Properties

Label 9.14.a
Level 99
Weight 1414
Character orbit 9.a
Rep. character χ9(1,)\chi_{9}(1,\cdot)
Character field Q\Q
Dimension 55
Newform subspaces 33
Sturm bound 1414
Trace bound 22

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Defining parameters

Level: N N == 9=32 9 = 3^{2}
Weight: k k == 14 14
Character orbit: [χ][\chi] == 9.a (trivial)
Character field: Q\Q
Newform subspaces: 3 3
Sturm bound: 1414
Trace bound: 22
Distinguishing TpT_p: 22

Dimensions

The following table gives the dimensions of various subspaces of M14(Γ0(9))M_{14}(\Gamma_0(9)).

Total New Old
Modular forms 15 6 9
Cusp forms 11 5 6
Eisenstein series 4 1 3

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

33TotalCuspEisenstein
AllNewOldAllNewOldAllNewOld
++772255552233220022
-884444663333221111

Trace form

5q+66q2+11924q410506q552520q7+1830552q84437036q10+10510500q1135372882q13+124741392q1454505456q16+33656058q17+205818292q19415819704q20++3130819722738q98+O(q100) 5 q + 66 q^{2} + 11924 q^{4} - 10506 q^{5} - 52520 q^{7} + 1830552 q^{8} - 4437036 q^{10} + 10510500 q^{11} - 35372882 q^{13} + 124741392 q^{14} - 54505456 q^{16} + 33656058 q^{17} + 205818292 q^{19} - 415819704 q^{20}+ \cdots + 3130819722738 q^{98}+O(q^{100}) Copy content Toggle raw display

Decomposition of S14new(Γ0(9))S_{14}^{\mathrm{new}}(\Gamma_0(9)) 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
9.14.a.a 9.a 1.a 11 9.6519.651 Q\Q None 3.14.a.a 1212 00 3021030210 235088235088 - SU(2)\mathrm{SU}(2) q+12q28048q4+30210q5+235088q7+q+12q^{2}-8048q^{4}+30210q^{5}+235088q^{7}+\cdots
9.14.a.b 9.a 1.a 22 9.6519.651 Q(55)\Q(\sqrt{55}) None 9.14.a.b 00 00 00 266600-266600 ++ SU(2)\mathrm{SU}(2) q+βq2272q4520βq5133300q7+q+\beta q^{2}-272q^{4}-520\beta q^{5}-133300q^{7}+\cdots
9.14.a.c 9.a 1.a 22 9.6519.651 Q(1969)\Q(\sqrt{1969}) None 3.14.a.b 5454 00 40716-40716 21008-21008 - SU(2)\mathrm{SU}(2) q+(33β)q2+(1025854β)q4+(20358+)q5+q+(3^{3}-\beta )q^{2}+(10258-54\beta )q^{4}+(-20358+\cdots)q^{5}+\cdots

Decomposition of S14old(Γ0(9))S_{14}^{\mathrm{old}}(\Gamma_0(9)) into lower level spaces

S14old(Γ0(9)) S_{14}^{\mathrm{old}}(\Gamma_0(9)) \simeq S14new(Γ0(3))S_{14}^{\mathrm{new}}(\Gamma_0(3))2^{\oplus 2}