Properties

Label 900.3.u
Level 900900
Weight 33
Character orbit 900.u
Rep. character χ900(149,)\chi_{900}(149,\cdot)
Character field Q(ζ6)\Q(\zeta_{6})
Dimension 7272
Newform subspaces 44
Sturm bound 540540
Trace bound 99

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Defining parameters

Level: N N == 900=223252 900 = 2^{2} \cdot 3^{2} \cdot 5^{2}
Weight: k k == 3 3
Character orbit: [χ][\chi] == 900.u (of order 66 and degree 22)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 45 45
Character field: Q(ζ6)\Q(\zeta_{6})
Newform subspaces: 4 4
Sturm bound: 540540
Trace bound: 99
Distinguishing TpT_p: 77

Dimensions

The following table gives the dimensions of various subspaces of M3(900,[χ])M_{3}(900, [\chi]).

Total New Old
Modular forms 756 72 684
Cusp forms 684 72 612
Eisenstein series 72 0 72

Trace form

72q14q9+36q118q2172q2930q31+8q39+72q41+204q49198q5118q5996q61+396q69108q79+158q81+168q91606q99+O(q100) 72 q - 14 q^{9} + 36 q^{11} - 8 q^{21} - 72 q^{29} - 30 q^{31} + 8 q^{39} + 72 q^{41} + 204 q^{49} - 198 q^{51} - 18 q^{59} - 96 q^{61} + 396 q^{69} - 108 q^{79} + 158 q^{81} + 168 q^{91} - 606 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S3new(900,[χ])S_{3}^{\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}
900.3.u.a 900.u 45.h 88 24.52324.523 8.0.303595776.1 None 36.3.g.a 00 00 00 00 SU(2)[C6]\mathrm{SU}(2)[C_{6}] q+(β1β5β7)q3+(3β13β4+)q7+q+(-\beta _{1}-\beta _{5}-\beta _{7})q^{3}+(-3\beta _{1}-3\beta _{4}+\cdots)q^{7}+\cdots
900.3.u.b 900.u 45.h 88 24.52324.523 8.0.12960000.1 None 180.3.o.a 00 00 00 00 SU(2)[C6]\mathrm{SU}(2)[C_{6}] q+3β1q3+(4β1+β6)q79β2q9+q+3\beta _{1}q^{3}+(4\beta _{1}+\beta _{6})q^{7}-9\beta _{2}q^{9}+\cdots
900.3.u.c 900.u 45.h 2424 24.52324.523 None 180.3.o.b 00 00 00 00 SU(2)[C6]\mathrm{SU}(2)[C_{6}]
900.3.u.d 900.u 45.h 3232 24.52324.523 None 900.3.p.d 00 00 00 00 SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Decomposition of S3old(900,[χ])S_{3}^{\mathrm{old}}(900, [\chi]) into lower level spaces

S3old(900,[χ]) S_{3}^{\mathrm{old}}(900, [\chi]) \simeq S3new(45,[χ])S_{3}^{\mathrm{new}}(45, [\chi])6^{\oplus 6}\oplusS3new(90,[χ])S_{3}^{\mathrm{new}}(90, [\chi])4^{\oplus 4}\oplusS3new(180,[χ])S_{3}^{\mathrm{new}}(180, [\chi])2^{\oplus 2}\oplusS3new(225,[χ])S_{3}^{\mathrm{new}}(225, [\chi])3^{\oplus 3}\oplusS3new(450,[χ])S_{3}^{\mathrm{new}}(450, [\chi])2^{\oplus 2}