Properties

Label 240.12.a
Level 240240
Weight 1212
Character orbit 240.a
Rep. character χ240(1,)\chi_{240}(1,\cdot)
Character field Q\Q
Dimension 4444
Newform subspaces 2222
Sturm bound 576576
Trace bound 77

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Defining parameters

Level: N N == 240=2435 240 = 2^{4} \cdot 3 \cdot 5
Weight: k k == 12 12
Character orbit: [χ][\chi] == 240.a (trivial)
Character field: Q\Q
Newform subspaces: 22 22
Sturm bound: 576576
Trace bound: 77
Distinguishing TpT_p: 77

Dimensions

The following table gives the dimensions of various subspaces of M12(Γ0(240))M_{12}(\Gamma_0(240)).

Total New Old
Modular forms 540 44 496
Cusp forms 516 44 472
Eisenstein series 24 0 24

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

223355FrickeTotalCuspEisenstein
AllNewOldAllNewOldAllNewOld
++++++++70705565656767556262330033
++++--65655560606262555757330033
++-++-67676661616464665858330033
++--++68686662626565665959330033
-++++-67675562626464555959330033
-++-++68686662626565665959330033
--++++66666660606363665757330033
----69695564646666556161330033
Plus space++272272232324924926026023232372371212001212
Minus space-268268212124724725625621212352351212001212

