Properties

Label 4368.2.a
Level 43684368
Weight 22
Character orbit 4368.a
Rep. character χ4368(1,)\chi_{4368}(1,\cdot)
Character field Q\Q
Dimension 7272
Newform subspaces 4545
Sturm bound 17921792
Trace bound 1111

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Defining parameters

Level: N N == 4368=243713 4368 = 2^{4} \cdot 3 \cdot 7 \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 4368.a (trivial)
Character field: Q\Q
Newform subspaces: 45 45
Sturm bound: 17921792
Trace bound: 1111
Distinguishing TpT_p: 55, 1111, 1717

Dimensions

The following table gives the dimensions of various subspaces of M2(Γ0(4368))M_{2}(\Gamma_0(4368)).

Total New Old
Modular forms 920 72 848
Cusp forms 873 72 801
Eisenstein series 47 0 47

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

2233771313FrickeDim
++++++++++66
++++++--44
++++-++-33
++++--++55
++-++++-66
++-++-++22
++--++++33
++----77
-++++++-44
-++++-++55
-++-++++33
-++---66
--++++++66
--++--55
---++-55
----++22
Plus space++3232
Minus space-4040

Trace form

72q4q7+72q98q118q1516q198q23+72q25+16q2916q31+16q378q3924q43+72q4916q51+16q5316q55+32q61+8q99+O(q100) 72 q - 4 q^{7} + 72 q^{9} - 8 q^{11} - 8 q^{15} - 16 q^{19} - 8 q^{23} + 72 q^{25} + 16 q^{29} - 16 q^{31} + 16 q^{37} - 8 q^{39} - 24 q^{43} + 72 q^{49} - 16 q^{51} + 16 q^{53} - 16 q^{55} + 32 q^{61}+ \cdots - 8 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(Γ0(4368))S_{2}^{\mathrm{new}}(\Gamma_0(4368)) 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 7 13
4368.2.a.a 4368.a 1.a 11 34.87934.879 Q\Q None 2184.2.a.i 00 1-1 3-3 1-1 ++ ++ ++ ++ SU(2)\mathrm{SU}(2) qq33q5q7+q9+2q11q13+q-q^{3}-3q^{5}-q^{7}+q^{9}+2q^{11}-q^{13}+\cdots
4368.2.a.b 4368.a 1.a 11 34.87934.879 Q\Q None 2184.2.a.j 00 1-1 2-2 1-1 ++ ++ ++ - SU(2)\mathrm{SU}(2) qq32q5q7+q9+4q11+q13+q-q^{3}-2q^{5}-q^{7}+q^{9}+4q^{11}+q^{13}+\cdots
4368.2.a.c 4368.a 1.a 11 34.87934.879 Q\Q None 1092.2.a.e 00 1-1 2-2 11 - ++ - ++ SU(2)\mathrm{SU}(2) qq32q5+q7+q9q13+2q15+q-q^{3}-2q^{5}+q^{7}+q^{9}-q^{13}+2q^{15}+\cdots
4368.2.a.d 4368.a 1.a 11 34.87934.879 Q\Q None 546.2.a.b 00 1-1 2-2 11 - ++ - - SU(2)\mathrm{SU}(2) qq32q5+q7+q9+4q11+q13+q-q^{3}-2q^{5}+q^{7}+q^{9}+4q^{11}+q^{13}+\cdots
4368.2.a.e 4368.a 1.a 11 34.87934.879 Q\Q None 546.2.a.f 00 1-1 1-1 1-1 - ++ ++ ++ SU(2)\mathrm{SU}(2) qq3q5q7+q95q11q13+q-q^{3}-q^{5}-q^{7}+q^{9}-5q^{11}-q^{13}+\cdots
4368.2.a.f 4368.a 1.a 11 34.87934.879 Q\Q None 2184.2.a.l 00 1-1 00 1-1 ++ ++ ++ ++ SU(2)\mathrm{SU}(2) qq3q7+q9+2q11q136q17+q-q^{3}-q^{7}+q^{9}+2q^{11}-q^{13}-6q^{17}+\cdots
