Properties

Label 14.8.a
Level 1414
Weight 88
Character orbit 14.a
Rep. character χ14(1,)\chi_{14}(1,\cdot)
Character field Q\Q
Dimension 44
Newform subspaces 33
Sturm bound 1616
Trace bound 22

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Defining parameters

Level: N N == 14=27 14 = 2 \cdot 7
Weight: k k == 8 8
Character orbit: [χ][\chi] == 14.a (trivial)
Character field: Q\Q
Newform subspaces: 3 3
Sturm bound: 1616
Trace bound: 22
Distinguishing TpT_p: 33

Dimensions

The following table gives the dimensions of various subspaces of M8(Γ0(14))M_{8}(\Gamma_0(14)).

Total New Old
Modular forms 16 4 12
Cusp forms 12 4 8
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.

2277FrickeTotalCuspEisenstein
AllNewOldAllNewOldAllNewOld
++++++551144441133110011
++--330033220022110011
-++-441133331122110011
--++442222332211110011
Plus space++993366773344220022
Minus space-771166551144220022

Trace form

4q+16q278q3+256q4+174q5+688q6+1024q8+8720q95776q10972q114992q123734q13+5488q1441368q15+16384q16+516q172832q18+27165244q99+O(q100) 4 q + 16 q^{2} - 78 q^{3} + 256 q^{4} + 174 q^{5} + 688 q^{6} + 1024 q^{8} + 8720 q^{9} - 5776 q^{10} - 972 q^{11} - 4992 q^{12} - 3734 q^{13} + 5488 q^{14} - 41368 q^{15} + 16384 q^{16} + 516 q^{17} - 2832 q^{18}+ \cdots - 27165244 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S8new(Γ0(14))S_{8}^{\mathrm{new}}(\Gamma_0(14)) 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 7
14.8.a.a 14.a 1.a 11 4.3734.373 Q\Q None 14.8.a.a 8-8 82-82 448448 343-343 ++ ++ SU(2)\mathrm{SU}(2) q8q282q3+26q4+448q5+q-8q^{2}-82q^{3}+2^{6}q^{4}+448q^{5}+\cdots
14.8.a.b 14.a 1.a 11 4.3734.373 Q\Q None 14.8.a.b 88 66-66 400-400 343-343 - ++ SU(2)\mathrm{SU}(2) q+8q266q3+26q4202q5+q+8q^{2}-66q^{3}+2^{6}q^{4}-20^{2}q^{5}+\cdots
14.8.a.c 14.a 1.a 22 4.3734.373 Q(1969)\Q(\sqrt{1969}) None 14.8.a.c 1616 7070 126126 686686 - - SU(2)\mathrm{SU}(2) q+8q2+(35β)q3+26q4+(63+9β)q5+q+8q^{2}+(35-\beta )q^{3}+2^{6}q^{4}+(63+9\beta )q^{5}+\cdots

Decomposition of S8old(Γ0(14))S_{8}^{\mathrm{old}}(\Gamma_0(14)) into lower level spaces

S8old(Γ0(14)) S_{8}^{\mathrm{old}}(\Gamma_0(14)) \simeq S8new(Γ0(2))S_{8}^{\mathrm{new}}(\Gamma_0(2))2^{\oplus 2}\oplusS8new(Γ0(7))S_{8}^{\mathrm{new}}(\Gamma_0(7))2^{\oplus 2}