Properties

Label 2183.1.d.d
Level 2183
Weight 1
Character orbit 2183.d
Analytic conductor 1.089
Analytic rank 0
Dimension 2
Projective image \(S_{4}\)
CM/RM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 2183 = 37 \cdot 59 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 2183.d (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(1.08945892258\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{-2}) \)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Projective image \(S_{4}\)
Projective field Galois closure of 4.2.2183.1
Artin image size \(48\)
Artin image $\GL(2,3)$
Artin field Galois closure of 8.2.10403062487.1

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \sqrt{-2}\). We also show the integral \(q\)-expansion of the trace form.

\(f(q)\) \(=\) \( q + q^{2} -\beta q^{5} - q^{7} - q^{8} - q^{9} +O(q^{10})\) \( q + q^{2} -\beta q^{5} - q^{7} - q^{8} - q^{9} -\beta q^{10} + \beta q^{11} - q^{13} - q^{14} - q^{16} -\beta q^{17} - q^{18} + \beta q^{19} + \beta q^{22} - q^{25} - q^{26} -\beta q^{29} - q^{31} -\beta q^{34} + \beta q^{35} + q^{37} + \beta q^{38} + \beta q^{40} - q^{41} + \beta q^{45} -\beta q^{47} - q^{50} - q^{53} + 2 q^{55} + q^{56} -\beta q^{58} - q^{59} + q^{61} - q^{62} + q^{63} + q^{64} + \beta q^{65} + \beta q^{67} + \beta q^{70} - q^{71} + q^{72} -\beta q^{73} + q^{74} -\beta q^{77} + \beta q^{80} + q^{81} - q^{82} -2 q^{85} -\beta q^{88} + q^{89} + \beta q^{90} + q^{91} -\beta q^{94} + 2 q^{95} + q^{97} -\beta q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{2} - 2q^{7} - 2q^{8} - 2q^{9} + O(q^{10}) \) \( 2q + 2q^{2} - 2q^{7} - 2q^{8} - 2q^{9} - 2q^{13} - 2q^{14} - 2q^{16} - 2q^{18} - 2q^{25} - 2q^{26} - 2q^{31} + 2q^{37} - 2q^{41} - 2q^{50} - 2q^{53} + 4q^{55} + 2q^{56} - 2q^{59} + 2q^{61} - 2q^{62} + 2q^{63} + 2q^{64} - 2q^{71} + 2q^{72} + 2q^{74} + 2q^{81} - 2q^{82} - 4q^{85} + 2q^{89} + 2q^{91} + 4q^{95} + 2q^{97} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2183\mathbb{Z}\right)^\times\).

\(n\) \(297\) \(1889\)
\(\chi(n)\) \(-1\) \(-1\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
2182.1
1.41421i
1.41421i
1.00000 0 0 1.41421i 0 −1.00000 −1.00000 −1.00000 1.41421i
2182.2 1.00000 0 0 1.41421i 0 −1.00000 −1.00000 −1.00000 1.41421i
\(n\): 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
2183.d Odd 1 yes

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{1}^{\mathrm{new}}(2183, [\chi])\):

\( T_{2} - 1 \)
\( T_{3} \)