4368.2.a.g 4368.a 1.a 11 34.87934.879 Q\Q None 2184.2.a.k 00 1-1 00 11 ++ ++ - ++ SU(2)\mathrm{SU}(2) qq3+q7+q9+2q11q132q17+q-q^{3}+q^{7}+q^{9}+2q^{11}-q^{13}-2q^{17}+\cdots
4368.2.a.h 4368.a 1.a 11 34.87934.879 Q\Q None 546.2.a.c 00 1-1 11 11 - ++ - ++ SU(2)\mathrm{SU}(2) qq3+q5+q7+q93q11q13+q-q^{3}+q^{5}+q^{7}+q^{9}-3q^{11}-q^{13}+\cdots
4368.2.a.i 4368.a 1.a 11 34.87934.879 Q\Q None 273.2.a.b 00 1-1 11 11 - ++ - ++ SU(2)\mathrm{SU}(2) qq3+q5+q7+q9+2q11q13+q-q^{3}+q^{5}+q^{7}+q^{9}+2q^{11}-q^{13}+\cdots
4368.2.a.j 4368.a 1.a 11 34.87934.879 Q\Q None 2184.2.a.m 00 1-1 22 1-1 ++ ++ ++ ++ SU(2)\mathrm{SU}(2) qq3+2q5q7+q94q11q13+q-q^{3}+2q^{5}-q^{7}+q^{9}-4q^{11}-q^{13}+\cdots
4368.2.a.k 4368.a 1.a 11 34.87934.879 Q\Q None 546.2.a.g 00 1-1 22 1-1 - ++ ++ ++ SU(2)\mathrm{SU}(2) qq3+2q5q7+q9+4q11q13+q-q^{3}+2q^{5}-q^{7}+q^{9}+4q^{11}-q^{13}+\cdots
4368.2.a.l 4368.a 1.a 11 34.87934.879 Q\Q None 546.2.a.d 00 1-1 33 1-1 - ++ ++ - SU(2)\mathrm{SU}(2) qq3+3q5q7+q93q11+q13+q-q^{3}+3q^{5}-q^{7}+q^{9}-3q^{11}+q^{13}+\cdots
4368.2.a.m 4368.a 1.a 11 34.87934.879 Q\Q None 2184.2.a.b 00 11 3-3 1-1 ++ - ++ ++ SU(2)\mathrm{SU}(2) q+q33q5q7+q96q11q13+q+q^{3}-3q^{5}-q^{7}+q^{9}-6q^{11}-q^{13}+\cdots
4368.2.a.n 4368.a 1.a 11 34.87934.879 Q\Q None 2184.2.a.a 00 11 3-3 1-1 ++ - ++ ++ SU(2)\mathrm{SU}(2) q+q33q5q7+q9+5q11q13+q+q^{3}-3q^{5}-q^{7}+q^{9}+5q^{11}-q^{13}+\cdots
4368.2.a.o 4368.a 1.a 11 34.87934.879 Q\Q None 1092.2.a.a 00 11 2-2 1-1 - - ++ ++ SU(2)\mathrm{SU}(2) q+q32q5q7+q9q132q15+q+q^{3}-2q^{5}-q^{7}+q^{9}-q^{13}-2q^{15}+\cdots
4368.2.a.p 4368.a 1.a 11 34.87934.879 Q\Q None 2184.2.a.c 00 11 2-2 1-1 ++ - ++ - SU(2)\mathrm{SU}(2) q+q32q5q7+q9+4q11+q13+q+q^{3}-2q^{5}-q^{7}+q^{9}+4q^{11}+q^{13}+\cdots
4368.2.a.q 4368.a 1.a 11 34.87934.879 Q\Q None 273.2.a.a 00 11 1-1 1-1 - - ++ - SU(2)\mathrm{SU}(2) q+q3q5q7+q9+2q11+q13+q+q^{3}-q^{5}-q^{7}+q^{9}+2q^{11}+q^{13}+\cdots
4368.2.a.r 4368.a 1.a 11 34.87934.879 Q\Q None 1092.2.a.b 00 11 1-1 11 - - - - SU(2)\mathrm{SU}(2) q+q3q5+q7+q92q11+q13+q+q^{3}-q^{5}+q^{7}+q^{9}-2q^{11}+q^{13}+\cdots
4368.2.a.s 4368.a 1.a 11 34.87934.879 Q\Q None 546.2.a.a 00 11 1-1 11 - - - - SU(2)\mathrm{SU}(2) q+q3q5+q7+q9+q11+q13+q+q^{3}-q^{5}+q^{7}+q^{9}+q^{11}+q^{13}+\cdots
4368.2.a.t 4368.a 1.a 11 34.87934.879 Q\Q None 2184.2.a.d 00 11 00 11 ++ - - ++ SU(2)\mathrm{SU}(2) q+q3+q7+q92q11q132q17+q+q^{3}+q^{7}+q^{9}-2q^{11}-q^{13}-2q^{17}+\cdots
