Properties

Label 39.10.a
Level 3939
Weight 1010
Character orbit 39.a
Rep. character χ39(1,)\chi_{39}(1,\cdot)
Character field Q\Q
Dimension 1818
Newform subspaces 44
Sturm bound 4646
Trace bound 11

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Defining parameters

Level: N N == 39=313 39 = 3 \cdot 13
Weight: k k == 10 10
Character orbit: [χ][\chi] == 39.a (trivial)
Character field: Q\Q
Newform subspaces: 4 4
Sturm bound: 4646
Trace bound: 11
Distinguishing TpT_p: 22

Dimensions

The following table gives the dimensions of various subspaces of M10(Γ0(39))M_{10}(\Gamma_0(39)).

Total New Old
Modular forms 44 18 26
Cusp forms 40 18 22
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.

331313FrickeTotalCuspEisenstein
AllNewOldAllNewOldAllNewOld
++++++10104466994455110011
++--1212557711115566110011
-++-1212666611116655110011
--++10103377993366110011
Plus space++20207713131818771111220022
Minus space-242411111313222211111111220022

Trace form

18q+68q2+4952q4+1136q58748q67472q7+69360q8+118098q9+1140q10146784q11+57996q1257122q13422192q14163944q15+1448116q16+963049824q99+O(q100) 18 q + 68 q^{2} + 4952 q^{4} + 1136 q^{5} - 8748 q^{6} - 7472 q^{7} + 69360 q^{8} + 118098 q^{9} + 1140 q^{10} - 146784 q^{11} + 57996 q^{12} - 57122 q^{13} - 422192 q^{14} - 163944 q^{15} + 1448116 q^{16}+ \cdots - 963049824 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S10new(Γ0(39))S_{10}^{\mathrm{new}}(\Gamma_0(39)) 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 13
39.10.a.a 39.a 1.a 33 20.08620.086 Q[x]/(x3)\mathbb{Q}[x]/(x^{3} - \cdots) None 39.10.a.a 18-18 243243 888-888 14406-14406 - - SU(2)\mathrm{SU}(2) q+(6+β1)q2+34q3+(3286β1+)q4+q+(-6+\beta _{1})q^{2}+3^{4}q^{3}+(328-6\beta _{1}+\cdots)q^{4}+\cdots
39.10.a.b 39.a 1.a 44 20.08620.086 Q[x]/(x4)\mathbb{Q}[x]/(x^{4} - \cdots) None 39.10.a.b 3636 324-324 1044-1044 58685868 ++ ++ SU(2)\mathrm{SU}(2) q+(9+β1)q234q3+(118+23β1+)q4+q+(9+\beta _{1})q^{2}-3^{4}q^{3}+(118+23\beta _{1}+\cdots)q^{4}+\cdots
39.10.a.c 39.a 1.a 55 20.08620.086 Q[x]/(x5)\mathbb{Q}[x]/(x^{5} - \cdots) None 39.10.a.c 5252 405-405 26242624 4802-4802 ++ - SU(2)\mathrm{SU}(2) q+(10+β1)q234q3+(326+8β1+)q4+q+(10+\beta _{1})q^{2}-3^{4}q^{3}+(326+8\beta _{1}+\cdots)q^{4}+\cdots
39.10.a.d 39.a 1.a 66 20.08620.086 Q[x]/(x6)\mathbb{Q}[x]/(x^{6} - \cdots) None 39.10.a.d 2-2 486486 444444 58685868 - ++ SU(2)\mathrm{SU}(2) qβ1q2+34q3+(3116β1+β3+)q4+q-\beta _{1}q^{2}+3^{4}q^{3}+(311-6\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots

Decomposition of S10old(Γ0(39))S_{10}^{\mathrm{old}}(\Gamma_0(39)) into lower level spaces

S10old(Γ0(39)) S_{10}^{\mathrm{old}}(\Gamma_0(39)) \simeq S10new(Γ0(3))S_{10}^{\mathrm{new}}(\Gamma_0(3))2^{\oplus 2}\oplusS10new(Γ0(13))S_{10}^{\mathrm{new}}(\Gamma_0(13))2^{\oplus 2}