Properties

Label 1629.2.a
Level 16291629
Weight 22
Character orbit 1629.a
Rep. character χ1629(1,)\chi_{1629}(1,\cdot)
Character field Q\Q
Dimension 7575
Newform subspaces 99
Sturm bound 364364
Trace bound 44

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Defining parameters

Level: N N == 1629=32181 1629 = 3^{2} \cdot 181
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1629.a (trivial)
Character field: Q\Q
Newform subspaces: 9 9
Sturm bound: 364364
Trace bound: 44
Distinguishing TpT_p: 22

Dimensions

The following table gives the dimensions of various subspaces of M2(Γ0(1629))M_{2}(\Gamma_0(1629)).

Total New Old
Modular forms 186 75 111
Cusp forms 179 75 104
Eisenstein series 7 0 7

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

33181181FrickeTotalCuspEisenstein
AllNewOldAllNewOldAllNewOld
++++++414110103131404010103030110011
++--515120203131494920202929220022
-++-525225252727505025252525220022
--++424220202222404020202020220022
Plus space++838330305353808030305050330033
Minus space-10310345455858999945455454440044

Trace form

75q+q2+77q4+2q5+3q8+4q10+4q114q13+2q14+81q168q17+10q19+8q23+57q2518q26+18q28+6q292q31+17q32+51q98+O(q100) 75 q + q^{2} + 77 q^{4} + 2 q^{5} + 3 q^{8} + 4 q^{10} + 4 q^{11} - 4 q^{13} + 2 q^{14} + 81 q^{16} - 8 q^{17} + 10 q^{19} + 8 q^{23} + 57 q^{25} - 18 q^{26} + 18 q^{28} + 6 q^{29} - 2 q^{31} + 17 q^{32}+ \cdots - 51 q^{98}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(Γ0(1629))S_{2}^{\mathrm{new}}(\Gamma_0(1629)) 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} 3 181
1629.2.a.a 1629.a 1.a 33 13.00813.008 Q(ζ14)+\Q(\zeta_{14})^+ None 543.2.a.a 22 00 11 7-7 - - SU(2)\mathrm{SU}(2) q+(1β1)q2+(12β1+β2)q4+β1q5+q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+\beta _{1}q^{5}+\cdots
1629.2.a.b 1629.a 1.a 55 13.00813.008 5.5.170701.1 None 543.2.a.b 11 00 3-3 99 - ++ SU(2)\mathrm{SU}(2) qβ2q2+(1+β1+β2β4)q4+(β2+)q5+q-\beta _{2}q^{2}+(1+\beta _{1}+\beta _{2}-\beta _{4})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots
1629.2.a.c 1629.a 1.a 55 13.00813.008 5.5.24217.1 None 181.2.a.a 33 00 55 2-2 - ++ SU(2)\mathrm{SU}(2) q+(1+β1)q2+(1β2+β4)q4+(1+)q5+q+(1+\beta _{1})q^{2}+(1-\beta _{2}+\beta _{4})q^{4}+(1+\cdots)q^{5}+\cdots
1629.2.a.d 1629.a 1.a 77 13.00813.008 Q[x]/(x7)\mathbb{Q}[x]/(x^{7} - \cdots) None 543.2.a.c 44 00 33 1-1 - ++ SU(2)\mathrm{SU}(2) q+(1β1)q2+(2β1+β2)q4+β3q5+q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots
1629.2.a.e 1629.a 1.a 88 13.00813.008 Q[x]/(x8)\mathbb{Q}[x]/(x^{8} - \cdots) None 543.2.a.d 3-3 00 5-5 3-3 - - SU(2)\mathrm{SU}(2) qβ1q2+(β1+β2)q4+(1β2+)q5+q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots
1629.2.a.f 1629.a 1.a 88 13.00813.008 Q[x]/(x8)\mathbb{Q}[x]/(x^{8} - \cdots) None 543.2.a.e 3-3 00 22 2-2 - ++ SU(2)\mathrm{SU}(2) q+β6q2+(2+β1+β5)q4+(β2+)q5+q+\beta _{6}q^{2}+(2+\beta _{1}+\beta _{5})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots
1629.2.a.g 1629.a 1.a 99 13.00813.008 Q[x]/(x9)\mathbb{Q}[x]/(x^{9} - \cdots) None 181.2.a.b 3-3 00 1-1 22 - - SU(2)\mathrm{SU}(2) qβ1q2+(1+β2)q4β3q5+(1+)q7+q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+(-1+\cdots)q^{7}+\cdots
1629.2.a.h 1629.a 1.a 1010 13.00813.008 Q[x]/(x10)\mathbb{Q}[x]/(x^{10} - \cdots) None 1629.2.a.h 00 00 00 10-10 ++ ++ SU(2)\mathrm{SU}(2) q+β1q2+β2q4β5q5+(1+β4+)q7+q+\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{5}q^{5}+(-1+\beta _{4}+\cdots)q^{7}+\cdots
1629.2.a.i 1629.a 1.a 2020 13.00813.008 Q[x]/(x20)\mathbb{Q}[x]/(x^{20} - \cdots) None 1629.2.a.i 00 00 00 1414 ++ - SU(2)\mathrm{SU}(2) q+β1q2+(2+β2)q4β14q5+(1+)q7+q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{14}q^{5}+(1+\cdots)q^{7}+\cdots

Decomposition of S2old(Γ0(1629))S_{2}^{\mathrm{old}}(\Gamma_0(1629)) into lower level spaces

S2old(Γ0(1629)) S_{2}^{\mathrm{old}}(\Gamma_0(1629)) \simeq S2new(Γ0(181))S_{2}^{\mathrm{new}}(\Gamma_0(181))3^{\oplus 3}\oplusS2new(Γ0(543))S_{2}^{\mathrm{new}}(\Gamma_0(543))2^{\oplus 2}