Properties

Label 63.10.a
Level 6363
Weight 1010
Character orbit 63.a
Rep. character χ63(1,)\chi_{63}(1,\cdot)
Character field Q\Q
Dimension 2323
Newform subspaces 88
Sturm bound 8080
Trace bound 22

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Defining parameters

Level: N N == 63=327 63 = 3^{2} \cdot 7
Weight: k k == 10 10
Character orbit: [χ][\chi] == 63.a (trivial)
Character field: Q\Q
Newform subspaces: 8 8
Sturm bound: 8080
Trace bound: 22
Distinguishing TpT_p: 22

Dimensions

The following table gives the dimensions of various subspaces of M10(Γ0(63))M_{10}(\Gamma_0(63)).

Total New Old
Modular forms 76 23 53
Cusp forms 68 23 45
Eisenstein series 8 0 8

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

3377FrickeTotalCuspEisenstein
AllNewOldAllNewOldAllNewOld
++++++18184414141616441212220022
++--20206614141818661212220022
-++-20207713131818771111220022
--++18186612121616661010220022
Plus space++363610102626323210102222440044
Minus space-404013132727363613132323440044

Trace form

23q17q2+6913q43868q5+2401q726061q8+8524q10+46268q11193804q1388837q14+2002885q16173862q17640366q19+37228q202882468q22+98001617q98+O(q100) 23 q - 17 q^{2} + 6913 q^{4} - 3868 q^{5} + 2401 q^{7} - 26061 q^{8} + 8524 q^{10} + 46268 q^{11} - 193804 q^{13} - 88837 q^{14} + 2002885 q^{16} - 173862 q^{17} - 640366 q^{19} + 37228 q^{20} - 2882468 q^{22}+ \cdots - 98001617 q^{98}+O(q^{100}) Copy content Toggle raw display

Decomposition of S10new(Γ0(63))S_{10}^{\mathrm{new}}(\Gamma_0(63)) 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 7
63.10.a.a 63.a 1.a 11 32.44732.447 Q\Q None 21.10.a.a 2424 00 144144 24012401 - - SU(2)\mathrm{SU}(2) q+24q2+26q4+122q5+74q7+q+24q^{2}+2^{6}q^{4}+12^{2}q^{5}+7^{4}q^{7}+\cdots
63.10.a.b 63.a 1.a 22 32.44732.447 Q(345)\Q(\sqrt{345}) None 21.10.a.c 30-30 00 1128-1128 48024802 - - SU(2)\mathrm{SU}(2) q+(15β)q2+(58+30β)q4+(564+)q5+q+(-15-\beta )q^{2}+(58+30\beta )q^{4}+(-564+\cdots)q^{5}+\cdots
63.10.a.c 63.a 1.a 22 32.44732.447 Q(2353)\Q(\sqrt{2353}) None 21.10.a.b 9-9 00 1170-1170 4802-4802 - ++ SU(2)\mathrm{SU}(2) q+(4β)q2+(92+9β)q4+(620+)q5+q+(-4-\beta )q^{2}+(92+9\beta )q^{4}+(-620+\cdots)q^{5}+\cdots
63.10.a.d 63.a 1.a 22 32.44732.447 Q(193)\Q(\sqrt{193}) None 7.10.a.a 66 00 22382238 4802-4802 - ++ SU(2)\mathrm{SU}(2) q+(3+β)q2+(310+6β)q4+(1119+)q5+q+(3+\beta )q^{2}+(-310+6\beta )q^{4}+(1119+\cdots)q^{5}+\cdots
63.10.a.e 63.a 1.a 33 32.44732.447 Q[x]/(x3)\mathbb{Q}[x]/(x^{3} - \cdots) None 7.10.a.b 21-21 00 1554-1554 72037203 - - SU(2)\mathrm{SU}(2) q+(7+β2)q2+(519+7β18β2)q4+q+(-7+\beta _{2})q^{2}+(519+7\beta _{1}-8\beta _{2})q^{4}+\cdots
63.10.a.f 63.a 1.a 33 32.44732.447 Q[x]/(x3)\mathbb{Q}[x]/(x^{3} - \cdots) None 21.10.a.d 1313 00 2398-2398 7203-7203 - ++ SU(2)\mathrm{SU}(2) q+(4+β1)q2+(555+7β15β2)q4+q+(4+\beta _{1})q^{2}+(555+7\beta _{1}-5\beta _{2})q^{4}+\cdots
63.10.a.g 63.a 1.a 44 32.44732.447 Q[x]/(x4)\mathbb{Q}[x]/(x^{4} - \cdots) None 63.10.a.g 00 00 00 9604-9604 ++ ++ SU(2)\mathrm{SU}(2) q+β1q2+(446+β3)q4+(20β1+)q5+q+\beta _{1}q^{2}+(446+\beta _{3})q^{4}+(-20\beta _{1}+\cdots)q^{5}+\cdots
63.10.a.h 63.a 1.a 66 32.44732.447 Q[x]/(x6)\mathbb{Q}[x]/(x^{6} - \cdots) None 63.10.a.h 00 00 00 1440614406 ++ - SU(2)\mathrm{SU}(2) q+β1q2+(357+β3)q4+(24β1β2+)q5+q+\beta _{1}q^{2}+(357+\beta _{3})q^{4}+(24\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots

Decomposition of S10old(Γ0(63))S_{10}^{\mathrm{old}}(\Gamma_0(63)) into lower level spaces

S10old(Γ0(63)) S_{10}^{\mathrm{old}}(\Gamma_0(63)) \simeq S10new(Γ0(3))S_{10}^{\mathrm{new}}(\Gamma_0(3))4^{\oplus 4}\oplusS10new(Γ0(7))S_{10}^{\mathrm{new}}(\Gamma_0(7))3^{\oplus 3}\oplusS10new(Γ0(9))S_{10}^{\mathrm{new}}(\Gamma_0(9))2^{\oplus 2}\oplusS10new(Γ0(21))S_{10}^{\mathrm{new}}(\Gamma_0(21))2^{\oplus 2}