Properties

Label 1116.2.a
Level 11161116
Weight 22
Character orbit 1116.a
Rep. character χ1116(1,)\chi_{1116}(1,\cdot)
Character field Q\Q
Dimension 1212
Newform subspaces 99
Sturm bound 384384
Trace bound 77

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Defining parameters

Level: N N == 1116=223231 1116 = 2^{2} \cdot 3^{2} \cdot 31
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1116.a (trivial)
Character field: Q\Q
Newform subspaces: 9 9
Sturm bound: 384384
Trace bound: 77
Distinguishing TpT_p: 55, 77

Dimensions

The following table gives the dimensions of various subspaces of M2(Γ0(1116))M_{2}(\Gamma_0(1116)).

Total New Old
Modular forms 204 12 192
Cusp forms 181 12 169
Eisenstein series 23 0 23

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

22333131FrickeTotalCuspEisenstein
AllNewOldAllNewOldAllNewOld
++++++++20200020201717001717330033
++++--32320032322828002828440044
++-++-32320032322828002828440044
++--++20200020201616001616440044
-++++-22222220202020221818220022
-++-++28282226262626222424220022
--++++28284424242626442222220022
----22224418182020441616220022
Plus space++969666909085856679791111001111
Minus space-1081086610210296966690901212001212

Trace form

12q+2q5+2q74q116q132q1714q19+6q23+6q2510q2918q35+8q37+2q416q43+16q472q498q538q55+18q59+10q97+O(q100) 12 q + 2 q^{5} + 2 q^{7} - 4 q^{11} - 6 q^{13} - 2 q^{17} - 14 q^{19} + 6 q^{23} + 6 q^{25} - 10 q^{29} - 18 q^{35} + 8 q^{37} + 2 q^{41} - 6 q^{43} + 16 q^{47} - 2 q^{49} - 8 q^{53} - 8 q^{55} + 18 q^{59}+ \cdots - 10 q^{97}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(Γ0(1116))S_{2}^{\mathrm{new}}(\Gamma_0(1116)) 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 3 31
1116.2.a.a 1116.a 1.a 11 8.9118.911 Q\Q None 372.2.a.d 00 00 3-3 1-1 - - - SU(2)\mathrm{SU}(2) q3q5q7+2q13q19+6q23+q-3q^{5}-q^{7}+2q^{13}-q^{19}+6q^{23}+\cdots
1116.2.a.b 1116.a 1.a 11 8.9118.911 Q\Q None 124.2.a.b 00 00 1-1 33 - - ++ SU(2)\mathrm{SU}(2) qq5+3q76q114q135q19+q-q^{5}+3q^{7}-6q^{11}-4q^{13}-5q^{19}+\cdots
1116.2.a.c 1116.a 1.a 11 8.9118.911 Q\Q None 372.2.a.a 00 00 11 1-1 - - - SU(2)\mathrm{SU}(2) q+q5q76q13+8q17+7q19+q+q^{5}-q^{7}-6q^{13}+8q^{17}+7q^{19}+\cdots
1116.2.a.d 1116.a 1.a 11 8.9118.911 Q\Q None 372.2.a.c 00 00 22 44 - - - SU(2)\mathrm{SU}(2) q+2q5+4q7+2q13+4q194q23+q+2q^{5}+4q^{7}+2q^{13}+4q^{19}-4q^{23}+\cdots
1116.2.a.e 1116.a 1.a 11 8.9118.911 Q\Q None 372.2.a.b 00 00 33 5-5 - - ++ SU(2)\mathrm{SU}(2) q+3q55q72q114q13+4q17+q+3q^{5}-5q^{7}-2q^{11}-4q^{13}+4q^{17}+\cdots
1116.2.a.f 1116.a 1.a 11 8.9118.911 Q\Q None 124.2.a.a 00 00 33 1-1 - - - SU(2)\mathrm{SU}(2) q+3q5q7+6q11+2q136q17+q+3q^{5}-q^{7}+6q^{11}+2q^{13}-6q^{17}+\cdots
1116.2.a.g 1116.a 1.a 22 8.9118.911 Q(17)\Q(\sqrt{17}) None 372.2.a.e 00 00 3-3 1-1 - - ++ SU(2)\mathrm{SU}(2) q+(1β)q5+(1+β)q7+(2+)q11+q+(-1-\beta )q^{5}+(-1+\beta )q^{7}+(-2+\cdots)q^{11}+\cdots
1116.2.a.h 1116.a 1.a 22 8.9118.911 Q(3)\Q(\sqrt{3}) None 1116.2.a.h 00 00 00 2-2 - ++ - SU(2)\mathrm{SU}(2) q+βq5q72βq114q134βq17+q+\beta q^{5}-q^{7}-2\beta q^{11}-4q^{13}-4\beta q^{17}+\cdots
1116.2.a.i 1116.a 1.a 22 8.9118.911 Q(7)\Q(\sqrt{7}) None 1116.2.a.i 00 00 00 66 - ++ ++ SU(2)\mathrm{SU}(2) q+βq5+3q7+2q13+q19+2βq23+q+\beta q^{5}+3q^{7}+2q^{13}+q^{19}+2\beta q^{23}+\cdots

Decomposition of S2old(Γ0(1116))S_{2}^{\mathrm{old}}(\Gamma_0(1116)) into lower level spaces