Properties

Label 9196.2.a
Level 91969196
Weight 22
Character orbit 9196.a
Rep. character χ9196(1,)\chi_{9196}(1,\cdot)
Character field Q\Q
Dimension 163163
Newform subspaces 2424
Sturm bound 26402640
Trace bound 1313

Related objects

Downloads

Learn more

Defining parameters

Level: N N == 9196=2211219 9196 = 2^{2} \cdot 11^{2} \cdot 19
Weight: k k == 2 2
Character orbit: [χ][\chi] == 9196.a (trivial)
Character field: Q\Q
Newform subspaces: 24 24
Sturm bound: 26402640
Trace bound: 1313
Distinguishing TpT_p: 33, 55, 77, 1313

Dimensions

The following table gives the dimensions of various subspaces of M2(Γ0(9196))M_{2}(\Gamma_0(9196)).

Total New Old
Modular forms 1356 163 1193
Cusp forms 1285 163 1122
Eisenstein series 71 0 71

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

2211111919FrickeTotalCuspEisenstein
AllNewOldAllNewOldAllNewOld
++++++++16216200162162151151001511511111001111
++++--18018000180180168168001681681212001212
++-++-17717700177177165165001651651212001212
++--++16516500165165153153001531531212001212
-++++-16816841411271271621624141121121660066
-++-++16816837371311311621623737125125660066
--++++16816840401281281621624040122122660066
----16816845451231231621624545117117660066
Plus space++663663777758658662862877775515513535003535
Minus space-693693868660760765765786865715713636003636

