Properties

Label 280.3.c.g
Level $280$
Weight $3$
Character orbit 280.c
Analytic conductor $7.629$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $8$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 280.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.62944740209\)
Analytic rank: \(0\)
Dimension: \(80\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 80q + 12q^{4} - 224q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 80q + 12q^{4} - 224q^{9} + 92q^{14} - 72q^{15} - 172q^{16} - 104q^{25} - 68q^{30} - 564q^{36} - 112q^{39} - 40q^{44} - 224q^{46} + 192q^{49} + 332q^{50} - 356q^{56} + 124q^{60} + 396q^{64} + 472q^{65} + 352q^{70} + 800q^{71} + 672q^{74} + 480q^{79} - 896q^{81} + 408q^{84} + 528q^{86} + 1176q^{95} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
69.1 −1.99206 0.178090i 5.14158i 3.93657 + 0.709530i −3.67215 3.39343i −0.915664 + 10.2423i 3.38765 + 6.12567i −7.71550 2.11449i −17.4359 6.71078 + 7.41387i
69.2 −1.99206 0.178090i 5.14158i 3.93657 + 0.709530i 3.67215 + 3.39343i 0.915664 10.2423i −3.38765 + 6.12567i −7.71550 2.11449i −17.4359 −6.71078 7.41387i
69.3 −1.99206 + 0.178090i 5.14158i 3.93657 0.709530i 3.67215 3.39343i 0.915664 + 10.2423i −3.38765 6.12567i −7.71550 + 2.11449i −17.4359 −6.71078 + 7.41387i
69.4 −1.99206 + 0.178090i 5.14158i 3.93657 0.709530i −3.67215 + 3.39343i −0.915664 10.2423i 3.38765 6.12567i −7.71550 + 2.11449i −17.4359 6.71078 7.41387i
69.5 −1.94895 0.448973i 3.68915i 3.59685 + 1.75006i −0.693644 + 4.95165i −1.65633 + 7.18999i 4.51720 5.34742i −6.22436 5.02567i −4.60986 3.57504 9.33912i
69.6 −1.94895 0.448973i 3.68915i 3.59685 + 1.75006i 0.693644 4.95165i 1.65633 7.18999i −4.51720 5.34742i −6.22436 5.02567i −4.60986 −3.57504 + 9.33912i
69.7 −1.94895 + 0.448973i 3.68915i 3.59685 1.75006i 0.693644 + 4.95165i 1.65633 + 7.18999i −4.51720 + 5.34742i −6.22436 + 5.02567i −4.60986 −3.57504 9.33912i
69.8 −1.94895 + 0.448973i 3.68915i 3.59685 1.75006i −0.693644 4.95165i −1.65633 7.18999i 4.51720 + 5.34742i −6.22436 + 5.02567i −4.60986 3.57504 + 9.33912i
69.9 −1.79455 0.882954i 1.20162i 2.44078 + 3.16900i 1.26609 4.83705i −1.06097 + 2.15635i −2.96368 + 6.34166i −1.58202 7.84202i 7.55612 −6.54294 + 7.56240i
69.10 −1.79455 0.882954i 1.20162i 2.44078 + 3.16900i −1.26609 + 4.83705i 1.06097 2.15635i 2.96368 + 6.34166i −1.58202 7.84202i 7.55612 6.54294 7.56240i
69.11 −1.79455 + 0.882954i 1.20162i 2.44078 3.16900i −1.26609 4.83705i 1.06097 + 2.15635i 2.96368 6.34166i −1.58202 + 7.84202i 7.55612 6.54294 + 7.56240i
69.12 −1.79455 + 0.882954i 1.20162i 2.44078 3.16900i 1.26609 + 4.83705i −1.06097 2.15635i −2.96368 6.34166i −1.58202 + 7.84202i 7.55612 −6.54294 7.56240i
69.13 −1.65383 1.12465i 2.74983i 1.47034 + 3.71996i −4.72637 1.63138i −3.09259 + 4.54776i 1.41172 6.85617i 1.75195 7.80581i 1.43843 5.98192 + 8.01353i
69.14 −1.65383 1.12465i 2.74983i 1.47034 + 3.71996i 4.72637 + 1.63138i 3.09259 4.54776i −1.41172 6.85617i 1.75195 7.80581i 1.43843 −5.98192 8.01353i
