Properties

Label 11.12.a
Level 1111
Weight 1212
Character orbit 11.a
Rep. character χ11(1,)\chi_{11}(1,\cdot)
Character field Q\Q
Dimension 88
Newform subspaces 22
Sturm bound 1212
Trace bound 11

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Defining parameters

Level: N N == 11 11
Weight: k k == 12 12
Character orbit: [χ][\chi] == 11.a (trivial)
Character field: Q\Q
Newform subspaces: 2 2
Sturm bound: 1212
Trace bound: 11
Distinguishing TpT_p: 22

Dimensions

The following table gives the dimensions of various subspaces of M12(Γ0(11))M_{12}(\Gamma_0(11)).

Total New Old
Modular forms 12 8 4
Cusp forms 10 8 2
Eisenstein series 2 0 2

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
++775522665511110011
-553322443311110011

Trace form

8q+32q2233q3+9076q415703q5+10942q6+73958q756676q8+307703q9+449510q10322102q11+1431584q12+1964714q13+1988732q142772689q15+113395848049q99+O(q100) 8 q + 32 q^{2} - 233 q^{3} + 9076 q^{4} - 15703 q^{5} + 10942 q^{6} + 73958 q^{7} - 56676 q^{8} + 307703 q^{9} + 449510 q^{10} - 322102 q^{11} + 1431584 q^{12} + 1964714 q^{13} + 1988732 q^{14} - 2772689 q^{15}+ \cdots - 113395848049 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S12new(Γ0(11))S_{12}^{\mathrm{new}}(\Gamma_0(11)) 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
11.12.a.a 11.a 1.a 33 8.4528.452 3.3.202533.1 None 11.12.a.a 00 393-393 7305-7305 5082-5082 - SU(2)\mathrm{SU}(2) qβ1q2+(1312β14β2)q3+q-\beta _{1}q^{2}+(-131-2\beta _{1}-4\beta _{2})q^{3}+\cdots
11.12.a.b 11.a 1.a 55 8.4528.452 Q[x]/(x5)\mathbb{Q}[x]/(x^{5} - \cdots) None 11.12.a.b 3232 160160 8398-8398 7904079040 ++ SU(2)\mathrm{SU}(2) q+(6+β1)q2+(25β3)q3+(1239+)q4+q+(6+\beta _{1})q^{2}+(2^{5}-\beta _{3})q^{3}+(1239+\cdots)q^{4}+\cdots

Decomposition of S12old(Γ0(11))S_{12}^{\mathrm{old}}(\Gamma_0(11)) into lower level spaces

S12old(Γ0(11)) S_{12}^{\mathrm{old}}(\Gamma_0(11)) \simeq S12new(Γ0(1))S_{12}^{\mathrm{new}}(\Gamma_0(1))2^{\oplus 2}