Properties

Label 1331.2.a
Level 13311331
Weight 22
Character orbit 1331.a
Rep. character χ1331(1,)\chi_{1331}(1,\cdot)
Character field Q\Q
Dimension 100100
Newform subspaces 66
Sturm bound 242242
Trace bound 33

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Defining parameters

Level: N N == 1331=113 1331 = 11^{3}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1331.a (trivial)
Character field: Q\Q
Newform subspaces: 6 6
Sturm bound: 242242
Trace bound: 33
Distinguishing TpT_p: 22, 33

Dimensions

The following table gives the dimensions of various subspaces of M2(Γ0(1331))M_{2}(\Gamma_0(1331)).

Total New Old
Modular forms 132 100 32
Cusp forms 111 100 11
Eisenstein series 21 0 21

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

1111TotalCuspEisenstein
AllNewOldAllNewOldAllNewOld
++55554040151545454040551010001010
-77776060171766666060661111001111

Trace form

100qq3+100q4q5+99q94q124q145q15+96q168q203q23+97q256q267q275q318q34+86q367q3712q38++67q97+O(q100) 100 q - q^{3} + 100 q^{4} - q^{5} + 99 q^{9} - 4 q^{12} - 4 q^{14} - 5 q^{15} + 96 q^{16} - 8 q^{20} - 3 q^{23} + 97 q^{25} - 6 q^{26} - 7 q^{27} - 5 q^{31} - 8 q^{34} + 86 q^{36} - 7 q^{37} - 12 q^{38}+ \cdots + 67 q^{97}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(Γ0(1331))S_{2}^{\mathrm{new}}(\Gamma_0(1331)) 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} 11
1331.2.a.a 1331.a 1.a 55 10.62810.628 Q(ζ22)+\Q(\zeta_{22})^+ Q(11)\Q(\sqrt{-11}) 1331.2.a.a 00 5-5 4-4 00 ++ N(U(1))N(\mathrm{U}(1)) q+(1β2+β4)q32q4+(2+)q5+q+(-1-\beta _{2}+\beta _{4})q^{3}-2q^{4}+(-2+\cdots)q^{5}+\cdots
1331.2.a.b 1331.a 1.a 55 10.62810.628 Q(ζ22)+\Q(\zeta_{22})^+ Q(11)\Q(\sqrt{-11}) 1331.2.a.b 00 66 77 00 - N(U(1))N(\mathrm{U}(1)) q+(2+β22β3+β4)q32q4+(1+)q5+q+(2+\beta _{2}-2\beta _{3}+\beta _{4})q^{3}-2q^{4}+(1+\cdots)q^{5}+\cdots
1331.2.a.c 1331.a 1.a 1010 10.62810.628 10.10.\cdots.1 None 1331.2.a.c 00 2-2 12-12 00 ++ SU(2)\mathrm{SU}(2) q+β1q2β2q3+(1+β2)q4+(2+)q5+q+\beta _{1}q^{2}-\beta _{2}q^{3}+(1+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots
1331.2.a.d 1331.a 1.a 2525 10.62810.628 None 1331.2.a.d 5-5 3-3 3-3 19-19 ++ SU(2)\mathrm{SU}(2)
1331.2.a.e 1331.a 1.a 2525 10.62810.628 None 1331.2.a.d 55 3-3 3-3 1919 - SU(2)\mathrm{SU}(2)
1331.2.a.f 1331.a 1.a 3030 10.62810.628 None 1331.2.a.f 00 66 1414 00 - SU(2)\mathrm{SU}(2)

Decomposition of S2old(Γ0(1331))S_{2}^{\mathrm{old}}(\Gamma_0(1331)) into lower level spaces

S2old(Γ0(1331)) S_{2}^{\mathrm{old}}(\Gamma_0(1331)) \simeq S2new(Γ0(11))S_{2}^{\mathrm{new}}(\Gamma_0(11))3^{\oplus 3}\oplusS2new(Γ0(121))S_{2}^{\mathrm{new}}(\Gamma_0(121))2^{\oplus 2}