Properties

Label 300.9.g
Level 300300
Weight 99
Character orbit 300.g
Rep. character χ300(101,)\chi_{300}(101,\cdot)
Character field Q\Q
Dimension 5151
Newform subspaces 88
Sturm bound 540540
Trace bound 77

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Defining parameters

Level: N N == 300=22352 300 = 2^{2} \cdot 3 \cdot 5^{2}
Weight: k k == 9 9
Character orbit: [χ][\chi] == 300.g (of order 22 and degree 11)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 3 3
Character field: Q\Q
Newform subspaces: 8 8
Sturm bound: 540540
Trace bound: 77
Distinguishing TpT_p: 77

Dimensions

The following table gives the dimensions of various subspaces of M9(300,[χ])M_{9}(300, [\chi]).

Total New Old
Modular forms 498 51 447
Cusp forms 462 51 411
Eisenstein series 36 0 36

Trace form

51q91q31994q71939q9+54466q13323276q19274396q21+93869q27+1220744q311440060q33882062q37+3798264q39+6461026q43+44800155q49++191259250q99+O(q100) 51 q - 91 q^{3} - 1994 q^{7} - 1939 q^{9} + 54466 q^{13} - 323276 q^{19} - 274396 q^{21} + 93869 q^{27} + 1220744 q^{31} - 1440060 q^{33} - 882062 q^{37} + 3798264 q^{39} + 6461026 q^{43} + 44800155 q^{49}+ \cdots + 191259250 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S9new(300,[χ])S_{9}^{\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}
300.9.g.a 300.g 3.b 11 122.214122.214 Q\Q Q(3)\Q(\sqrt{-3}) 12.9.c.a 00 81-81 00 4034-4034 U(1)[D2]\mathrm{U}(1)[D_{2}] q34q34034q7+38q9+35806q13+q-3^{4}q^{3}-4034q^{7}+3^{8}q^{9}+35806q^{13}+\cdots
300.9.g.b 300.g 3.b 11 122.214122.214 Q\Q Q(3)\Q(\sqrt{-3}) 300.9.g.b 00 81-81 00 239-239 U(1)[D2]\mathrm{U}(1)[D_{2}] q34q3239q7+38q9+20641q13+q-3^{4}q^{3}-239q^{7}+3^{8}q^{9}+20641q^{13}+\cdots
300.9.g.c 300.g 3.b 11 122.214122.214 Q\Q Q(3)\Q(\sqrt{-3}) 300.9.g.b 00 8181 00 239239 U(1)[D2]\mathrm{U}(1)[D_{2}] q+34q3+239q7+38q920641q13+q+3^{4}q^{3}+239q^{7}+3^{8}q^{9}-20641q^{13}+\cdots
300.9.g.d 300.g 3.b 22 122.214122.214 Q(110)\Q(\sqrt{-110}) None 12.9.c.b 00 102102 00 61886188 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+(51+β)q3+3094q7+(1359+)q9+q+(51+\beta )q^{3}+3094q^{7}+(-1359+\cdots)q^{9}+\cdots
300.9.g.e 300.g 3.b 1010 122.214122.214 Q[x]/(x10)\mathbb{Q}[x]/(x^{10} - \cdots) None 300.9.g.e 00 137-137 00 1048-1048 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+(14β1)q3+(104+2β1β3+)q7+q+(-14-\beta _{1})q^{3}+(-104+2\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots
300.9.g.f 300.g 3.b 1010 122.214122.214 Q[x]/(x10)\mathbb{Q}[x]/(x^{10} - \cdots) None 60.9.g.a 00 112-112 00 4148-4148 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+(11+β1)q3+(41711β1+)q7+q+(-11+\beta _{1})q^{3}+(-417-11\beta _{1}+\cdots)q^{7}+\cdots
300.9.g.g 300.g 3.b 1010 122.214122.214 Q[x]/(x10)\mathbb{Q}[x]/(x^{10} - \cdots) None 300.9.g.e 00 137137 00 10481048 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+(14+β1)q3+(1042β1+β3)q7+q+(14+\beta _{1})q^{3}+(104-2\beta _{1}+\beta _{3})q^{7}+\cdots
300.9.g.h 300.g 3.b 1616 122.214122.214 Q[x]/(x16)\mathbb{Q}[x]/(x^{16} - \cdots) None 60.9.b.a 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] qβ1q3β7q7+(922+β2)q9β3q11+q-\beta _{1}q^{3}-\beta _{7}q^{7}+(922+\beta _{2})q^{9}-\beta _{3}q^{11}+\cdots

Decomposition of S9old(300,[χ])S_{9}^{\mathrm{old}}(300, [\chi]) into lower level spaces