Properties

Label 6.16.a
Level 66
Weight 1616
Character orbit 6.a
Rep. character χ6(1,)\chi_{6}(1,\cdot)
Character field Q\Q
Dimension 33
Newform subspaces 33
Sturm bound 1616
Trace bound 33

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Defining parameters

Level: N N == 6=23 6 = 2 \cdot 3
Weight: k k == 16 16
Character orbit: [χ][\chi] == 6.a (trivial)
Character field: Q\Q
Newform subspaces: 3 3
Sturm bound: 1616
Trace bound: 33
Distinguishing TpT_p: 55

Dimensions

The following table gives the dimensions of various subspaces of M16(Γ0(6))M_{16}(\Gamma_0(6)).

Total New Old
Modular forms 17 3 14
Cusp forms 13 3 10
Eisenstein series 4 0 4

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
++++++551144441133110011
++--440044330033110011
-++-441133331122110011
--++441133331122110011
Plus space++992277772255220022
Minus space-881177661155220022

Trace form

3q+128q22187q3+49152q4351654q5+279936q6247368q7+2097152q8+14348907q9+35497728q10+54814524q1135831808q12+236812146q13550077440q14++262176169041756q99+O(q100) 3 q + 128 q^{2} - 2187 q^{3} + 49152 q^{4} - 351654 q^{5} + 279936 q^{6} - 247368 q^{7} + 2097152 q^{8} + 14348907 q^{9} + 35497728 q^{10} + 54814524 q^{11} - 35831808 q^{12} + 236812146 q^{13} - 550077440 q^{14}+ \cdots + 262176169041756 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S16new(Γ0(6))S_{16}^{\mathrm{new}}(\Gamma_0(6)) 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
6.16.a.a 6.a 1.a 11 8.5628.562 Q\Q None 6.16.a.a 128-128 2187-2187 314490-314490 20250562025056 ++ ++ SU(2)\mathrm{SU}(2) q27q237q3+214q4314490q5+q-2^{7}q^{2}-3^{7}q^{3}+2^{14}q^{4}-314490q^{5}+\cdots
6.16.a.b 6.a 1.a 11 8.5628.562 Q\Q None 6.16.a.b 128128 2187-2187 114810-114810 3034528-3034528 - ++ SU(2)\mathrm{SU}(2) q+27q237q3+214q4114810q5+q+2^{7}q^{2}-3^{7}q^{3}+2^{14}q^{4}-114810q^{5}+\cdots
6.16.a.c 6.a 1.a 11 8.5628.562 Q\Q None 6.16.a.c 128128 21872187 7764677646 762104762104 - - SU(2)\mathrm{SU}(2) q+27q2+37q3+214q4+77646q5+q+2^{7}q^{2}+3^{7}q^{3}+2^{14}q^{4}+77646q^{5}+\cdots

Decomposition of S16old(Γ0(6))S_{16}^{\mathrm{old}}(\Gamma_0(6)) into lower level spaces

S16old(Γ0(6)) S_{16}^{\mathrm{old}}(\Gamma_0(6)) \simeq S16new(Γ0(1))S_{16}^{\mathrm{new}}(\Gamma_0(1))4^{\oplus 4}\oplusS16new(Γ0(2))S_{16}^{\mathrm{new}}(\Gamma_0(2))2^{\oplus 2}\oplusS16new(Γ0(3))S_{16}^{\mathrm{new}}(\Gamma_0(3))2^{\oplus 2}