Trace form

163q2q37q5+3q7+151q98q13+2q15q17+q1910q218q23+152q2520q2710q29+4q3119q3522q374q3918q41+8q97+O(q100) 163 q - 2 q^{3} - 7 q^{5} + 3 q^{7} + 151 q^{9} - 8 q^{13} + 2 q^{15} - q^{17} + q^{19} - 10 q^{21} - 8 q^{23} + 152 q^{25} - 20 q^{27} - 10 q^{29} + 4 q^{31} - 19 q^{35} - 22 q^{37} - 4 q^{39} - 18 q^{41}+ \cdots - 8 q^{97}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(Γ0(9196))S_{2}^{\mathrm{new}}(\Gamma_0(9196)) 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} 2 11 19
9196.2.a.a 9196.a 1.a 11 73.43073.430 Q\Q None 9196.2.a.a 00 1-1 11 2-2 - ++ ++ SU(2)\mathrm{SU}(2) qq3+q52q72q96q13+q-q^{3}+q^{5}-2q^{7}-2q^{9}-6q^{13}+\cdots
9196.2.a.b 9196.a 1.a 11 73.43073.430 Q\Q None 836.2.a.a 00 1-1 11 00 - - ++ SU(2)\mathrm{SU}(2) qq3+q52q9+2q13q15+q-q^{3}+q^{5}-2q^{9}+2q^{13}-q^{15}+\cdots
9196.2.a.c 9196.a 1.a 11 73.43073.430 Q\Q None 9196.2.a.a 00 1-1 11 22 - ++ - SU(2)\mathrm{SU}(2) qq3+q5+2q72q9+6q13+q-q^{3}+q^{5}+2q^{7}-2q^{9}+6q^{13}+\cdots
9196.2.a.d 9196.a 1.a 11 73.43073.430 Q\Q None 9196.2.a.d 00 00 3-3 00 - - ++ SU(2)\mathrm{SU}(2) q3q53q9q13+7q17q19+q-3q^{5}-3q^{9}-q^{13}+7q^{17}-q^{19}+\cdots
9196.2.a.e 9196.a 1.a 11 73.43073.430 Q\Q None 9196.2.a.d 00 00 3-3 00 - - - SU(2)\mathrm{SU}(2) q3q53q9+q137q17+q19+q-3q^{5}-3q^{9}+q^{13}-7q^{17}+q^{19}+\cdots
9196.2.a.f 9196.a 1.a 11 73.43073.430 Q\Q None 76.2.a.a 00 22 1-1 33 - - - SU(2)\mathrm{SU}(2) q+2q3q5+3q7+q9+4q13+q+2q^{3}-q^{5}+3q^{7}+q^{9}+4q^{13}+\cdots
9196.2.a.g 9196.a 1.a 11 73.43073.430 Q\Q None 836.2.a.b 00 22 22 00 - - ++ SU(2)\mathrm{SU}(2) q+2q3+2q5+q94q13+4q15+q+2q^{3}+2q^{5}+q^{9}-4q^{13}+4q^{15}+\cdots
9196.2.a.h 9196.a 1.a 22 73.43073.430 Q(2)\Q(\sqrt{2}) None 836.2.a.c 00 2-2 2-2 00 - - - SU(2)\mathrm{SU}(2) q+(1+β)q3q5+βq72βq9+q+(-1+\beta )q^{3}-q^{5}+\beta q^{7}-2\beta q^{9}+\cdots
9196.2.a.i 9196.a 1.a 66 73.43073.430 6.6.34963625.1 None 836.2.j.a 00 2-2 7-7 4-4 - - ++ SU(2)\mathrm{SU}(2) qβ1q3+(1+β5)q5+(1+β1+)q7+q-\beta _{1}q^{3}+(-1+\beta _{5})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots
9196.2.a.j 9196.a 1.a 66 73.43073.430 6.6.34963625.1 None 836.2.j.a 00 2-2 7-7 44 - ++ - SU(2)\mathrm{SU}(2) qβ1q3+(1+β5)q5+(1β1β2+)q7+q-\beta _{1}q^{3}+(-1+\beta _{5})q^{5}+(1-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots
9196.2.a.k 9196.a 1.a 66 73.43073.430 Q[x]/(x6)\mathbb{Q}[x]/(x^{6} - \cdots) None 836.2.a.d 00 2-2 00 2-2 - - ++ SU(2)\mathrm{SU}(2) qβ1q3β5q5β4q7+(2+β2+)q9+q-\beta _{1}q^{3}-\beta _{5}q^{5}-\beta _{4}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots
9196.2.a.l 9196.a 1.a 66 73.43073.430 6.6.114134848.1 None 9196.2.a.l 00 00 4-4 4-4 - ++ - SU(2)\mathrm{SU}(2) qβ1q3+(1+β5)q5+(β1β4+)q7+q-\beta _{1}q^{3}+(-1+\beta _{5})q^{5}+(-\beta _{1}-\beta _{4}+\cdots)q^{7}+\cdots
9196.2.a.m 9196.a 1.a 66 73.43073.430 6.6.114134848.1 None 9196.2.a.l 00 00 4-4 44 - ++ ++ SU(2)\mathrm{SU}(2) qβ1q3+(1+β5)q5+(β1+β4+)q7+q-\beta _{1}q^{3}+(-1+\beta _{5})q^{5}+(\beta _{1}+\beta _{4}+\cdots)q^{7}+\cdots