4368.2.a.u 4368.a 1.a 11 34.87934.879 Q\Q None 1092.2.a.c 00 11 00 11 - - - ++ SU(2)\mathrm{SU}(2) q+q3+q7+q9+2q11q13+4q17+q+q^{3}+q^{7}+q^{9}+2q^{11}-q^{13}+4q^{17}+\cdots
4368.2.a.v 4368.a 1.a 11 34.87934.879 Q\Q None 2184.2.a.e 00 11 11 1-1 ++ - ++ - SU(2)\mathrm{SU}(2) q+q3+q5q7+q95q11+q13+q+q^{3}+q^{5}-q^{7}+q^{9}-5q^{11}+q^{13}+\cdots
4368.2.a.w 4368.a 1.a 11 34.87934.879 Q\Q None 1092.2.a.d 00 11 11 1-1 - - ++ ++ SU(2)\mathrm{SU}(2) q+q3+q5q7+q9+6q11q13+q+q^{3}+q^{5}-q^{7}+q^{9}+6q^{11}-q^{13}+\cdots
4368.2.a.x 4368.a 1.a 11 34.87934.879 Q\Q None 2184.2.a.g 00 11 22 1-1 ++ - ++ ++ SU(2)\mathrm{SU}(2) q+q3+2q5q7+q9+4q11q13+q+q^{3}+2q^{5}-q^{7}+q^{9}+4q^{11}-q^{13}+\cdots
4368.2.a.y 4368.a 1.a 11 34.87934.879 Q\Q None 2184.2.a.f 00 11 22 11 ++ - - - SU(2)\mathrm{SU}(2) q+q3+2q5+q7+q9+q13+2q15+q+q^{3}+2q^{5}+q^{7}+q^{9}+q^{13}+2q^{15}+\cdots
4368.2.a.z 4368.a 1.a 11 34.87934.879 Q\Q None 546.2.a.e 00 11 33 11 - - - ++ SU(2)\mathrm{SU}(2) q+q3+3q5+q7+q9q11q13+q+q^{3}+3q^{5}+q^{7}+q^{9}-q^{11}-q^{13}+\cdots
4368.2.a.ba 4368.a 1.a 11 34.87934.879 Q\Q None 2184.2.a.h 00 11 44 1-1 ++ - ++ ++ SU(2)\mathrm{SU}(2) q+q3+4q5q7+q96q11q13+q+q^{3}+4q^{5}-q^{7}+q^{9}-6q^{11}-q^{13}+\cdots
4368.2.a.bb 4368.a 1.a 22 34.87934.879 Q(17)\Q(\sqrt{17}) None 2184.2.a.q 00 2-2 3-3 22 ++ ++ - - SU(2)\mathrm{SU}(2) qq3+(1β)q5+q7+q9+(2+)q11+q-q^{3}+(-1-\beta )q^{5}+q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots
4368.2.a.bc 4368.a 1.a 22 34.87934.879 Q(33)\Q(\sqrt{33}) None 1092.2.a.g 00 2-2 11 2-2 - ++ ++ ++ SU(2)\mathrm{SU}(2) qq3+βq5q7+q92q11q13+q-q^{3}+\beta q^{5}-q^{7}+q^{9}-2q^{11}-q^{13}+\cdots
4368.2.a.bd 4368.a 1.a 22 34.87934.879 Q(33)\Q(\sqrt{33}) None 2184.2.a.r 00 2-2 11 22 ++ ++ - ++ SU(2)\mathrm{SU}(2) qq3+βq5+q7+q9+(2β)q11+q-q^{3}+\beta q^{5}+q^{7}+q^{9}+(2-\beta )q^{11}+\cdots
4368.2.a.be 4368.a 1.a 22 34.87934.879 Q(17)\Q(\sqrt{17}) None 546.2.a.j 00 2-2 33 22 - ++ - - SU(2)\mathrm{SU}(2) qq3+(1+β)q5+q7+q9+(1+)q11+q-q^{3}+(1+\beta )q^{5}+q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots
4368.2.a.bf 4368.a 1.a 22 34.87934.879 Q(17)\Q(\sqrt{17}) None 2184.2.a.n 00 22 3-3 22 ++ - - - SU(2)\mathrm{SU}(2) q+q3+(1β)q5+q7+q9+(2+)q11+q+q^{3}+(-1-\beta )q^{5}+q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots
4368.2.a.bg 4368.a 1.a 22 34.87934.879 Q(41)\Q(\sqrt{41}) None 546.2.a.i 00 22 1-1 2-2 - - ++ - SU(2)\mathrm{SU}(2) q+q3βq5q7+q9+(2β)q11+q+q^{3}-\beta q^{5}-q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots
