Properties

Label 546.2.j
Level 546546
Weight 22
Character orbit 546.j
Rep. character χ546(289,)\chi_{546}(289,\cdot)
Character field Q(ζ3)\Q(\zeta_{3})
Dimension 3636
Newform subspaces 55
Sturm bound 224224
Trace bound 33

Related objects

Downloads

Learn more

Defining parameters

Level: N N == 546=23713 546 = 2 \cdot 3 \cdot 7 \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 546.j (of order 33 and degree 22)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 91 91
Character field: Q(ζ3)\Q(\zeta_{3})
Newform subspaces: 5 5
Sturm bound: 224224
Trace bound: 33
Distinguishing TpT_p: 55

Dimensions

The following table gives the dimensions of various subspaces of M2(546,[χ])M_{2}(546, [\chi]).

Total New Old
Modular forms 240 36 204
Cusp forms 208 36 172
Eisenstein series 32 0 32

Trace form

36q+2q3+36q4+2q718q9+8q10+4q11+2q12+2q13+36q16+8q17+6q192q214q2216q236q254q264q27+2q28+8q99+O(q100) 36 q + 2 q^{3} + 36 q^{4} + 2 q^{7} - 18 q^{9} + 8 q^{10} + 4 q^{11} + 2 q^{12} + 2 q^{13} + 36 q^{16} + 8 q^{17} + 6 q^{19} - 2 q^{21} - 4 q^{22} - 16 q^{23} - 6 q^{25} - 4 q^{26} - 4 q^{27} + 2 q^{28}+ \cdots - 8 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(546,[χ])S_{2}^{\mathrm{new}}(546, [\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}
546.2.j.a 546.j 91.h 22 4.3604.360 Q(3)\Q(\sqrt{-3}) None 546.2.j.a 22 11 00 11 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+q2+ζ6q3+q4+ζ6q6+(23ζ6)q7+q+q^{2}+\zeta_{6}q^{3}+q^{4}+\zeta_{6}q^{6}+(2-3\zeta_{6})q^{7}+\cdots
546.2.j.b 546.j 91.h 88 4.3604.360 8.0.6498455769.2 None 546.2.j.b 8-8 4-4 2-2 33 SU(2)[C3]\mathrm{SU}(2)[C_{3}] qq2β4q3+q4+β2q5+β4q6+q-q^{2}-\beta _{4}q^{3}+q^{4}+\beta _{2}q^{5}+\beta _{4}q^{6}+\cdots
546.2.j.c 546.j 91.h 88 4.3604.360 8.0.447703281.1 None 546.2.j.c 88 4-4 22 33 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+q2+(1+β2)q3+q4+(1β2+)q5+q+q^{2}+(-1+\beta _{2})q^{3}+q^{4}+(1-\beta _{2}+\cdots)q^{5}+\cdots
546.2.j.d 546.j 91.h 88 4.3604.360 8.0.447703281.1 None 546.2.j.d 88 44 22 3-3 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+q2β3q3+q4+(2β1+2β2β3+)q5+q+q^{2}-\beta _{3}q^{3}+q^{4}+(2\beta _{1}+2\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots
546.2.j.e 546.j 91.h 1010 4.3604.360 Q[x]/(x10)\mathbb{Q}[x]/(x^{10} - \cdots) None 546.2.j.e 10-10 55 2-2 2-2 SU(2)[C3]\mathrm{SU}(2)[C_{3}] qq2+(1+β5)q3+q4β1q5+(1+)q6+q-q^{2}+(1+\beta _{5})q^{3}+q^{4}-\beta _{1}q^{5}+(-1+\cdots)q^{6}+\cdots

Decomposition of S2old(546,[χ])S_{2}^{\mathrm{old}}(546, [\chi]) into lower level spaces

S2old(546,[χ]) S_{2}^{\mathrm{old}}(546, [\chi]) \simeq S2new(91,[χ])S_{2}^{\mathrm{new}}(91, [\chi])4^{\oplus 4}\oplusS2new(182,[χ])S_{2}^{\mathrm{new}}(182, [\chi])2^{\oplus 2}\oplusS2new(273,[χ])S_{2}^{\mathrm{new}}(273, [\chi])2^{\oplus 2}