Properties

Label 16.8.a
Level 1616
Weight 88
Character orbit 16.a
Rep. character χ16(1,)\chi_{16}(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 == 16=24 16 = 2^{4}
Weight: k k == 8 8
Character orbit: [χ][\chi] == 16.a (trivial)
Character field: Q\Q
Newform subspaces: 3 3
Sturm bound: 1616
Trace bound: 33
Distinguishing TpT_p: 33

Dimensions

The following table gives the dimensions of various subspaces of M8(Γ0(16))M_{8}(\Gamma_0(16)).

Total New Old
Modular forms 17 4 13
Cusp forms 11 3 8
Eisenstein series 6 1 5

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

22TotalCuspEisenstein
AllNewOldAllNewOldAllNewOld
++992277662244330033
-882266551144331122

Trace form

3q+28q3+138q5+664q7+2575q9+4596q113278q1323288q1512714q17+41292q193360q21151992q23+1349q25+383320q27+120066q29438432q31++13726148q99+O(q100) 3 q + 28 q^{3} + 138 q^{5} + 664 q^{7} + 2575 q^{9} + 4596 q^{11} - 3278 q^{13} - 23288 q^{15} - 12714 q^{17} + 41292 q^{19} - 3360 q^{21} - 151992 q^{23} + 1349 q^{25} + 383320 q^{27} + 120066 q^{29} - 438432 q^{31}+ \cdots + 13726148 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S8new(Γ0(16))S_{8}^{\mathrm{new}}(\Gamma_0(16)) 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
16.8.a.a 16.a 1.a 11 4.9984.998 Q\Q None 8.8.a.b 00 44-44 430430 12241224 ++ SU(2)\mathrm{SU}(2) q44q3+430q5+1224q7251q9+q-44q^{3}+430q^{5}+1224q^{7}-251q^{9}+\cdots
16.8.a.b 16.a 1.a 11 4.9984.998 Q\Q None 2.8.a.a 00 12-12 210-210 1016-1016 - SU(2)\mathrm{SU}(2) q12q3210q51016q72043q9+q-12q^{3}-210q^{5}-1016q^{7}-2043q^{9}+\cdots
16.8.a.c 16.a 1.a 11 4.9984.998 Q\Q None 8.8.a.a 00 8484 82-82 456456 ++ SU(2)\mathrm{SU}(2) q+84q382q5+456q7+4869q9+q+84q^{3}-82q^{5}+456q^{7}+4869q^{9}+\cdots

Decomposition of S8old(Γ0(16))S_{8}^{\mathrm{old}}(\Gamma_0(16)) into lower level spaces

S8old(Γ0(16)) S_{8}^{\mathrm{old}}(\Gamma_0(16)) \simeq S8new(Γ0(2))S_{8}^{\mathrm{new}}(\Gamma_0(2))4^{\oplus 4}\oplusS8new(Γ0(8))S_{8}^{\mathrm{new}}(\Gamma_0(8))2^{\oplus 2}