4368.2.a.bh 4368.a 1.a 22 34.87934.879 Q(57)\Q(\sqrt{57}) None 546.2.a.h 00 22 1-1 2-2 - - ++ ++ SU(2)\mathrm{SU}(2) q+q3βq5q7+q9+(2+β)q11+q+q^{3}-\beta q^{5}-q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots
4368.2.a.bi 4368.a 1.a 22 34.87934.879 Q(17)\Q(\sqrt{17}) None 2184.2.a.o 00 22 1-1 22 ++ - - ++ SU(2)\mathrm{SU}(2) q+q3βq5+q7+q9+(2+β)q11+q+q^{3}-\beta q^{5}+q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots
4368.2.a.bj 4368.a 1.a 22 34.87934.879 Q(2)\Q(\sqrt{2}) None 273.2.a.c 00 22 00 2-2 - - ++ ++ SU(2)\mathrm{SU}(2) q+q3q7+q92q11q13+(2+)q17+q+q^{3}-q^{7}+q^{9}-2q^{11}-q^{13}+(2+\cdots)q^{17}+\cdots
4368.2.a.bk 4368.a 1.a 22 34.87934.879 Q(17)\Q(\sqrt{17}) None 2184.2.a.p 00 22 11 2-2 ++ - ++ ++ SU(2)\mathrm{SU}(2) q+q3+βq5q7+q9+2q11q13+q+q^{3}+\beta q^{5}-q^{7}+q^{9}+2q^{11}-q^{13}+\cdots
4368.2.a.bl 4368.a 1.a 22 34.87934.879 Q(5)\Q(\sqrt{5}) None 1092.2.a.f 00 22 22 2-2 - - ++ - SU(2)\mathrm{SU}(2) q+q3+(1+β)q5q7+q9+(1+)q11+q+q^{3}+(1+\beta )q^{5}-q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots
4368.2.a.bm 4368.a 1.a 33 34.87934.879 3.3.2089.1 None 2184.2.a.s 00 3-3 00 3-3 ++ ++ ++ ++ SU(2)\mathrm{SU}(2) qq3β1q5q7+q9+(β1β2)q11+q-q^{3}-\beta _{1}q^{5}-q^{7}+q^{9}+(-\beta _{1}-\beta _{2})q^{11}+\cdots
4368.2.a.bn 4368.a 1.a 33 34.87934.879 3.3.1373.1 None 1092.2.a.h 00 3-3 11 33 - ++ - - SU(2)\mathrm{SU}(2) qq3+β2q5+q7+q9β1q11+q-q^{3}+\beta _{2}q^{5}+q^{7}+q^{9}-\beta _{1}q^{11}+\cdots
4368.2.a.bo 4368.a 1.a 33 34.87934.879 3.3.961.1 None 2184.2.a.t 00 3-3 22 33 ++ ++ - - SU(2)\mathrm{SU}(2) qq3+(1β1)q5+q7+q9+(3+)q11+q-q^{3}+(1-\beta _{1})q^{5}+q^{7}+q^{9}+(-3+\cdots)q^{11}+\cdots
4368.2.a.bp 4368.a 1.a 33 34.87934.879 3.3.316.1 None 2184.2.a.u 00 3-3 33 3-3 ++ ++ ++ - SU(2)\mathrm{SU}(2) qq3+(1β1)q5q7+q9+(1+)q11+q-q^{3}+(1-\beta _{1})q^{5}-q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots
4368.2.a.bq 4368.a 1.a 33 34.87934.879 3.3.316.1 None 273.2.a.d 00 33 3-3 33 - - - ++ SU(2)\mathrm{SU}(2) q+q3+(1β1)q5+q7+q9+(1+)q11+q+q^{3}+(-1-\beta _{1})q^{5}+q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots
4368.2.a.br 4368.a 1.a 44 34.87934.879 4.4.17428.1 None 273.2.a.e 00 4-4 3-3 4-4 - ++ ++ - SU(2)\mathrm{SU}(2) qq3+(1β2)q5q7+q9+β1q11+q-q^{3}+(-1-\beta _{2})q^{5}-q^{7}+q^{9}+\beta _{1}q^{11}+\cdots
4368.2.a.bs 4368.a 1.a 44 34.87934.879 4.4.138892.1 None 2184.2.a.v 00 44 22 44 ++ - - - SU(2)\mathrm{SU}(2) q+q3+(1+β1)q5+q7+q9+(1β2+)q11+q+q^{3}+(1+\beta _{1})q^{5}+q^{7}+q^{9}+(1-\beta _{2}+\cdots)q^{11}+\cdots

