Properties

Label 300.3.l
Level 300300
Weight 33
Character orbit 300.l
Rep. character χ300(107,)\chi_{300}(107,\cdot)
Character field Q(ζ4)\Q(\zeta_{4})
Dimension 136136
Newform subspaces 88
Sturm bound 180180
Trace bound 66

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Defining parameters

Level: N N == 300=22352 300 = 2^{2} \cdot 3 \cdot 5^{2}
Weight: k k == 3 3
Character orbit: [χ][\chi] == 300.l (of order 44 and degree 22)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 60 60
Character field: Q(i)\Q(i)
Newform subspaces: 8 8
Sturm bound: 180180
Trace bound: 66
Distinguishing TpT_p: 77, 1717, 1919

Dimensions

The following table gives the dimensions of various subspaces of M3(300,[χ])M_{3}(300, [\chi]).

Total New Old
Modular forms 264 152 112
Cusp forms 216 136 80
Eisenstein series 48 16 32

Trace form

136q4q6+20q12+8q13+48q16+24q18+24q21+76q22+84q28+40q33164q36+40q37236q42504q46196q48304q52+72q57180q58+72q97+O(q100) 136 q - 4 q^{6} + 20 q^{12} + 8 q^{13} + 48 q^{16} + 24 q^{18} + 24 q^{21} + 76 q^{22} + 84 q^{28} + 40 q^{33} - 164 q^{36} + 40 q^{37} - 236 q^{42} - 504 q^{46} - 196 q^{48} - 304 q^{52} + 72 q^{57} - 180 q^{58}+ \cdots - 72 q^{97}+O(q^{100}) Copy content Toggle raw display

Decomposition of S3new(300,[χ])S_{3}^{\mathrm{new}}(300, [\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}
300.3.l.a 300.l 60.l 44 8.1748.174 Q(i,14)\Q(i, \sqrt{14}) None 300.3.l.a 8-8 44 00 00 SU(2)[C4]\mathrm{SU}(2)[C_{4}] q2q2+(1+β2+β3)q3+4q4+(2+)q6+q-2q^{2}+(1+\beta _{2}+\beta _{3})q^{3}+4q^{4}+(-2+\cdots)q^{6}+\cdots
300.3.l.b 300.l 60.l 44 8.1748.174 Q(i,14)\Q(i, \sqrt{14}) None 300.3.l.a 00 4-4 00 00 SU(2)[C4]\mathrm{SU}(2)[C_{4}] q2β2q2+(1β2+β3)q34q4+q-2\beta _{2}q^{2}+(-1-\beta _{2}+\beta _{3})q^{3}-4q^{4}+\cdots
300.3.l.c 300.l 60.l 44 8.1748.174 Q(i,14)\Q(i, \sqrt{14}) None 300.3.l.a 00 44 00 00 SU(2)[C4]\mathrm{SU}(2)[C_{4}] q2β2q2+(1+β1β2)q34q4+q-2\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{3}-4q^{4}+\cdots
300.3.l.d 300.l 60.l 44 8.1748.174 Q(i,14)\Q(i, \sqrt{14}) None 300.3.l.a 88 4-4 00 00 SU(2)[C4]\mathrm{SU}(2)[C_{4}] q+2q2+(1+β1+β2)q3+4q4+q+2q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+4q^{4}+\cdots
300.3.l.e 300.l 60.l 88 8.1748.174 8.0.3317760000.4 Q(15)\Q(\sqrt{-15}) 300.3.l.e 00 00 00 00 U(1)[D4]\mathrm{U}(1)[D_{4}] q+β1q2+3β5q3+(4β4+β6)q4+q+\beta _{1}q^{2}+3\beta _{5}q^{3}+(4\beta _{4}+\beta _{6})q^{4}+\cdots
300.3.l.f 300.l 60.l 88 8.1748.174 8.0.40960000.1 Q(5)\Q(\sqrt{-5}) 300.3.l.f 00 00 00 00 U(1)[D4]\mathrm{U}(1)[D_{4}] qβ6q2+(β3+β7)q34β2q4+q-\beta _{6}q^{2}+(-\beta _{3}+\beta _{7})q^{3}-4\beta _{2}q^{4}+\cdots
300.3.l.g 300.l 60.l 4040 8.1748.174 None 60.3.l.a 00 00 00 00 SU(2)[C4]\mathrm{SU}(2)[C_{4}]
300.3.l.h 300.l 60.l 6464 8.1748.174 None 300.3.l.h 00 00 00 00 SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Decomposition of S3old(300,[χ])S_{3}^{\mathrm{old}}(300, [\chi]) into lower level spaces

S3old(300,[χ]) S_{3}^{\mathrm{old}}(300, [\chi]) \simeq S3new(60,[χ])S_{3}^{\mathrm{new}}(60, [\chi])2^{\oplus 2}