Properties

Label 504.6.s
Level 504504
Weight 66
Character orbit 504.s
Rep. character χ504(289,)\chi_{504}(289,\cdot)
Character field Q(ζ3)\Q(\zeta_{3})
Dimension 100100
Newform subspaces 88
Sturm bound 576576
Trace bound 55

Related objects

Downloads

Learn more

Defining parameters

Level: N N == 504=23327 504 = 2^{3} \cdot 3^{2} \cdot 7
Weight: k k == 6 6
Character orbit: [χ][\chi] == 504.s (of order 33 and degree 22)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 7 7
Character field: Q(ζ3)\Q(\zeta_{3})
Newform subspaces: 8 8
Sturm bound: 576576
Trace bound: 55
Distinguishing TpT_p: 55

Dimensions

The following table gives the dimensions of various subspaces of M6(504,[χ])M_{6}(504, [\chi]).

Total New Old
Modular forms 992 100 892
Cusp forms 928 100 828
Eisenstein series 64 0 64

Trace form

100q50q524q710q11560q13614q172994q19+722q2332020q2514464q29+2238q3127162q35+5414q376384q41+17288q439426q47+47152q97+O(q100) 100 q - 50 q^{5} - 24 q^{7} - 10 q^{11} - 560 q^{13} - 614 q^{17} - 2994 q^{19} + 722 q^{23} - 32020 q^{25} - 14464 q^{29} + 2238 q^{31} - 27162 q^{35} + 5414 q^{37} - 6384 q^{41} + 17288 q^{43} - 9426 q^{47}+ \cdots - 47152 q^{97}+O(q^{100}) Copy content Toggle raw display

Decomposition of S6new(504,[χ])S_{6}^{\mathrm{new}}(504, [\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}
504.6.s.a 504.s 7.c 88 80.83380.833 Q[x]/(x8)\mathbb{Q}[x]/(x^{8} - \cdots) None 168.6.q.a 00 00 64-64 4242 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+(24β1β2)q5+(2231β13β3+)q7+q+(-2^{4}\beta _{1}-\beta _{2})q^{5}+(22-31\beta _{1}-3\beta _{3}+\cdots)q^{7}+\cdots
504.6.s.b 504.s 7.c 1010 80.83380.833 Q[x]/(x10+)\mathbb{Q}[x]/(x^{10} + \cdots) None 56.6.i.b 00 00 81-81 116116 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+(2424β3β4β5)q5+(15+)q7+q+(-2^{4}-2^{4}\beta _{3}-\beta _{4}-\beta _{5})q^{5}+(15+\cdots)q^{7}+\cdots
504.6.s.c 504.s 7.c 1010 80.83380.833 Q[x]/(x10+)\mathbb{Q}[x]/(x^{10} + \cdots) None 168.6.q.c 00 00 66 97-97 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+(β1β5)q5+(59β1+β3+β5+)q7+q+(\beta _{1}-\beta _{5})q^{5}+(-5-9\beta _{1}+\beta _{3}+\beta _{5}+\cdots)q^{7}+\cdots
504.6.s.d 504.s 7.c 1010 80.83380.833 Q[x]/(x10)\mathbb{Q}[x]/(x^{10} - \cdots) None 56.6.i.a 00 00 3131 92-92 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+(6β1+β5+β7)q5+(2413β1+)q7+q+(-6\beta _{1}+\beta _{5}+\beta _{7})q^{5}+(-2^{4}-13\beta _{1}+\cdots)q^{7}+\cdots
504.6.s.e 504.s 7.c 1010 80.83380.833 Q[x]/(x10)\mathbb{Q}[x]/(x^{10} - \cdots) None 168.6.q.b 00 00 7575 113-113 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+(15β1β2+β4)q5+(133β1+)q7+q+(-15\beta _{1}-\beta _{2}+\beta _{4})q^{5}+(-13-3\beta _{1}+\cdots)q^{7}+\cdots
504.6.s.f 504.s 7.c 1212 80.83380.833 Q[x]/(x12)\mathbb{Q}[x]/(x^{12} - \cdots) None 168.6.q.d 00 00 17-17 144144 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+(3β1β2+β4)q5+(8+9β1+)q7+q+(-3\beta _{1}-\beta _{2}+\beta _{4})q^{5}+(8+9\beta _{1}+\cdots)q^{7}+\cdots
504.6.s.g 504.s 7.c 2020 80.83380.833 Q[x]/(x20)\mathbb{Q}[x]/(x^{20} - \cdots) None 504.6.s.g 00 00 19-19 12-12 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+(β12β2β3)q5+(25β2+)q7+q+(-\beta _{1}-2\beta _{2}-\beta _{3})q^{5}+(2-5\beta _{2}+\cdots)q^{7}+\cdots
504.6.s.h 504.s 7.c 2020 80.83380.833 Q[x]/(x20)\mathbb{Q}[x]/(x^{20} - \cdots) None 504.6.s.g 00 00 1919 12-12 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+(β1+2β2+β3)q5+(25β2+β6+)q7+q+(\beta _{1}+2\beta _{2}+\beta _{3})q^{5}+(2-5\beta _{2}+\beta _{6}+\cdots)q^{7}+\cdots

Decomposition of S6old(504,[χ])S_{6}^{\mathrm{old}}(504, [\chi]) into lower level spaces