Trace form

44q+486q3169920q7+2598156q91081688q111518750q15+18693312q19+13479496q23+429687500q25+28697814q27155346416q29+58859328q31+1045524112q37+63872594712q99+O(q100) 44 q + 486 q^{3} - 169920 q^{7} + 2598156 q^{9} - 1081688 q^{11} - 1518750 q^{15} + 18693312 q^{19} + 13479496 q^{23} + 429687500 q^{25} + 28697814 q^{27} - 155346416 q^{29} + 58859328 q^{31} + 1045524112 q^{37}+ \cdots - 63872594712 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S12new(Γ0(240))S_{12}^{\mathrm{new}}(\Gamma_0(240)) 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 5
240.12.a.a 240.a 1.a 11 184.402184.402 Q\Q None 30.12.a.f 00 243-243 3125-3125 10556-10556 - ++ ++ SU(2)\mathrm{SU}(2) q35q355q510556q7+310q9+q-3^{5}q^{3}-5^{5}q^{5}-10556q^{7}+3^{10}q^{9}+\cdots
240.12.a.b 240.a 1.a 11 184.402184.402 Q\Q None 30.12.a.c 00 243-243 31253125 56672-56672 - ++ - SU(2)\mathrm{SU}(2) q35q3+55q556672q7+310q9+q-3^{5}q^{3}+5^{5}q^{5}-56672q^{7}+3^{10}q^{9}+\cdots
240.12.a.c 240.a 1.a 11 184.402184.402 Q\Q None 30.12.a.d 00 243243 3125-3125 29348-29348 - - ++ SU(2)\mathrm{SU}(2) q+35q355q529348q7+310q9+q+3^{5}q^{3}-5^{5}q^{5}-29348q^{7}+3^{10}q^{9}+\cdots
240.12.a.d 240.a 1.a 11 184.402184.402 Q\Q None 30.12.a.a 00 243243 3125-3125 2287622876 - - ++ SU(2)\mathrm{SU}(2) q+35q355q5+22876q7+310q9+q+3^{5}q^{3}-5^{5}q^{5}+22876q^{7}+3^{10}q^{9}+\cdots
240.12.a.e 240.a 1.a 11 184.402184.402 Q\Q None 15.12.a.a 00 243243 31253125 27984-27984 - - - SU(2)\mathrm{SU}(2) q+35q3+55q527984q7+310q9+q+3^{5}q^{3}+5^{5}q^{5}-27984q^{7}+3^{10}q^{9}+\cdots
240.12.a.f 240.a 1.a 11 184.402184.402 Q\Q None 30.12.a.e 00 243243 31253125 51525152 - - - SU(2)\mathrm{SU}(2) q+35q3+55q5+5152q7+310q9+q+3^{5}q^{3}+5^{5}q^{5}+5152q^{7}+3^{10}q^{9}+\cdots
240.12.a.g 240.a 1.a 11 184.402184.402 Q\Q None 30.12.a.b 00 243243 31253125 5737657376 - - - SU(2)\mathrm{SU}(2) q+35q3+55q5+57376q7+310q9+q+3^{5}q^{3}+5^{5}q^{5}+57376q^{7}+3^{10}q^{9}+\cdots
240.12.a.h 240.a 1.a 22 184.402184.402 Q(1119913)\Q(\sqrt{1119913}) None 60.12.a.c 00 486-486 6250-6250 36496-36496 - ++ ++ SU(2)\mathrm{SU}(2) q35q355q5+(18248β)q7+q-3^{5}q^{3}-5^{5}q^{5}+(-18248-\beta )q^{7}+\cdots
240.12.a.i 240.a 1.a 22 184.402184.402 Q(534073)\Q(\sqrt{534073}) None 120.12.a.a 00 486-486 6250-6250 11440-11440 ++ ++ ++ SU(2)\mathrm{SU}(2) q35q355q5+(5720β)q7+q-3^{5}q^{3}-5^{5}q^{5}+(-5720-\beta )q^{7}+\cdots
240.12.a.j 240.a 1.a 22 184.402184.402 Q(1609)\Q(\sqrt{1609}) None 15.12.a.b 00 486-486 6250-6250 1086410864 - ++ ++ SU(2)\mathrm{SU}(2) q35q355q5+(5432319β)q7+q-3^{5}q^{3}-5^{5}q^{5}+(5432-319\beta )q^{7}+\cdots
240.12.a.k 240.a 1.a 22 184.402184.402 Q(1009)\Q(\sqrt{1009}) None 120.12.a.b 00 486-486 62506250 1944819448 ++ ++ - SU(2)\mathrm{SU}(2) q35q3+55q5+(972483β)q7+q-3^{5}q^{3}+5^{5}q^{5}+(9724-83\beta )q^{7}+\cdots
240.12.a.l 240.a 1.a 22 184.402184.402 Q(193)\Q(\sqrt{193}) None 60.12.a.d 00 486-486 62506250 4450444504 - ++ - SU(2)\mathrm{SU}(2) q35q3+55q5+(2225229β)q7+q-3^{5}q^{3}+5^{5}q^{5}+(22252-29\beta )q^{7}+\cdots
240.12.a.m 240.a 1.a 22 184.402184.402 Q(1801)\Q(\sqrt{1801}) None 15.12.a.c 00 486486 6250-6250 7784-7784 - - ++ SU(2)\mathrm{SU}(2) q+35q355q5+(389214β)q7+q+3^{5}q^{3}-5^{5}q^{5}+(-3892-14\beta )q^{7}+\cdots
240.12.a.n 240.a 1.a 22 184.402184.402 Q(26929)\Q(\sqrt{26929}) None 60.12.a.a 00 486486 6250-6250 1181611816 - - ++ SU(2)\mathrm{SU}(2) q+35q355q5+(5908β)q7+310q9+q+3^{5}q^{3}-5^{5}q^{5}+(5908-\beta )q^{7}+3^{10}q^{9}+\cdots
240.12.a.o 240.a 1.a 22 184.402184.402 Q(25489)\Q(\sqrt{25489}) None 60.12.a.b 00 486486 62506250 65584-65584 - - - SU(2)\mathrm{SU}(2) q+35q3+55q5+(32792β)q7+q+3^{5}q^{3}+5^{5}q^{5}+(-32792-\beta )q^{7}+\cdots
240.12.a.p 240.a 1.a 33 184.402184.402 Q[x]/(x3)\mathbb{Q}[x]/(x^{3} - \cdots) None 120.12.a.g 00 729-729 9375-9375 51485148 ++ ++ ++ SU(2)\mathrm{SU}(2) q35q355q5+(1716+β1+3β2)q7+q-3^{5}q^{3}-5^{5}q^{5}+(1716+\beta _{1}+3\beta _{2})q^{7}+\cdots
240.12.a.q 240.a 1.a 33 184.402184.402 Q[x]/(x3)\mathbb{Q}[x]/(x^{3} - \cdots) None 120.12.a.h 00 729-729 93759375 64368-64368 ++ ++ - SU(2)\mathrm{SU}(2) q35q3+55q5+(21456β1+)q7+q-3^{5}q^{3}+5^{5}q^{5}+(-21456-\beta _{1}+\cdots)q^{7}+\cdots
240.12.a.r 240.a 1.a 33 184.402184.402 Q[x]/(x3)\mathbb{Q}[x]/(x^{3} - \cdots) None 15.12.a.d 00 729-729 93759375 1460814608 - ++ - SU(2)\mathrm{SU}(2) q35q3+55q5+(4868+β1+4β2)q7+q-3^{5}q^{3}+5^{5}q^{5}+(4868+\beta _{1}+4\beta _{2})q^{7}+\cdots
240.12.a.s 240.a 1.a 33 184.402184.402 Q[x]/(x3)\mathbb{Q}[x]/(x^{3} - \cdots) None 120.12.a.d 00 729729 9375-9375 49148-49148 ++ - ++ SU(2)\mathrm{SU}(2) q+35q355q5+(16383β1+)q7+q+3^{5}q^{3}-5^{5}q^{5}+(-16383-\beta _{1}+\cdots)q^{7}+\cdots
240.12.a.t 240.a 1.a 33 184.402184.402 Q[x]/(x3)\mathbb{Q}[x]/(x^{3} - \cdots) None 120.12.a.c 00 729729 9375-9375 91089108 ++ - ++ SU(2)\mathrm{SU}(2) q+35q355q5+(30363β1+β2)q7+q+3^{5}q^{3}-5^{5}q^{5}+(3036-3\beta _{1}+\beta _{2})q^{7}+\cdots
240.12.a.u 240.a 1.a 33 184.402184.402 Q[x]/(x3)\mathbb{Q}[x]/(x^{3} - \cdots) None 120.12.a.f 00 729729 93759375 34848-34848 ++ - - SU(2)\mathrm{SU}(2) q+35q3+55q5+(11616β1+)q7+q+3^{5}q^{3}+5^{5}q^{5}+(-11616-\beta _{1}+\cdots)q^{7}+\cdots
240.12.a.v 240.a 1.a 33 184.402184.402 Q[x]/(x3)\mathbb{Q}[x]/(x^{3} - \cdots) None 120.12.a.e 00 729729 93759375 2340823408 ++ - - SU(2)\mathrm{SU}(2) q+35q3+55q5+(7803β1)q7+q+3^{5}q^{3}+5^{5}q^{5}+(7803-\beta _{1})q^{7}+\cdots

