Properties

Label 242.2.a
Level 242242
Weight 22
Character orbit 242.a
Rep. character χ242(1,)\chi_{242}(1,\cdot)
Character field Q\Q
Dimension 1010
Newform subspaces 66
Sturm bound 6666
Trace bound 33

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Defining parameters

Level: N N == 242=2112 242 = 2 \cdot 11^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 242.a (trivial)
Character field: Q\Q
Newform subspaces: 6 6
Sturm bound: 6666
Trace bound: 33
Distinguishing TpT_p: 33, 77

Dimensions

The following table gives the dimensions of various subspaces of M2(Γ0(242))M_{2}(\Gamma_0(242)).

Total New Old
Modular forms 45 10 35
Cusp forms 22 10 12
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.

221111FrickeTotalCuspEisenstein
AllNewOldAllNewOldAllNewOld
++++++992277442222550055
++--1313331010773344660066
-++-12124488664422660066
--++1111111010551144660066
Plus space++20203317179933661111001111
Minus space-2525771818131377661212001212

Trace form

10q2q3+10q42q5+8q92q124q15+10q162q204q23+4q252q268q278q314q34+8q3610q372q384q42++60q97+O(q100) 10 q - 2 q^{3} + 10 q^{4} - 2 q^{5} + 8 q^{9} - 2 q^{12} - 4 q^{15} + 10 q^{16} - 2 q^{20} - 4 q^{23} + 4 q^{25} - 2 q^{26} - 8 q^{27} - 8 q^{31} - 4 q^{34} + 8 q^{36} - 10 q^{37} - 2 q^{38} - 4 q^{42}+ \cdots + 60 q^{97}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(Γ0(242))S_{2}^{\mathrm{new}}(\Gamma_0(242)) 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
242.2.a.a 242.a 1.a 11 1.9321.932 Q\Q None 242.2.a.a 1-1 2-2 3-3 22 ++ - SU(2)\mathrm{SU}(2) qq22q3+q43q5+2q6+2q7+q-q^{2}-2q^{3}+q^{4}-3q^{5}+2q^{6}+2q^{7}+\cdots
242.2.a.b 242.a 1.a 11 1.9321.932 Q\Q None 242.2.a.a 11 2-2 3-3 2-2 - - SU(2)\mathrm{SU}(2) q+q22q3+q43q52q62q7+q+q^{2}-2q^{3}+q^{4}-3q^{5}-2q^{6}-2q^{7}+\cdots
242.2.a.c 242.a 1.a 22 1.9321.932 Q(3)\Q(\sqrt{3}) None 242.2.a.c 2-2 2-2 00 6-6 ++ ++ SU(2)\mathrm{SU}(2) qq2+(1+β)q3+q4βq5+(1+)q6+q-q^{2}+(-1+\beta )q^{3}+q^{4}-\beta q^{5}+(1+\cdots)q^{6}+\cdots
242.2.a.d 242.a 1.a 22 1.9321.932 Q(5)\Q(\sqrt{5}) None 22.2.c.a 2-2 33 22 44 ++ - SU(2)\mathrm{SU}(2) qq2+(1+β)q3+q4+(22β)q5+q-q^{2}+(1+\beta )q^{3}+q^{4}+(2-2\beta )q^{5}+\cdots
242.2.a.e 242.a 1.a 22 1.9321.932 Q(3)\Q(\sqrt{3}) None 242.2.a.c 22 2-2 00 66 - ++ SU(2)\mathrm{SU}(2) q+q2+(1+β)q3+q4βq5+(1+)q6+q+q^{2}+(-1+\beta )q^{3}+q^{4}-\beta q^{5}+(-1+\cdots)q^{6}+\cdots
242.2.a.f 242.a 1.a 22 1.9321.932 Q(5)\Q(\sqrt{5}) None 22.2.c.a 22 33 22 4-4 - ++ SU(2)\mathrm{SU}(2) q+q2+(1+β)q3+q4+(22β)q5+q+q^{2}+(1+\beta )q^{3}+q^{4}+(2-2\beta )q^{5}+\cdots

Decomposition of S2old(Γ0(242))S_{2}^{\mathrm{old}}(\Gamma_0(242)) into lower level spaces

S2old(Γ0(242)) S_{2}^{\mathrm{old}}(\Gamma_0(242)) \simeq S2new(Γ0(11))S_{2}^{\mathrm{new}}(\Gamma_0(11))4^{\oplus 4}\oplusS2new(Γ0(121))S_{2}^{\mathrm{new}}(\Gamma_0(121))2^{\oplus 2}