Properties

Label 1568.2.t
Level 15681568
Weight 22
Character orbit 1568.t
Rep. character χ1568(177,)\chi_{1568}(177,\cdot)
Character field Q(ζ6)\Q(\zeta_{6})
Dimension 7272
Newform subspaces 88
Sturm bound 448448
Trace bound 1717

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Defining parameters

Level: N N == 1568=2572 1568 = 2^{5} \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1568.t (of order 66 and degree 22)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 56 56
Character field: Q(ζ6)\Q(\zeta_{6})
Newform subspaces: 8 8
Sturm bound: 448448
Trace bound: 1717
Distinguishing TpT_p: 33, 1717

Dimensions

The following table gives the dimensions of various subspaces of M2(1568,[χ])M_{2}(1568, [\chi]).

Total New Old
Modular forms 512 88 424
Cusp forms 384 72 312
Eisenstein series 128 16 112

Trace form

72q+30q9+4q15+2q17+6q23+22q25+10q31+14q33+4q39+8q41+30q47+4q5520q578q65+64q71+10q7342q7916q8120q87+40q97+O(q100) 72 q + 30 q^{9} + 4 q^{15} + 2 q^{17} + 6 q^{23} + 22 q^{25} + 10 q^{31} + 14 q^{33} + 4 q^{39} + 8 q^{41} + 30 q^{47} + 4 q^{55} - 20 q^{57} - 8 q^{65} + 64 q^{71} + 10 q^{73} - 42 q^{79} - 16 q^{81} - 20 q^{87}+ \cdots - 40 q^{97}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(1568,[χ])S_{2}^{\mathrm{new}}(1568, [\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}
1568.2.t.a 1568.t 56.p 44 12.52112.521 Q(3,7)\Q(\sqrt{-3}, \sqrt{-7}) Q(7)\Q(\sqrt{-7}) 392.2.b.a 00 00 00 00 U(1)[D6]\mathrm{U}(1)[D_{6}] q+(33β1)q9+β2q11+(8+8β1+)q23+q+(-3-3\beta _{1})q^{9}+\beta _{2}q^{11}+(8+8\beta _{1}+\cdots)q^{23}+\cdots
1568.2.t.b 1568.t 56.p 44 12.52112.521 Q(2,3)\Q(\sqrt{-2}, \sqrt{-3}) None 56.2.b.a 00 00 00 00 SU(2)[C6]\mathrm{SU}(2)[C_{6}] q+β1q3+(β1+β3)q5β2q9+q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{3})q^{5}-\beta _{2}q^{9}+\cdots
1568.2.t.c 1568.t 56.p 44 12.52112.521 Q(2,3)\Q(\sqrt{-2}, \sqrt{-3}) None 56.2.b.a 00 00 00 00 SU(2)[C6]\mathrm{SU}(2)[C_{6}] q+β1q3+(β1+β3)q5β2q9+q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{3})q^{5}-\beta _{2}q^{9}+\cdots
1568.2.t.d 1568.t 56.p 88 12.52112.521 8.0.432972864.2 None 56.2.b.b 00 00 00 00 SU(2)[C6]\mathrm{SU}(2)[C_{6}] qβ2q3β3q5+(2+2β1+β4β7)q9+q-\beta _{2}q^{3}-\beta _{3}q^{5}+(2+2\beta _{1}+\beta _{4}-\beta _{7})q^{9}+\cdots
1568.2.t.e 1568.t 56.p 88 12.52112.521 8.0.432972864.2 None 56.2.b.b 00 00 00 00 SU(2)[C6]\mathrm{SU}(2)[C_{6}] qβ2q3β3q5+(2+2β1+β4β7)q9+q-\beta _{2}q^{3}-\beta _{3}q^{5}+(2+2\beta _{1}+\beta _{4}-\beta _{7})q^{9}+\cdots
1568.2.t.f 1568.t 56.p 88 12.52112.521 8.0.\cdots.10 Q(14)\Q(\sqrt{-14}) 392.2.b.d 00 00 00 00 U(1)[D6]\mathrm{U}(1)[D_{6}] q+β5q3+β3q5+(3β1β6)q9+(2β4+)q13+q+\beta _{5}q^{3}+\beta _{3}q^{5}+(3\beta _{1}-\beta _{6})q^{9}+(-2\beta _{4}+\cdots)q^{13}+\cdots
1568.2.t.g 1568.t 56.p 1212 12.52112.521 12.0.\cdots.1 None 56.2.p.a 00 00 00 00 SU(2)[C6]\mathrm{SU}(2)[C_{6}] qβ10q3+(β4+β7)q5+(β1+)q9+q-\beta _{10}q^{3}+(-\beta _{4}+\beta _{7})q^{5}+(-\beta _{1}+\cdots)q^{9}+\cdots
1568.2.t.h 1568.t 56.p 2424 12.52112.521 None 392.2.b.g 00 00 00 00 SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Decomposition of S2old(1568,[χ])S_{2}^{\mathrm{old}}(1568, [\chi]) into lower level spaces

S2old(1568,[χ]) S_{2}^{\mathrm{old}}(1568, [\chi]) \simeq S2new(56,[χ])S_{2}^{\mathrm{new}}(56, [\chi])6^{\oplus 6}\oplusS2new(224,[χ])S_{2}^{\mathrm{new}}(224, [\chi])2^{\oplus 2}\oplusS2new(392,[χ])S_{2}^{\mathrm{new}}(392, [\chi])3^{\oplus 3}