Properties

Label 512.2.g
Level 512512
Weight 22
Character orbit 512.g
Rep. character χ512(65,)\chi_{512}(65,\cdot)
Character field Q(ζ8)\Q(\zeta_{8})
Dimension 4848
Newform subspaces 88
Sturm bound 128128
Trace bound 55

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Defining parameters

Level: N N == 512=29 512 = 2^{9}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 512.g (of order 88 and degree 44)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 32 32
Character field: Q(ζ8)\Q(\zeta_{8})
Newform subspaces: 8 8
Sturm bound: 128128
Trace bound: 55
Distinguishing TpT_p: 33, 55

Dimensions

The following table gives the dimensions of various subspaces of M2(512,[χ])M_{2}(512, [\chi]).

Total New Old
Modular forms 320 80 240
Cusp forms 192 48 144
Eisenstein series 128 32 96

Trace form

48q+16q9+16q2532q33+16q41+16q5732q65+16q73+16q8932q97+O(q100) 48 q + 16 q^{9} + 16 q^{25} - 32 q^{33} + 16 q^{41} + 16 q^{57} - 32 q^{65} + 16 q^{73} + 16 q^{89} - 32 q^{97}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(512,[χ])S_{2}^{\mathrm{new}}(512, [\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}
512.2.g.a 512.g 32.g 44 4.0884.088 Q(ζ8)\Q(\zeta_{8}) None 32.2.g.a 00 4-4 8-8 4-4 SU(2)[C8]\mathrm{SU}(2)[C_{8}] q+(1ζ83)q3+(22ζ8+ζ82+)q5+q+(-1-\zeta_{8}^{3})q^{3}+(-2-2\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{5}+\cdots
512.2.g.b 512.g 32.g 44 4.0884.088 Q(ζ8)\Q(\zeta_{8}) None 32.2.g.a 00 4-4 88 44 SU(2)[C8]\mathrm{SU}(2)[C_{8}] q+(1ζ83)q3+(2+2ζ8ζ82+)q5+q+(-1-\zeta_{8}^{3})q^{3}+(2+2\zeta_{8}-\zeta_{8}^{2}+\cdots)q^{5}+\cdots
512.2.g.c 512.g 32.g 44 4.0884.088 Q(ζ8)\Q(\zeta_{8}) None 32.2.g.a 00 44 8-8 44 SU(2)[C8]\mathrm{SU}(2)[C_{8}] q+(1+ζ83)q3+(22ζ8+ζ82+)q5+q+(1+\zeta_{8}^{3})q^{3}+(-2-2\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{5}+\cdots
512.2.g.d 512.g 32.g 44 4.0884.088 Q(ζ8)\Q(\zeta_{8}) None 32.2.g.a 00 44 88 4-4 SU(2)[C8]\mathrm{SU}(2)[C_{8}] q+(1+ζ83)q3+(2+2ζ8ζ82+ζ83)q5+q+(1+\zeta_{8}^{3})q^{3}+(2+2\zeta_{8}-\zeta_{8}^{2}+\zeta_{8}^{3})q^{5}+\cdots
512.2.g.e 512.g 32.g 88 4.0884.088 8.0.18939904.2 None 32.2.g.b 00 4-4 8-8 88 SU(2)[C8]\mathrm{SU}(2)[C_{8}] q+(1+β4β5)q3+(1β6)q5+q+(-1+\beta _{4}-\beta _{5})q^{3}+(-1-\beta _{6})q^{5}+\cdots
512.2.g.f 512.g 32.g 88 4.0884.088 8.0.18939904.2 None 32.2.g.b 00 4-4 88 8-8 SU(2)[C8]\mathrm{SU}(2)[C_{8}] q+(1+β4β5)q3+(1+β6)q5+q+(-1+\beta _{4}-\beta _{5})q^{3}+(1+\beta _{6})q^{5}+\cdots
512.2.g.g 512.g 32.g 88 4.0884.088 8.0.18939904.2 None 32.2.g.b 00 44 8-8 8-8 SU(2)[C8]\mathrm{SU}(2)[C_{8}] q+(1+β3β4+β7)q3+(1β4+)q5+q+(1+\beta _{3}-\beta _{4}+\beta _{7})q^{3}+(-1-\beta _{4}+\cdots)q^{5}+\cdots
512.2.g.h 512.g 32.g 88 4.0884.088 8.0.18939904.2 None 32.2.g.b 00 44 88 88 SU(2)[C8]\mathrm{SU}(2)[C_{8}] q+(1+β3β4+β7)q3+(1+β4)q5+q+(1+\beta _{3}-\beta _{4}+\beta _{7})q^{3}+(1+\beta _{4})q^{5}+\cdots

Decomposition of S2old(512,[χ])S_{2}^{\mathrm{old}}(512, [\chi]) into lower level spaces

S2old(512,[χ]) S_{2}^{\mathrm{old}}(512, [\chi]) \simeq S2new(32,[χ])S_{2}^{\mathrm{new}}(32, [\chi])5^{\oplus 5}\oplusS2new(128,[χ])S_{2}^{\mathrm{new}}(128, [\chi])3^{\oplus 3}\oplusS2new(256,[χ])S_{2}^{\mathrm{new}}(256, [\chi])2^{\oplus 2}