Decomposition of S2old(Γ0(4368))S_{2}^{\mathrm{old}}(\Gamma_0(4368)) into lower level spaces

S2old(Γ0(4368)) S_{2}^{\mathrm{old}}(\Gamma_0(4368)) \simeq S2new(Γ0(14))S_{2}^{\mathrm{new}}(\Gamma_0(14))16^{\oplus 16}\oplusS2new(Γ0(21))S_{2}^{\mathrm{new}}(\Gamma_0(21))10^{\oplus 10}\oplusS2new(Γ0(24))S_{2}^{\mathrm{new}}(\Gamma_0(24))8^{\oplus 8}\oplusS2new(Γ0(26))S_{2}^{\mathrm{new}}(\Gamma_0(26))16^{\oplus 16}\oplusS2new(Γ0(39))S_{2}^{\mathrm{new}}(\Gamma_0(39))10^{\oplus 10}\oplusS2new(Γ0(42))S_{2}^{\mathrm{new}}(\Gamma_0(42))8^{\oplus 8}\oplusS2new(Γ0(48))S_{2}^{\mathrm{new}}(\Gamma_0(48))4^{\oplus 4}\oplusS2new(Γ0(52))S_{2}^{\mathrm{new}}(\Gamma_0(52))12^{\oplus 12}\oplusS2new(Γ0(56))S_{2}^{\mathrm{new}}(\Gamma_0(56))8^{\oplus 8}\oplusS2new(Γ0(78))S_{2}^{\mathrm{new}}(\Gamma_0(78))8^{\oplus 8}\oplusS2new(Γ0(84))S_{2}^{\mathrm{new}}(\Gamma_0(84))6^{\oplus 6}\oplusS2new(Γ0(91))S_{2}^{\mathrm{new}}(\Gamma_0(91))10^{\oplus 10}\oplusS2new(Γ0(104))S_{2}^{\mathrm{new}}(\Gamma_0(104))8^{\oplus 8}\oplusS2new(Γ0(112))S_{2}^{\mathrm{new}}(\Gamma_0(112))4^{\oplus 4}\oplusS2new(Γ0(156))S_{2}^{\mathrm{new}}(\Gamma_0(156))6^{\oplus 6}\oplusS2new(Γ0(168))S_{2}^{\mathrm{new}}(\Gamma_0(168))4^{\oplus 4}\oplusS2new(Γ0(182))S_{2}^{\mathrm{new}}(\Gamma_0(182))8^{\oplus 8}\oplusS2new(Γ0(208))S_{2}^{\mathrm{new}}(\Gamma_0(208))4^{\oplus 4}\oplusS2new(Γ0(273))S_{2}^{\mathrm{new}}(\Gamma_0(273))5^{\oplus 5}\oplusS2new(Γ0(312))S_{2}^{\mathrm{new}}(\Gamma_0(312))4^{\oplus 4}\oplusS2new(Γ0(336))S_{2}^{\mathrm{new}}(\Gamma_0(336))2^{\oplus 2}\oplusS2new(Γ0(364))S_{2}^{\mathrm{new}}(\Gamma_0(364))6^{\oplus 6}\oplusS2new(Γ0(546))S_{2}^{\mathrm{new}}(\Gamma_0(546))4^{\oplus 4}\oplusS2new(Γ0(624))S_{2}^{\mathrm{new}}(\Gamma_0(624))2^{\oplus 2}\oplusS2new(Γ0(728))S_{2}^{\mathrm{new}}(\Gamma_0(728))4^{\oplus 4}\oplusS2new(Γ0(1092))S_{2}^{\mathrm{new}}(\Gamma_0(1092))3^{\oplus 3}\oplusS2new(Γ0(1456))S_{2}^{\mathrm{new}}(\Gamma_0(1456))2^{\oplus 2}\oplusS2new(Γ0(2184))S_{2}^{\mathrm{new}}(\Gamma_0(2184))2^{\oplus 2}