Properties

Label 560.2.bw
Level 560560
Weight 22
Character orbit 560.bw
Rep. character χ560(289,)\chi_{560}(289,\cdot)
Character field Q(ζ6)\Q(\zeta_{6})
Dimension 4444
Newform subspaces 66
Sturm bound 192192
Trace bound 99

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Defining parameters

Level: N N == 560=2457 560 = 2^{4} \cdot 5 \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 560.bw (of order 66 and degree 22)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 35 35
Character field: Q(ζ6)\Q(\zeta_{6})
Newform subspaces: 6 6
Sturm bound: 192192
Trace bound: 99
Distinguishing TpT_p: 33

Dimensions

The following table gives the dimensions of various subspaces of M2(560,[χ])M_{2}(560, [\chi]).

Total New Old
Modular forms 216 52 164
Cusp forms 168 44 124
Eisenstein series 48 8 40

Trace form

44qq5+16q9+2q11+10q15+14q1914q215q25+14q31+13q3516q3916q41+12q4520q49+26q5118q55+30q592q61++8q99+O(q100) 44 q - q^{5} + 16 q^{9} + 2 q^{11} + 10 q^{15} + 14 q^{19} - 14 q^{21} - 5 q^{25} + 14 q^{31} + 13 q^{35} - 16 q^{39} - 16 q^{41} + 12 q^{45} - 20 q^{49} + 26 q^{51} - 18 q^{55} + 30 q^{59} - 2 q^{61}+ \cdots + 8 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(560,[χ])S_{2}^{\mathrm{new}}(560, [\chi]) into newform subspaces

Label Char Prim Dim AA Field CM Minimal twist Traces Sato-Tate qq-expansion
a2a_{2} a3a_{3} a5a_{5} a7a_{7}
560.2.bw.a 560.bw 35.j 44 4.4724.472 Q(3,19)\Q(\sqrt{-3}, \sqrt{-19}) None 140.2.q.a 00 6-6 2-2 3-3 SU(2)[C6]\mathrm{SU}(2)[C_{6}] q+(1β2)q3+(1+β1β3)q5+q+(-1-\beta _{2})q^{3}+(-1+\beta _{1}-\beta _{3})q^{5}+\cdots
560.2.bw.b 560.bw 35.j 44 4.4724.472 Q(ζ12)\Q(\zeta_{12}) None 35.2.j.a 00 00 2-2 00 SU(2)[C6]\mathrm{SU}(2)[C_{6}] q+ζ12q3+(2ζ12ζ122+2ζ123)q5+q+\zeta_{12}q^{3}+(-2\zeta_{12}-\zeta_{12}^{2}+2\zeta_{12}^{3})q^{5}+\cdots
560.2.bw.c 560.bw 35.j 44 4.4724.472 Q(ζ12)\Q(\zeta_{12}) None 70.2.i.a 00 00 2-2 00 SU(2)[C6]\mathrm{SU}(2)[C_{6}] q+3ζ12q3+(2ζ12ζ1222ζ123)q5+q+3\zeta_{12}q^{3}+(2\zeta_{12}-\zeta_{12}^{2}-2\zeta_{12}^{3})q^{5}+\cdots
560.2.bw.d 560.bw 35.j 44 4.4724.472 Q(ζ12)\Q(\zeta_{12}) None 70.2.i.b 00 00 44 00 SU(2)[C6]\mathrm{SU}(2)[C_{6}] q+(ζ12+2ζ122ζ123)q5+(2ζ12+)q7+q+(\zeta_{12}+2\zeta_{12}^{2}-\zeta_{12}^{3})q^{5}+(-2\zeta_{12}+\cdots)q^{7}+\cdots
560.2.bw.e 560.bw 35.j 44 4.4724.472 Q(3,19)\Q(\sqrt{-3}, \sqrt{-19}) None 140.2.q.a 00 66 11 33 SU(2)[C6]\mathrm{SU}(2)[C_{6}] q+(1+β2)q3+(1β1β2)q5+(2β2+)q7+q+(1+\beta _{2})q^{3}+(1-\beta _{1}-\beta _{2})q^{5}+(2\beta _{2}+\cdots)q^{7}+\cdots
560.2.bw.f 560.bw 35.j 2424 4.4724.472 None 280.2.bg.a 00 00 00 00 SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Decomposition of S2old(560,[χ])S_{2}^{\mathrm{old}}(560, [\chi]) into lower level spaces

S2old(560,[χ]) S_{2}^{\mathrm{old}}(560, [\chi]) \simeq S2new(35,[χ])S_{2}^{\mathrm{new}}(35, [\chi])5^{\oplus 5}\oplusS2new(70,[χ])S_{2}^{\mathrm{new}}(70, [\chi])4^{\oplus 4}\oplusS2new(140,[χ])S_{2}^{\mathrm{new}}(140, [\chi])3^{\oplus 3}\oplusS2new(280,[χ])S_{2}^{\mathrm{new}}(280, [\chi])2^{\oplus 2}