Properties

Label 252.2.j
Level 252252
Weight 22
Character orbit 252.j
Rep. character χ252(85,)\chi_{252}(85,\cdot)
Character field Q(ζ3)\Q(\zeta_{3})
Dimension 1212
Newform subspaces 22
Sturm bound 9696
Trace bound 33

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Defining parameters

Level: N N == 252=22327 252 = 2^{2} \cdot 3^{2} \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 252.j (of order 33 and degree 22)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 9 9
Character field: Q(ζ3)\Q(\zeta_{3})
Newform subspaces: 2 2
Sturm bound: 9696
Trace bound: 33
Distinguishing TpT_p: 55

Dimensions

The following table gives the dimensions of various subspaces of M2(252,[χ])M_{2}(252, [\chi]).

Total New Old
Modular forms 108 12 96
Cusp forms 84 12 72
Eisenstein series 24 0 24

Trace form

12q+2q5+4q9+4q112q15+4q17+12q192q218q23+14q29+6q31+8q338q3512q3720q39+6q416q4310q456q47+32q99+O(q100) 12 q + 2 q^{5} + 4 q^{9} + 4 q^{11} - 2 q^{15} + 4 q^{17} + 12 q^{19} - 2 q^{21} - 8 q^{23} + 14 q^{29} + 6 q^{31} + 8 q^{33} - 8 q^{35} - 12 q^{37} - 20 q^{39} + 6 q^{41} - 6 q^{43} - 10 q^{45} - 6 q^{47}+ \cdots - 32 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(252,[χ])S_{2}^{\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}
252.2.j.a 252.j 9.c 66 2.0122.012 6.0.309123.1 None 252.2.j.a 00 2-2 1-1 33 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+(β2+β4)q3+(β1+β5)q5+(1+)q7+q+(\beta _{2}+\beta _{4})q^{3}+(-\beta _{1}+\beta _{5})q^{5}+(1+\cdots)q^{7}+\cdots
252.2.j.b 252.j 9.c 66 2.0122.012 6.0.309123.1 None 252.2.j.b 00 22 33 3-3 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+(1+β3+β4)q3+(β1β2β3+)q5+q+(1+\beta _{3}+\beta _{4})q^{3}+(-\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots

Decomposition of S2old(252,[χ])S_{2}^{\mathrm{old}}(252, [\chi]) into lower level spaces

S2old(252,[χ]) S_{2}^{\mathrm{old}}(252, [\chi]) \simeq S2new(18,[χ])S_{2}^{\mathrm{new}}(18, [\chi])4^{\oplus 4}\oplusS2new(36,[χ])S_{2}^{\mathrm{new}}(36, [\chi])2^{\oplus 2}\oplusS2new(63,[χ])S_{2}^{\mathrm{new}}(63, [\chi])3^{\oplus 3}\oplusS2new(126,[χ])S_{2}^{\mathrm{new}}(126, [\chi])2^{\oplus 2}