Properties

Label 36.2.h
Level 3636
Weight 22
Character orbit 36.h
Rep. character χ36(11,)\chi_{36}(11,\cdot)
Character field Q(ζ6)\Q(\zeta_{6})
Dimension 88
Newform subspaces 11
Sturm bound 1212
Trace bound 00

Related objects

Downloads

Learn more

Defining parameters

Level: N N == 36=2232 36 = 2^{2} \cdot 3^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 36.h (of order 66 and degree 22)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 36 36
Character field: Q(ζ6)\Q(\zeta_{6})
Newform subspaces: 1 1
Sturm bound: 1212
Trace bound: 00

Dimensions

The following table gives the dimensions of various subspaces of M2(36,[χ])M_{2}(36, [\chi]).

Total New Old
Modular forms 16 16 0
Cusp forms 8 8 0
Eisenstein series 8 8 0

Trace form

8q3q2q46q53q66q98q10+6q122q13+12q14q16+18q18+18q206q21+3q22+3q246q2512q28+6q2918q30++4q97+O(q100) 8 q - 3 q^{2} - q^{4} - 6 q^{5} - 3 q^{6} - 6 q^{9} - 8 q^{10} + 6 q^{12} - 2 q^{13} + 12 q^{14} - q^{16} + 18 q^{18} + 18 q^{20} - 6 q^{21} + 3 q^{22} + 3 q^{24} - 6 q^{25} - 12 q^{28} + 6 q^{29} - 18 q^{30}+ \cdots + 4 q^{97}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(36,[χ])S_{2}^{\mathrm{new}}(36, [\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}
36.2.h.a 36.h 36.h 88 0.2870.287 8.0.170772624.1 None 36.2.h.a 3-3 00 6-6 00 SU(2)[C6]\mathrm{SU}(2)[C_{6}] q+(1β1+β4+β7)q2+(β2β3+)q3+q+(1-\beta _{1}+\beta _{4}+\beta _{7})q^{2}+(-\beta _{2}-\beta _{3}+\cdots)q^{3}+\cdots