Properties

Label 80.6.c
Level 8080
Weight 66
Character orbit 80.c
Rep. character χ80(49,)\chi_{80}(49,\cdot)
Character field Q\Q
Dimension 1414
Newform subspaces 44
Sturm bound 7272
Trace bound 55

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Defining parameters

Level: N N == 80=245 80 = 2^{4} \cdot 5
Weight: k k == 6 6
Character orbit: [χ][\chi] == 80.c (of order 22 and degree 11)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 5 5
Character field: Q\Q
Newform subspaces: 4 4
Sturm bound: 7272
Trace bound: 55
Distinguishing TpT_p: 33

Dimensions

The following table gives the dimensions of various subspaces of M6(80,[χ])M_{6}(80, [\chi]).

Total New Old
Modular forms 66 16 50
Cusp forms 54 14 40
Eisenstein series 12 2 10

Trace form

14q+18q5974q9+728q11+1192q15984q19+1304q21586q25+8260q299344q3112712q35+10544q39+3580q4110578q4531222q49+73088q51+152024q99+O(q100) 14 q + 18 q^{5} - 974 q^{9} + 728 q^{11} + 1192 q^{15} - 984 q^{19} + 1304 q^{21} - 586 q^{25} + 8260 q^{29} - 9344 q^{31} - 12712 q^{35} + 10544 q^{39} + 3580 q^{41} - 10578 q^{45} - 31222 q^{49} + 73088 q^{51}+ \cdots - 152024 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S6new(80,[χ])S_{6}^{\mathrm{new}}(80, [\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}
80.6.c.a 80.c 5.b 22 12.83112.831 Q(11)\Q(\sqrt{-11}) None 5.6.b.a 00 00 90-90 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q3βq3+(455β)q59βq7+q-3\beta q^{3}+(-45-5\beta )q^{5}-9\beta q^{7}+\cdots
80.6.c.b 80.c 5.b 22 12.83112.831 Q(31)\Q(\sqrt{-31}) None 20.6.c.a 00 00 10-10 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] qβq3+(5+5β)q511βq7+119q9+q-\beta q^{3}+(-5+5\beta )q^{5}-11\beta q^{7}+119q^{9}+\cdots
80.6.c.c 80.c 5.b 22 12.83112.831 Q(1)\Q(\sqrt{-1}) None 10.6.b.a 00 00 110110 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+7βq3+(5β+55)q579βq7+q+7\beta q^{3}+(-5\beta+55)q^{5}-79\beta q^{7}+\cdots
80.6.c.d 80.c 5.b 88 12.83112.831 Q[x]/(x8+)\mathbb{Q}[x]/(x^{8} + \cdots) None 40.6.c.a 00 00 88 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+β1q3+(1β2)q5+(β2β6+)q7+q+\beta _{1}q^{3}+(1-\beta _{2})q^{5}+(-\beta _{2}-\beta _{6}+\cdots)q^{7}+\cdots

Decomposition of S6old(80,[χ])S_{6}^{\mathrm{old}}(80, [\chi]) into lower level spaces

S6old(80,[χ]) S_{6}^{\mathrm{old}}(80, [\chi]) \simeq S6new(5,[χ])S_{6}^{\mathrm{new}}(5, [\chi])5^{\oplus 5}\oplusS6new(10,[χ])S_{6}^{\mathrm{new}}(10, [\chi])4^{\oplus 4}\oplusS6new(20,[χ])S_{6}^{\mathrm{new}}(20, [\chi])3^{\oplus 3}\oplusS6new(40,[χ])S_{6}^{\mathrm{new}}(40, [\chi])2^{\oplus 2}