Properties

Label 1840.2.m.g
Level $1840$
Weight $2$
Character orbit 1840.m
Analytic conductor $14.692$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1840.m (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.6924739719\)
Analytic rank: \(0\)
Dimension: \(40\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 40q + 80q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 40q + 80q^{9} - 24q^{25} + 24q^{41} - 16q^{49} + 80q^{69} + 40q^{81} - 8q^{85} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1839.1 0 −3.28652 0 1.54120 + 1.62009i 0 2.73174i 0 7.80121 0
1839.2 0 −3.28652 0 −1.54120 + 1.62009i 0 2.73174i 0 7.80121 0
1839.3 0 −3.28652 0 −1.54120 1.62009i 0 2.73174i 0 7.80121 0
1839.4 0 −3.28652 0 1.54120 1.62009i 0 2.73174i 0 7.80121 0
1839.5 0 −2.49894 0 −2.19676 + 0.417445i 0 3.04922i 0 3.24468 0
1839.6 0 −2.49894 0 2.19676 + 0.417445i 0 3.04922i 0 3.24468 0
1839.7 0 −2.49894 0 2.19676 0.417445i 0 3.04922i 0 3.24468 0
1839.8 0 −2.49894 0 −2.19676 0.417445i 0 3.04922i 0 3.24468 0
1839.9 0 −2.20329 0 1.71768 1.43163i 0 0.642617i 0 1.85447 0
1839.10 0 −2.20329 0 −1.71768 + 1.43163i 0 0.642617i 0 1.85447 0
1839.11 0 −2.20329 0 −1.71768 1.43163i 0 0.642617i 0 1.85447 0
1839.12 0 −2.20329 0 1.71768 + 1.43163i 0 0.642617i 0 1.85447 0
1839.13 0 −1.49850 0 0.689327 + 2.12716i 0 4.18735i 0 −0.754490 0
1839.14 0 −1.49850 0 −0.689327 2.12716i 0 4.18735i 0 −0.754490 0
1839.15 0 −1.49850 0 −0.689327 + 2.12716i 0 4.18735i 0 −0.754490 0
1839.16 0 −1.49850 0 0.689327 2.12716i 0 4.18735i 0 −0.754490 0
1839.17 0 −0.924187 0 0.611037 2.15096i 0 1.51428i 0 −2.14588 0
1839.18 0 −0.924187 0 −0.611037 2.15096i 0 1.51428i 0 −2.14588 0
1839.19 0 −0.924187 0 −0.611037 + 2.15096i 0 1.51428i 0 −2.14588 0
1839.20 0 −0.924187 0 0.611037 + 2.15096i 0 1.51428i 0 −2.14588 0
See all 40 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1839.40
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
4.b odd 2 1 inner
5.b even 2 1 inner
20.d odd 2 1 inner
23.b odd 2 1 inner
92.b even 2 1 inner
115.c odd 2 1 inner
460.g even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1840.2.m.g 40
4.b odd 2 1 inner 1840.2.m.g 40
5.b even 2 1 inner 1840.2.m.g 40
20.d odd 2 1 inner 1840.2.m.g 40
23.b odd 2 1 inner 1840.2.m.g 40
92.b even 2 1 inner 1840.2.m.g 40
115.c odd 2 1 inner 1840.2.m.g 40
460.g even 2 1 inner 1840.2.m.g 40
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1840.2.m.g 40 1.a even 1 1 trivial
1840.2.m.g 40 4.b odd 2 1 inner
1840.2.m.g 40 5.b even 2 1 inner
1840.2.m.g 40 20.d odd 2 1 inner
1840.2.m.g 40 23.b odd 2 1 inner
1840.2.m.g 40 92.b even 2 1 inner
1840.2.m.g 40 115.c odd 2 1 inner
1840.2.m.g 40 460.g even 2 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(1840, [\chi])\):

\( T_{3}^{10} - 25 T_{3}^{8} + 220 T_{3}^{6} - 835 T_{3}^{4} + 1303 T_{3}^{2} - 628 \)
\( T_{7}^{10} + 37 T_{7}^{8} + 457 T_{7}^{6} + 2232 T_{7}^{4} + 3636 T_{7}^{2} + 1152 \)