69.15 −1.65383 + 1.12465i 2.74983i 1.47034 3.71996i 4.72637 1.63138i 3.09259 + 4.54776i −1.41172 + 6.85617i 1.75195 + 7.80581i 1.43843 −5.98192 + 8.01353i
69.16 −1.65383 + 1.12465i 2.74983i 1.47034 3.71996i −4.72637 + 1.63138i −3.09259 4.54776i 1.41172 + 6.85617i 1.75195 + 7.80581i 1.43843 5.98192 8.01353i
69.17 −1.61056 1.18579i 3.23212i 1.18782 + 3.81957i 3.82711 + 3.21764i −3.83261 + 5.20553i −6.97525 0.588096i 2.61615 7.56014i −1.44659 −2.34837 9.72035i
69.18 −1.61056 1.18579i 3.23212i 1.18782 + 3.81957i −3.82711 3.21764i 3.83261 5.20553i 6.97525 0.588096i 2.61615 7.56014i −1.44659 2.34837 + 9.72035i
69.19 −1.61056 + 1.18579i 3.23212i 1.18782 3.81957i −3.82711 + 3.21764i 3.83261 + 5.20553i 6.97525 + 0.588096i 2.61615 + 7.56014i −1.44659 2.34837 9.72035i
69.20 −1.61056 + 1.18579i 3.23212i 1.18782 3.81957i 3.82711 3.21764i −3.83261 5.20553i −6.97525 + 0.588096i 2.61615 + 7.56014i −1.44659 −2.34837 + 9.72035i
See all 80 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 69.80
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
7.b odd 2 1 inner
8.b even 2 1 inner
35.c odd 2 1 inner
40.f even 2 1 inner
56.h odd 2 1 inner
280.c odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 280.3.c.g 80
4.b odd 2 1 1120.3.c.g 80
5.b even 2 1 inner 280.3.c.g 80
7.b odd 2 1 inner 280.3.c.g 80
8.b even 2 1 inner 280.3.c.g 80
8.d odd 2 1 1120.3.c.g 80
20.d odd 2 1 1120.3.c.g 80
28.d even 2 1 1120.3.c.g 80
35.c odd 2 1 inner 280.3.c.g 80
40.e odd 2 1 1120.3.c.g 80
40.f even 2 1 inner 280.3.c.g 80
56.e even 2 1 1120.3.c.g 80
56.h odd 2 1 inner 280.3.c.g 80
140.c even 2 1 1120.3.c.g 80
280.c odd 2 1 inner 280.3.c.g 80
280.n even 2 1 1120.3.c.g 80
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
280.3.c.g 80 1.a even 1 1 trivial
280.3.c.g 80 5.b even 2 1 inner
280.3.c.g 80 7.b odd 2 1 inner
280.3.c.g 80 8.b even 2 1 inner
280.3.c.g 80 35.c odd 2 1 inner
280.3.c.g 80 40.f even 2 1 inner
280.3.c.g 80 56.h odd 2 1 inner
280.3.c.g 80 280.c odd 2 1 inner
1120.3.c.g 80 4.b odd 2 1
1120.3.c.g 80 8.d odd 2 1
1120.3.c.g 80 20.d odd 2 1
1120.3.c.g 80 28.d even 2 1
1120.3.c.g 80 40.e odd 2 1
1120.3.c.g 80 56.e even 2 1
1120.3.c.g 80 140.c even 2 1
1120.3.c.g 80 280.n even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{3}^{\mathrm{new}}(280, [\chi])\):

\(T_{3}^{20} + \cdots\)
\(19\!\cdots\!29\)\( T_{17}^{12} - \)\(64\!\cdots\!40\)\( T_{17}^{10} + \)\(13\!\cdots\!28\)\( T_{17}^{8} - \)\(17\!\cdots\!20\)\( T_{17}^{6} + \)\(12\!\cdots\!84\)\( T_{17}^{4} - \)\(36\!\cdots\!40\)\( T_{17}^{2} + \)\(11\!\cdots\!00\)\( \)">\(T_{17}^{20} - \cdots\)
\(11\!\cdots\!52\)\( T_{19}^{12} - \)\(25\!\cdots\!04\)\( T_{19}^{10} + \)\(32\!\cdots\!20\)\( T_{19}^{8} - \)\(22\!\cdots\!24\)\( T_{19}^{6} + \)\(85\!\cdots\!08\)\( T_{19}^{4} - \)\(16\!\cdots\!12\)\( T_{19}^{2} + \)\(10\!\cdots\!80\)\( \)">\(T_{19}^{20} - \cdots\)