Properties

Label 12.11.c.a
Level 12
Weight 11
Character orbit 12.c
Self dual Yes
Analytic conductor 7.624
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: \( k \) = \( 11 \)
Character orbit: \([\chi]\) = 12.c (of order \(2\) and degree \(1\))

Newform invariants

Self dual: Yes
Analytic conductor: \(7.62428703208\)
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

\(f(q)\) \(=\) \( q - 243q^{3} + 22082q^{7} + 59049q^{9} + O(q^{10}) \) \( q - 243q^{3} + 22082q^{7} + 59049q^{9} + 702218q^{13} - 2901574q^{19} - 5365926q^{21} + 9765625q^{25} - 14348907q^{27} + 49326674q^{31} + 135214586q^{37} - 170638974q^{39} - 282780982q^{43} + 205139475q^{49} + 705082482q^{57} - 197224726q^{61} + 1303920018q^{63} - 1437442918q^{67} - 4144040686q^{73} - 2373046875q^{75} + 3959005298q^{79} + 3486784401q^{81} + 15506377876q^{91} - 11986381782q^{93} + 884916482q^{97} + O(q^{100}) \)

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 −243.000 0 0 0 22082.0 0 59049.0 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
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 \(S_{11}^{\mathrm{new}}(12, [\chi])\).