Properties

Label 150.2.g
Level 150150
Weight 22
Character orbit 150.g
Rep. character χ150(31,)\chi_{150}(31,\cdot)
Character field Q(ζ5)\Q(\zeta_{5})
Dimension 1616
Newform subspaces 33
Sturm bound 6060
Trace bound 22

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Defining parameters

Level: N N == 150=2352 150 = 2 \cdot 3 \cdot 5^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 150.g (of order 55 and degree 44)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 25 25
Character field: Q(ζ5)\Q(\zeta_{5})
Newform subspaces: 3 3
Sturm bound: 6060
Trace bound: 22
Distinguishing TpT_p: 77

Dimensions

The following table gives the dimensions of various subspaces of M2(150,[χ])M_{2}(150, [\chi]).

Total New Old
Modular forms 136 16 120
Cusp forms 104 16 88
Eisenstein series 32 0 32

Trace form

16q+2q24q4+6q5+2q6+12q7+2q84q9+4q1012q11+12q13+6q154q168q178q188q194q20+4q218q2236q23++8q99+O(q100) 16 q + 2 q^{2} - 4 q^{4} + 6 q^{5} + 2 q^{6} + 12 q^{7} + 2 q^{8} - 4 q^{9} + 4 q^{10} - 12 q^{11} + 12 q^{13} + 6 q^{15} - 4 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 4 q^{20} + 4 q^{21} - 8 q^{22} - 36 q^{23}+ \cdots + 8 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(150,[χ])S_{2}^{\mathrm{new}}(150, [\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}
150.2.g.a 150.g 25.d 44 1.1981.198 Q(ζ10)\Q(\zeta_{10}) None 150.2.g.a 1-1 11 55 66 SU(2)[C5]\mathrm{SU}(2)[C_{5}] q+(1+ζ10ζ102+ζ103)q2+q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots
150.2.g.b 150.g 25.d 44 1.1981.198 Q(ζ10)\Q(\zeta_{10}) None 150.2.g.b 11 11 55 88 SU(2)[C5]\mathrm{SU}(2)[C_{5}] q+(1ζ10+ζ102ζ103)q2+ζ103q3+q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{3}q^{3}+\cdots
150.2.g.c 150.g 25.d 88 1.1981.198 8.0.1064390625.3 None 150.2.g.c 22 2-2 4-4 2-2 SU(2)[C5]\mathrm{SU}(2)[C_{5}] qβ2q2+β5q3+β5q4+(1+β1+)q5+q-\beta _{2}q^{2}+\beta _{5}q^{3}+\beta _{5}q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots

Decomposition of S2old(150,[χ])S_{2}^{\mathrm{old}}(150, [\chi]) into lower level spaces

S2old(150,[χ]) S_{2}^{\mathrm{old}}(150, [\chi]) \simeq S2new(25,[χ])S_{2}^{\mathrm{new}}(25, [\chi])4^{\oplus 4}\oplusS2new(50,[χ])S_{2}^{\mathrm{new}}(50, [\chi])2^{\oplus 2}\oplusS2new(75,[χ])S_{2}^{\mathrm{new}}(75, [\chi])2^{\oplus 2}