstrut +\mathstrut 15621585304991234q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/12\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(7\)
\(\chi(n)\) \(-1\) \(1\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
5.1
0
0 6561.00 0 0 0 4.74355e6 0 4.30467e7 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
3.b Odd 1 CM by \(\Q(\sqrt{-3}) \) yes

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{5} \) acting on \(S_{17}^{\mathrm{new}}(12, [\chi])\).