Properties

Label 252.3.z
Level 252252
Weight 33
Character orbit 252.z
Rep. character χ252(73,)\chi_{252}(73,\cdot)
Character field Q(ζ6)\Q(\zeta_{6})
Dimension 1414
Newform subspaces 55
Sturm bound 144144
Trace bound 77

Related objects

Downloads

Learn more

Defining parameters

Level: N N == 252=22327 252 = 2^{2} \cdot 3^{2} \cdot 7
Weight: k k == 3 3
Character orbit: [χ][\chi] == 252.z (of order 66 and degree 22)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 7 7
Character field: Q(ζ6)\Q(\zeta_{6})
Newform subspaces: 5 5
Sturm bound: 144144
Trace bound: 77
Distinguishing TpT_p: 55, 1111

Dimensions

The following table gives the dimensions of various subspaces of M3(252,[χ])M_{3}(252, [\chi]).

Total New Old
Modular forms 216 14 202
Cusp forms 168 14 154
Eisenstein series 48 0 48

Trace form

14q+3q5+4q73q113q17+45q1921q23+68q25+108q29+105q31+99q35+35q37136q43141q47100q49105q53231q59+39q61+69q95+O(q100) 14 q + 3 q^{5} + 4 q^{7} - 3 q^{11} - 3 q^{17} + 45 q^{19} - 21 q^{23} + 68 q^{25} + 108 q^{29} + 105 q^{31} + 99 q^{35} + 35 q^{37} - 136 q^{43} - 141 q^{47} - 100 q^{49} - 105 q^{53} - 231 q^{59} + 39 q^{61}+ \cdots - 69 q^{95}+O(q^{100}) Copy content Toggle raw display

Decomposition of S3new(252,[χ])S_{3}^{\mathrm{new}}(252, [\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}
252.3.z.a 252.z 7.d 22 6.8676.867 Q(3)\Q(\sqrt{-3}) None 28.3.h.a 00 00 3-3 14-14 SU(2)[C6]\mathrm{SU}(2)[C_{6}] q+(2+ζ6)q57q7+(1515ζ6)q11+q+(-2+\zeta_{6})q^{5}-7q^{7}+(15-15\zeta_{6})q^{11}+\cdots
252.3.z.b 252.z 7.d 22 6.8676.867 Q(3)\Q(\sqrt{-3}) None 84.3.m.a 00 00 3-3 1313 SU(2)[C6]\mathrm{SU}(2)[C_{6}] q+(2+ζ6)q5+(5+3ζ6)q7+(3+)q11+q+(-2+\zeta_{6})q^{5}+(5+3\zeta_{6})q^{7}+(-3+\cdots)q^{11}+\cdots
252.3.z.c 252.z 7.d 22 6.8676.867 Q(3)\Q(\sqrt{-3}) Q(3)\Q(\sqrt{-3}) 252.3.z.c 00 00 00 11-11 U(1)[D6]\mathrm{U}(1)[D_{6}] q+(8+5ζ6)q7+(15+30ζ6)q13+q+(-8+5\zeta_{6})q^{7}+(-15+30\zeta_{6})q^{13}+\cdots
252.3.z.d 252.z 7.d 44 6.8676.867 Q(3,7)\Q(\sqrt{-3}, \sqrt{-7}) None 252.3.z.d 00 00 00 1414 SU(2)[C6]\mathrm{SU}(2)[C_{6}] q+β2q5+(7+7β1)q7+(2β2+β3)q11+q+\beta _{2}q^{5}+(7+7\beta _{1})q^{7}+(-2\beta _{2}+\beta _{3})q^{11}+\cdots
252.3.z.e 252.z 7.d 44 6.8676.867 Q(3,65)\Q(\sqrt{-3}, \sqrt{65}) None 84.3.m.b 00 00 99 22 SU(2)[C6]\mathrm{SU}(2)[C_{6}] q+(2+β1β3)q5+(1β2)q7+(8β1+)q11+q+(2+\beta _{1}-\beta _{3})q^{5}+(1-\beta _{2})q^{7}+(-8\beta _{1}+\cdots)q^{11}+\cdots

Decomposition of S3old(252,[χ])S_{3}^{\mathrm{old}}(252, [\chi]) into lower level spaces