Decomposition of S12old(Γ0(240))S_{12}^{\mathrm{old}}(\Gamma_0(240)) into lower level spaces

S12old(Γ0(240)) S_{12}^{\mathrm{old}}(\Gamma_0(240)) \simeq S12new(Γ0(1))S_{12}^{\mathrm{new}}(\Gamma_0(1))20^{\oplus 20}\oplusS12new(Γ0(3))S_{12}^{\mathrm{new}}(\Gamma_0(3))10^{\oplus 10}\oplusS12new(Γ0(4))S_{12}^{\mathrm{new}}(\Gamma_0(4))12^{\oplus 12}\oplusS12new(Γ0(5))S_{12}^{\mathrm{new}}(\Gamma_0(5))10^{\oplus 10}\oplusS12new(Γ0(6))S_{12}^{\mathrm{new}}(\Gamma_0(6))8^{\oplus 8}\oplusS12new(Γ0(8))S_{12}^{\mathrm{new}}(\Gamma_0(8))8^{\oplus 8}\oplusS12new(Γ0(10))S_{12}^{\mathrm{new}}(\Gamma_0(10))8^{\oplus 8}\oplusS12new(Γ0(12))S_{12}^{\mathrm{new}}(\Gamma_0(12))6^{\oplus 6}\oplusS12new(Γ0(15))S_{12}^{\mathrm{new}}(\Gamma_0(15))5^{\oplus 5}\oplusS12new(Γ0(16))S_{12}^{\mathrm{new}}(\Gamma_0(16))4^{\oplus 4}\oplusS12new(Γ0(20))S_{12}^{\mathrm{new}}(\Gamma_0(20))6^{\oplus 6}\oplusS12new(Γ0(24))S_{12}^{\mathrm{new}}(\Gamma_0(24))4^{\oplus 4}\oplusS12new(Γ0(30))S_{12}^{\mathrm{new}}(\Gamma_0(30))4^{\oplus 4}\oplusS12new(Γ0(40))S_{12}^{\mathrm{new}}(\Gamma_0(40))4^{\oplus 4}\oplusS12new(Γ0(48))S_{12}^{\mathrm{new}}(\Gamma_0(48))2^{\oplus 2}\oplusS12new(Γ0(60))S_{12}^{\mathrm{new}}(\Gamma_0(60))3^{\oplus 3}\oplusS12new(Γ0(80))S_{12}^{\mathrm{new}}(\Gamma_0(80))2^{\oplus 2}\oplusS12new(Γ0(120))S_{12}^{\mathrm{new}}(\Gamma_0(120))2^{\oplus 2}