9196.2.a.n 9196.a 1.a 66 73.43073.430 6.6.744786576.1 None 836.2.a.e 00 11 55 22 - - - SU(2)\mathrm{SU}(2) q+β1q3+(1+β5)q5+(1β1+β2+)q7+q+\beta _{1}q^{3}+(1+\beta _{5})q^{5}+(1-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots
9196.2.a.o 9196.a 1.a 77 73.43073.430 Q[x]/(x7)\mathbb{Q}[x]/(x^{7} - \cdots) None 9196.2.a.o 00 1-1 33 2-2 - - ++ SU(2)\mathrm{SU}(2) qβ1q3β4q5β2q7+(1+β2+)q9+q-\beta _{1}q^{3}-\beta _{4}q^{5}-\beta _{2}q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots
9196.2.a.p 9196.a 1.a 77 73.43073.430 Q[x]/(x7)\mathbb{Q}[x]/(x^{7} - \cdots) None 9196.2.a.o 00 1-1 33 22 - - - SU(2)\mathrm{SU}(2) qβ1q3β4q5+β2q7+(1+β2+)q9+q-\beta _{1}q^{3}-\beta _{4}q^{5}+\beta _{2}q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots
9196.2.a.q 9196.a 1.a 88 73.43073.430 Q[x]/(x8)\mathbb{Q}[x]/(x^{8} - \cdots) None 9196.2.a.q 00 1-1 00 2-2 - - ++ SU(2)\mathrm{SU}(2) qβ1q3β4q5+(β2+β3+β6+)q7+q-\beta _{1}q^{3}-\beta _{4}q^{5}+(-\beta _{2}+\beta _{3}+\beta _{6}+\cdots)q^{7}+\cdots
9196.2.a.r 9196.a 1.a 88 73.43073.430 Q[x]/(x8)\mathbb{Q}[x]/(x^{8} - \cdots) None 9196.2.a.q 00 1-1 00 22 - - - SU(2)\mathrm{SU}(2) qβ1q3β4q5+(β2β3β6)q7+q-\beta _{1}q^{3}-\beta _{4}q^{5}+(\beta _{2}-\beta _{3}-\beta _{6})q^{7}+\cdots
9196.2.a.s 9196.a 1.a 1010 73.43073.430 Q[x]/(x10)\mathbb{Q}[x]/(x^{10} - \cdots) None 836.2.j.b 00 00 88 5-5 - ++ - SU(2)\mathrm{SU}(2) qβ1q3+(1β7)q5+(β5β8+)q7+q-\beta _{1}q^{3}+(1-\beta _{7})q^{5}+(-\beta _{5}-\beta _{8}+\cdots)q^{7}+\cdots
9196.2.a.t 9196.a 1.a 1010 73.43073.430 Q[x]/(x10)\mathbb{Q}[x]/(x^{10} - \cdots) None 836.2.j.b 00 00 88 55 - - ++ SU(2)\mathrm{SU}(2) qβ1q3+(1β7)q5+(β5+β8)q7+q-\beta _{1}q^{3}+(1-\beta _{7})q^{5}+(\beta _{5}+\beta _{8})q^{7}+\cdots
9196.2.a.u 9196.a 1.a 1414 73.43073.430 Q[x]/(x14)\mathbb{Q}[x]/(x^{14} - \cdots) None 9196.2.a.u 00 2-2 6-6 4-4 - ++ - SU(2)\mathrm{SU}(2) qβ1q3+β6q5+β9q7+(1+β2+)q9+q-\beta _{1}q^{3}+\beta _{6}q^{5}+\beta _{9}q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots
9196.2.a.v 9196.a 1.a 1414 73.43073.430 Q[x]/(x14)\mathbb{Q}[x]/(x^{14} - \cdots) None 9196.2.a.u 00 2-2 6-6 44 - ++ ++ SU(2)\mathrm{SU}(2) qβ1q3+β6q5β9q7+(1+β2+)q9+q-\beta _{1}q^{3}+\beta _{6}q^{5}-\beta _{9}q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots
9196.2.a.w 9196.a 1.a 2020 73.43073.430 Q[x]/(x20)\mathbb{Q}[x]/(x^{20} - \cdots) None 836.2.j.c 00 66 22 4-4 - - - SU(2)\mathrm{SU}(2) q+β1q3+β14q5+β10q7+(1+β2+)q9+q+\beta _{1}q^{3}+\beta _{14}q^{5}+\beta _{10}q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots
9196.2.a.x 9196.a 1.a 2020 73.43073.430 Q[x]/(x20)\mathbb{Q}[x]/(x^{20} - \cdots) None 836.2.j.c 00 66 22 44 - ++ ++ SU(2)\mathrm{SU}(2) q+β1q3+β14q5β10q7+(1+β2+)q9+q+\beta _{1}q^{3}+\beta _{14}q^{5}-\beta _{10}q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots

Decomposition of S2old(Γ0(9196))S_{2}^{\mathrm{old}}(\Gamma_0(9196)) into lower level spaces