Properties

Label 48.22.a
Level 4848
Weight 2222
Character orbit 48.a
Rep. character χ48(1,)\chi_{48}(1,\cdot)
Character field Q\Q
Dimension 2121
Newform subspaces 1212
Sturm bound 176176
Trace bound 55

Related objects

Downloads

Learn more

Defining parameters

Level: N N == 48=243 48 = 2^{4} \cdot 3
Weight: k k == 22 22
Character orbit: [χ][\chi] == 48.a (trivial)
Character field: Q\Q
Newform subspaces: 12 12
Sturm bound: 176176
Trace bound: 55
Distinguishing TpT_p: 55

Dimensions

The following table gives the dimensions of various subspaces of M22(Γ0(48))M_{22}(\Gamma_0(48)).

Total New Old
Modular forms 174 21 153
Cusp forms 162 21 141
Eisenstein series 12 0 12

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

2233FrickeTotalCuspEisenstein
AllNewOldAllNewOldAllNewOld
++++++43435538384040553535330033
++--44446638384141663535330033
-++-44445539394141553636330033
--++43435538384040553535330033
Plus space++868610107676808010107070660066
Minus space-888811117777828211117171660066

Trace form

21q+59049q3+20783558q5+3921376q7+73222472421q967333320740q11+107655263398q131153300781250q15+1740714497002q17+82838787800292q19418452746476856q23+23 ⁣ ⁣40q99+O(q100) 21 q + 59049 q^{3} + 20783558 q^{5} + 3921376 q^{7} + 73222472421 q^{9} - 67333320740 q^{11} + 107655263398 q^{13} - 1153300781250 q^{15} + 1740714497002 q^{17} + 82838787800292 q^{19} - 418452746476856 q^{23}+ \cdots - 23\!\cdots\!40 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S22new(Γ0(48))S_{22}^{\mathrm{new}}(\Gamma_0(48)) into newform subspaces

Label Char Prim Dim AA Field CM Minimal twist Traces A-L signs Sato-Tate qq-expansion
a2a_{2} a3a_{3} a5a_{5} a7a_{7} 2 3
48.22.a.a 48.a 1.a 11 134.149134.149 Q\Q None 6.22.a.c 00 59049-59049 23245050-23245050 13229777681322977768 - ++ SU(2)\mathrm{SU}(2) q310q323245050q5+1322977768q7+q-3^{10}q^{3}-23245050q^{5}+1322977768q^{7}+\cdots
48.22.a.b 48.a 1.a 11 134.149134.149 Q\Q None 12.22.a.a 00 59049-59049 11268090-11268090 281914136-281914136 - ++ SU(2)\mathrm{SU}(2) q310q311268090q5281914136q7+q-3^{10}q^{3}-11268090q^{5}-281914136q^{7}+\cdots
48.22.a.c 48.a 1.a 11 134.149134.149 Q\Q None 6.22.a.a 00 59049-59049 2644455026444550 166115864-166115864 - ++ SU(2)\mathrm{SU}(2) q310q3+26444550q5166115864q7+q-3^{10}q^{3}+26444550q^{5}-166115864q^{7}+\cdots
48.22.a.d 48.a 1.a 11 134.149134.149 Q\Q None 3.22.a.b 00 5904959049 41512770-41512770 538429808-538429808 - - SU(2)\mathrm{SU}(2) q+310q341512770q5538429808q7+q+3^{10}q^{3}-41512770q^{5}-538429808q^{7}+\cdots
48.22.a.e 48.a 1.a 11 134.149134.149 Q\Q None 3.22.a.a 00 5904959049 31099503109950 363303920-363303920 - - SU(2)\mathrm{SU}(2) q+310q3+3109950q5363303920q7+q+3^{10}q^{3}+3109950q^{5}-363303920q^{7}+\cdots
48.22.a.f 48.a 1.a 11 134.149134.149 Q\Q None 6.22.a.b 00 5904959049 1295417412954174 479513104479513104 - - SU(2)\mathrm{SU}(2) q+310q3+12954174q5+479513104q7+q+3^{10}q^{3}+12954174q^{5}+479513104q^{7}+\cdots
48.22.a.g 48.a 1.a 22 134.149134.149 Q(649)\Q(\sqrt{649}) None 3.22.a.c 00 118098-118098 996876996876 679896112-679896112 - ++ SU(2)\mathrm{SU}(2) q310q3+(498438+53β)q5+(339948056+)q7+q-3^{10}q^{3}+(498438+53\beta )q^{5}+(-339948056+\cdots)q^{7}+\cdots
48.22.a.h 48.a 1.a 22 134.149134.149 Q(537541)\Q(\sqrt{537541}) None 24.22.a.a 00 118098-118098 2194862021948620 659451408659451408 ++ ++ SU(2)\mathrm{SU}(2) q310q3+(109743105β)q5+(329725704+)q7+q-3^{10}q^{3}+(10974310-5\beta )q^{5}+(329725704+\cdots)q^{7}+\cdots
48.22.a.i 48.a 1.a 22 134.149134.149 Q[x]/(x2)\mathbb{Q}[x]/(x^{2} - \cdots) None 12.22.a.b 00 118098118098 2882790028827900 509669728-509669728 - - SU(2)\mathrm{SU}(2) q+310q3+(144139505β)q5+(254834864+)q7+q+3^{10}q^{3}+(14413950-5\beta )q^{5}+(-254834864+\cdots)q^{7}+\cdots
48.22.a.j 48.a 1.a 33 134.149134.149 Q[x]/(x3)\mathbb{Q}[x]/(x^{3} - \cdots) None 24.22.a.d 00 177147-177147 52804985280498 852542376-852542376 ++ ++ SU(2)\mathrm{SU}(2) q310q3+(1760166β1)q5+(284180792+)q7+q-3^{10}q^{3}+(1760166-\beta _{1})q^{5}+(-284180792+\cdots)q^{7}+\cdots
48.22.a.k 48.a 1.a 33 134.149134.149 Q[x]/(x3)\mathbb{Q}[x]/(x^{3} - \cdots) None 24.22.a.b 00 177147177147 4833126-4833126 271431024-271431024 ++ - SU(2)\mathrm{SU}(2) q+310q3+(1611042β1)q5+q+3^{10}q^{3}+(-1611042-\beta _{1})q^{5}+\cdots
48.22.a.l 48.a 1.a 33 134.149134.149 Q[x]/(x3)\mathbb{Q}[x]/(x^{3} - \cdots) None 24.22.a.c 00 177147177147 20800262080026 12052820641205282064 ++ - SU(2)\mathrm{SU}(2) q+310q3+(693342+β1)q5+(401760688+)q7+q+3^{10}q^{3}+(693342+\beta _{1})q^{5}+(401760688+\cdots)q^{7}+\cdots

Decomposition of S22old(Γ0(48))S_{22}^{\mathrm{old}}(\Gamma_0(48)) into lower level spaces