Properties

Label 495.3.j
Level 495495
Weight 33
Character orbit 495.j
Rep. character χ495(298,)\chi_{495}(298,\cdot)
Character field Q(ζ4)\Q(\zeta_{4})
Dimension 100100
Newform subspaces 33
Sturm bound 216216
Trace bound 22

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Defining parameters

Level: N N == 495=32511 495 = 3^{2} \cdot 5 \cdot 11
Weight: k k == 3 3
Character orbit: [χ][\chi] == 495.j (of order 44 and degree 22)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 5 5
Character field: Q(i)\Q(i)
Newform subspaces: 3 3
Sturm bound: 216216
Trace bound: 22
Distinguishing TpT_p: 22

Dimensions

The following table gives the dimensions of various subspaces of M3(495,[χ])M_{3}(495, [\chi]).

Total New Old
Modular forms 304 100 204
Cusp forms 272 100 172
Eisenstein series 32 0 32

Trace form

100q4q28q5+12q8+12q1028q13512q1648q17104q20+70q23+90q25+96q26+140q288q3156q32132q3578q37320q38+172q98+O(q100) 100 q - 4 q^{2} - 8 q^{5} + 12 q^{8} + 12 q^{10} - 28 q^{13} - 512 q^{16} - 48 q^{17} - 104 q^{20} + 70 q^{23} + 90 q^{25} + 96 q^{26} + 140 q^{28} - 8 q^{31} - 56 q^{32} - 132 q^{35} - 78 q^{37} - 320 q^{38}+ \cdots - 172 q^{98}+O(q^{100}) Copy content Toggle raw display

Decomposition of S3new(495,[χ])S_{3}^{\mathrm{new}}(495, [\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}
495.3.j.a 495.j 5.c 2020 13.48813.488 Q[x]/(x20)\mathbb{Q}[x]/(x^{20} - \cdots) None 55.3.f.a 44 00 88 00 SU(2)[C4]\mathrm{SU}(2)[C_{4}] q+β5q2+(2β8β16)q4+β15q5+q+\beta _{5}q^{2}+(-2\beta _{8}-\beta _{16})q^{4}+\beta _{15}q^{5}+\cdots
495.3.j.b 495.j 5.c 4040 13.48813.488 None 165.3.i.a 8-8 00 16-16 00 SU(2)[C4]\mathrm{SU}(2)[C_{4}]
495.3.j.c 495.j 5.c 4040 13.48813.488 None 495.3.j.c 00 00 00 00 SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Decomposition of S3old(495,[χ])S_{3}^{\mathrm{old}}(495, [\chi]) into lower level spaces

S3old(495,[χ]) S_{3}^{\mathrm{old}}(495, [\chi]) \simeq S3new(15,[χ])S_{3}^{\mathrm{new}}(15, [\chi])4^{\oplus 4}\oplusS3new(45,[χ])S_{3}^{\mathrm{new}}(45, [\chi])2^{\oplus 2}\oplusS3new(55,[χ])S_{3}^{\mathrm{new}}(55, [\chi])3^{\oplus 3}\oplusS3new(165,[χ])S_{3}^{\mathrm{new}}(165, [\chi])2^{\oplus 2}