Properties

Label 600.2.b
Level 600600
Weight 22
Character orbit 600.b
Rep. character χ600(251,)\chi_{600}(251,\cdot)
Character field Q\Q
Dimension 7070
Newform subspaces 99
Sturm bound 240240
Trace bound 33

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Defining parameters

Level: N N == 600=23352 600 = 2^{3} \cdot 3 \cdot 5^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 600.b (of order 22 and degree 11)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 24 24
Character field: Q\Q
Newform subspaces: 9 9
Sturm bound: 240240
Trace bound: 33
Distinguishing TpT_p: 77, 1111, 2323, 4343

Dimensions

The following table gives the dimensions of various subspaces of M2(600,[χ])M_{2}(600, [\chi]).

Total New Old
Modular forms 132 82 50
Cusp forms 108 70 38
Eisenstein series 24 12 12

Trace form

70q+2q3+4q42q6+2q9+12q12+4q184q1920q22+30q24+14q27+4q2812q3410q3632q42+20q438q46+12q4822q49++16q99+O(q100) 70 q + 2 q^{3} + 4 q^{4} - 2 q^{6} + 2 q^{9} + 12 q^{12} + 4 q^{18} - 4 q^{19} - 20 q^{22} + 30 q^{24} + 14 q^{27} + 4 q^{28} - 12 q^{34} - 10 q^{36} - 32 q^{42} + 20 q^{43} - 8 q^{46} + 12 q^{48} - 22 q^{49}+ \cdots + 16 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(600,[χ])S_{2}^{\mathrm{new}}(600, [\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}
600.2.b.a 600.b 24.f 22 4.7914.791 Q(2)\Q(\sqrt{-2}) Q(2)\Q(\sqrt{-2}) 24.2.f.a 00 22 00 00 U(1)[D2]\mathrm{U}(1)[D_{2}] q+βq2+(1β)q32q4+(2+β)q6+q+\beta q^{2}+(1-\beta )q^{3}-2q^{4}+(2+\beta )q^{6}+\cdots
600.2.b.b 600.b 24.f 44 4.7914.791 Q(2,3)\Q(\sqrt{-2}, \sqrt{-3}) Q(2)\Q(\sqrt{-2}) 600.2.b.b 00 2-2 00 00 U(1)[D2]\mathrm{U}(1)[D_{2}] qβ1q2+(1β2)q32q4+(1+)q6+q-\beta _{1}q^{2}+(-1-\beta _{2})q^{3}-2q^{4}+(-1+\cdots)q^{6}+\cdots
600.2.b.c 600.b 24.f 44 4.7914.791 Q(3,5)\Q(\sqrt{-3}, \sqrt{5}) Q(15)\Q(\sqrt{-15}) 120.2.m.a 00 00 00 00 U(1)[D2]\mathrm{U}(1)[D_{2}] qβ2q2+(β1β2)q3+β3q4+(2+)q6+q-\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{3}+\beta _{3}q^{4}+(-2+\cdots)q^{6}+\cdots
600.2.b.d 600.b 24.f 44 4.7914.791 Q(2,3)\Q(\sqrt{-2}, \sqrt{-3}) Q(2)\Q(\sqrt{-2}) 600.2.b.b 00 22 00 00 U(1)[D2]\mathrm{U}(1)[D_{2}] q+β1q2+(1+β2)q32q4+(1+)q6+q+\beta _{1}q^{2}+(1+\beta _{2})q^{3}-2q^{4}+(-1+\cdots)q^{6}+\cdots
600.2.b.e 600.b 24.f 88 4.7914.791 8.0.1649659456.5 None 120.2.b.a 1-1 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] qβ1q2+β4q3+(β1+β3+β4)q4+q-\beta _{1}q^{2}+\beta _{4}q^{3}+(\beta _{1}+\beta _{3}+\beta _{4})q^{4}+\cdots
600.2.b.f 600.b 24.f 88 4.7914.791 8.0.1649659456.5 None 120.2.b.a 11 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+β1q2+β6q3+(β1+β3+β4)q4+q+\beta _{1}q^{2}+\beta _{6}q^{3}+(\beta _{1}+\beta _{3}+\beta _{4})q^{4}+\cdots
600.2.b.g 600.b 24.f 1212 4.7914.791 12.0.\cdots.1 None 600.2.b.g 00 2-2 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+β8q2β5q3+(1+β4)q4+(β4+)q6+q+\beta _{8}q^{2}-\beta _{5}q^{3}+(1+\beta _{4})q^{4}+(-\beta _{4}+\cdots)q^{6}+\cdots
600.2.b.h 600.b 24.f 1212 4.7914.791 12.0.\cdots.1 None 600.2.b.g 00 22 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] qβ1q2+β6q3+(1+β2)q4+(β2+)q6+q-\beta _{1}q^{2}+\beta _{6}q^{3}+(1+\beta _{2})q^{4}+(-\beta _{2}+\cdots)q^{6}+\cdots
600.2.b.i 600.b 24.f 1616 4.7914.791 Q[x]/(x16+)\mathbb{Q}[x]/(x^{16} + \cdots) None 120.2.m.b 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] qβ10q2+β5q3β14q4+(β7+β12+)q6+q-\beta _{10}q^{2}+\beta _{5}q^{3}-\beta _{14}q^{4}+(\beta _{7}+\beta _{12}+\cdots)q^{6}+\cdots

Decomposition of S2old(600,[χ])S_{2}^{\mathrm{old}}(600, [\chi]) into lower level spaces

S2old(600,[χ]) S_{2}^{\mathrm{old}}(600, [\chi]) \simeq S2new(24,[χ])S_{2}^{\mathrm{new}}(24, [\chi])3^{\oplus 3}\oplusS2new(120,[χ])S_{2}^{\mathrm{new}}(120, [\chi])2^{\oplus 2}