Properties

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

Related objects

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: Complex embeddings Normalized embeddings Satake parameters Satake angles

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.d yes 24
4.b odd 2 1 inner 2240.2.l.d yes 24
5.b even 2 1 2240.2.l.c 24
8.b even 2 1 2240.2.l.c 24
8.d odd 2 1 2240.2.l.c 24
20.d odd 2 1 2240.2.l.c 24
40.e odd 2 1 inner 2240.2.l.d yes 24
40.f even 2 1 inner 2240.2.l.d yes 24

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2240.2.l.c 24 5.b even 2 1
2240.2.l.c 24 8.b even 2 1
2240.2.l.c 24 8.d odd 2 1
2240.2.l.c 24 20.d odd 2 1
2240.2.l.d yes 24 1.a even 1 1 trivial
2240.2.l.d yes 24 4.b odd 2 1 inner
2240.2.l.d yes 24 40.e odd 2 1 inner
2240.2.l.d yes 24 40.f 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 $$S_{2}^{\mathrm{new}}(2240, [\chi])$$:

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