Properties

Label 2240.2.l.c
Level $2240$
Weight $2$
Character orbit 2240.l
Analytic conductor $17.886$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2240.l (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(17.8864900528\)
Analytic rank: \(0\)
Dimension: \(24\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24q - 4q^{5} + 12q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 24q - 4q^{5} + 12q^{9} - 4q^{13} - 24q^{37} - 48q^{45} - 24q^{49} + 88q^{53} + 36q^{65} + 20q^{77} + 16q^{81} - 56q^{85} - 40q^{89} + 24q^{93} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1569.1 0 −3.11575 0 −0.660542 2.13628i 0 1.00000i 0 6.70793 0
1569.2 0 −3.11575 0 −0.660542 + 2.13628i 0 1.00000i 0 6.70793 0
1569.3 0 −2.41750 0 −1.94498 1.10320i 0 1.00000i 0 2.84431 0
1569.4 0 −2.41750 0 −1.94498 + 1.10320i 0 1.00000i 0 2.84431 0
1569.5 0 −1.58895 0 1.82232 1.29582i 0 1.00000i 0 −0.475223 0
1569.6 0 −1.58895 0 1.82232 + 1.29582i 0 1.00000i 0 −0.475223 0
1569.7 0 −1.29255 0 0.437032 2.19294i 0 1.00000i 0 −1.32931 0
1569.8 0 −1.29255 0 0.437032 + 2.19294i 0 1.00000i 0 −1.32931 0
1569.9 0 −1.09381 0 −2.20510 0.370875i 0 1.00000i 0 −1.80358 0
1569.10 0 −1.09381 0 −2.20510 + 0.370875i 0 1.00000i 0 −1.80358 0
1569.11 0 −0.236390 0 1.55127 + 1.61046i 0 1.00000i 0 −2.94412 0
1569.12 0 −0.236390 0 1.55127 1.61046i 0 1.00000i 0 −2.94412 0
1569.13 0 0.236390 0 1.55127 1.61046i 0 1.00000i 0 −2.94412 0
1569.14 0 0.236390 0 1.55127 + 1.61046i 0 1.00000i 0 −2.94412 0
1569.15 0 1.09381 0 −2.20510 + 0.370875i 0 1.00000i 0 −1.80358 0
1569.16 0 1.09381 0 −2.20510 0.370875i 0 1.00000i 0 −1.80358 0
1569.17 0 1.29255 0 0.437032 + 2.19294i 0 1.00000i 0 −1.32931 0
1569.18 0 1.29255 0 0.437032 2.19294i 0 1.00000i 0 −1.32931 0
1569.19 0 1.58895 0 1.82232 + 1.29582i 0 1.00000i 0 −0.475223 0
1569.20 0 1.58895 0 1.82232 1.29582i 0 1.00000i 0 −0.475223 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1569.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
4.b odd 2 1 inner
40.e odd 2 1 inner
40.f even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2240.2.l.c 24
4.b odd 2 1 inner 2240.2.l.c 24
5.b even 2 1 2240.2.l.d yes 24
8.b even 2 1 2240.2.l.d yes 24
8.d odd 2 1 2240.2.l.d yes 24
20.d odd 2 1 2240.2.l.d yes 24
40.e odd 2 1 inner 2240.2.l.c 24
40.f even 2 1 inner 2240.2.l.c 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2240.2.l.c 24 1.a even 1 1 trivial
2240.2.l.c 24 4.b odd 2 1 inner
2240.2.l.c 24 40.e odd 2 1 inner
2240.2.l.c 24 40.f even 2 1 inner
2240.2.l.d yes 24 5.b even 2 1
2240.2.l.d yes 24 8.b even 2 1
2240.2.l.d yes 24 8.d odd 2 1
2240.2.l.d yes 24 20.d odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(2240, [\chi])\):

\( T_{3}^{12} - 21 T_{3}^{10} + 151 T_{3}^{8} - 463 T_{3}^{6} + 628 T_{3}^{4} - 320 T_{3}^{2} + 16 \)
\( T_{13}^{6} + T_{13}^{5} - 33 T_{13}^{4} + 3 T_{13}^{3} + 260 T_{13}^{2} - 124 T_{13} - 356 \)