Properties

Label 900.2.e
Level 900900
Weight 22
Character orbit 900.e
Rep. character χ900(251,)\chi_{900}(251,\cdot)
Character field Q\Q
Dimension 3838
Newform subspaces 77
Sturm bound 360360
Trace bound 1313

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Defining parameters

Level: N N == 900=223252 900 = 2^{2} \cdot 3^{2} \cdot 5^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 900.e (of order 22 and degree 11)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 12 12
Character field: Q\Q
Newform subspaces: 7 7
Sturm bound: 360360
Trace bound: 1313
Distinguishing TpT_p: 77, 1313

Dimensions

The following table gives the dimensions of various subspaces of M2(900,[χ])M_{2}(900, [\chi]).

Total New Old
Modular forms 204 38 166
Cusp forms 156 38 118
Eisenstein series 48 0 48

Trace form

38q+4q48q1316q16+16q22+32q284q34+12q37+40q466q498q5252q58+36q618q6416q7372q76+4q82+64q88+8q94+64q97+O(q100) 38 q + 4 q^{4} - 8 q^{13} - 16 q^{16} + 16 q^{22} + 32 q^{28} - 4 q^{34} + 12 q^{37} + 40 q^{46} - 6 q^{49} - 8 q^{52} - 52 q^{58} + 36 q^{61} - 8 q^{64} - 16 q^{73} - 72 q^{76} + 4 q^{82} + 64 q^{88} + 8 q^{94}+ \cdots - 64 q^{97}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(900,[χ])S_{2}^{\mathrm{new}}(900, [\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}
900.2.e.a 900.e 12.b 22 7.1877.187 Q(2)\Q(\sqrt{-2}) Q(1)\Q(\sqrt{-1}) 180.2.h.a 00 00 00 00 U(1)[D2]\mathrm{U}(1)[D_{2}] qβq22q4+2βq86q13+4q16+q-\beta q^{2}-2q^{4}+2\beta q^{8}-6q^{13}+4q^{16}+\cdots
900.2.e.b 900.e 12.b 22 7.1877.187 Q(2)\Q(\sqrt{-2}) Q(1)\Q(\sqrt{-1}) 36.2.b.a 00 00 00 00 U(1)[D2]\mathrm{U}(1)[D_{2}] q+βq22q42βq8+4q13+4q16+q+\beta q^{2}-2q^{4}-2\beta q^{8}+4q^{13}+4q^{16}+\cdots
900.2.e.c 900.e 12.b 22 7.1877.187 Q(2)\Q(\sqrt{-2}) Q(1)\Q(\sqrt{-1}) 180.2.h.a 00 00 00 00 U(1)[D2]\mathrm{U}(1)[D_{2}] qβq22q4+2βq8+6q13+4q16+q-\beta q^{2}-2q^{4}+2\beta q^{8}+6q^{13}+4q^{16}+\cdots
900.2.e.d 900.e 12.b 88 7.1877.187 8.0.18939904.2 None 180.2.e.a 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+β5q2+(1β3β4β7)q4+(2+)q7+q+\beta _{5}q^{2}+(1-\beta _{3}-\beta _{4}-\beta _{7})q^{4}+(-2+\cdots)q^{7}+\cdots
900.2.e.e 900.e 12.b 88 7.1877.187 8.0.64000000.1 None 900.2.e.e 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+β4q2β2q4+(1+β1β2+)q7+q+\beta _{4}q^{2}-\beta _{2}q^{4}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots
900.2.e.f 900.e 12.b 88 7.1877.187 8.0.207360000.2 None 180.2.h.b 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+β1q2+(1β5)q4+(β2+β7)q7+q+\beta _{1}q^{2}+(1-\beta _{5})q^{4}+(\beta _{2}+\beta _{7})q^{7}+\cdots
900.2.e.g 900.e 12.b 88 7.1877.187 8.0.64000000.1 None 900.2.e.e 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] qβ1q2+β4q4+(β4+β7)q7+q-\beta _{1}q^{2}+\beta _{4}q^{4}+(-\beta _{4}+\beta _{7})q^{7}+\cdots

Decomposition of S2old(900,[χ])S_{2}^{\mathrm{old}}(900, [\chi]) into lower level spaces

S2old(900,[χ]) S_{2}^{\mathrm{old}}(900, [\chi]) \simeq S2new(36,[χ])S_{2}^{\mathrm{new}}(36, [\chi])3^{\oplus 3}\oplusS2new(60,[χ])S_{2}^{\mathrm{new}}(60, [\chi])4^{\oplus 4}\oplusS2new(180,[χ])S_{2}^{\mathrm{new}}(180, [\chi])2^{\oplus 2}\oplusS2new(300,[χ])S_{2}^{\mathrm{new}}(300, [\chi])2^{\oplus 2}