Properties

Label 121.2.a
Level 121
Weight 2
Character orbit a
Rep. character \(\chi_{121}(1,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 4
Sturm bound 22
Trace bound 2

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Defining parameters

Level: \( N \) = \( 121 = 11^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 121.a (trivial)
Character field: \(\Q\)
Newforms: \( 4 \)
Sturm bound: \(22\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(121))\).

Total New Old
Modular forms 17 13 4
Cusp forms 6 4 2
Eisenstein series 11 9 2

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

\(11\)Dim.
\(+\)\(1\)
\(-\)\(3\)

Trace form

\(4q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 2q^{6} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 2q^{6} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 4q^{12} \) \(\mathstrut -\mathstrut 4q^{13} \) \(\mathstrut +\mathstrut 6q^{15} \) \(\mathstrut -\mathstrut 2q^{16} \) \(\mathstrut +\mathstrut 2q^{17} \) \(\mathstrut -\mathstrut 4q^{18} \) \(\mathstrut +\mathstrut 6q^{20} \) \(\mathstrut -\mathstrut 2q^{21} \) \(\mathstrut -\mathstrut 6q^{23} \) \(\mathstrut -\mathstrut 8q^{25} \) \(\mathstrut -\mathstrut 6q^{26} \) \(\mathstrut +\mathstrut 2q^{27} \) \(\mathstrut +\mathstrut 4q^{28} \) \(\mathstrut -\mathstrut 2q^{30} \) \(\mathstrut -\mathstrut 2q^{31} \) \(\mathstrut -\mathstrut 8q^{32} \) \(\mathstrut -\mathstrut 6q^{34} \) \(\mathstrut +\mathstrut 2q^{35} \) \(\mathstrut -\mathstrut 2q^{36} \) \(\mathstrut +\mathstrut 4q^{37} \) \(\mathstrut +\mathstrut 12q^{38} \) \(\mathstrut +\mathstrut 4q^{39} \) \(\mathstrut +\mathstrut 8q^{41} \) \(\mathstrut -\mathstrut 12q^{42} \) \(\mathstrut +\mathstrut 6q^{43} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut -\mathstrut 2q^{46} \) \(\mathstrut -\mathstrut 4q^{48} \) \(\mathstrut -\mathstrut 16q^{49} \) \(\mathstrut -\mathstrut 8q^{50} \) \(\mathstrut -\mathstrut 2q^{51} \) \(\mathstrut -\mathstrut 8q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 10q^{54} \) \(\mathstrut +\mathstrut 12q^{56} \) \(\mathstrut +\mathstrut 18q^{58} \) \(\mathstrut +\mathstrut 6q^{59} \) \(\mathstrut -\mathstrut 12q^{60} \) \(\mathstrut -\mathstrut 12q^{61} \) \(\mathstrut +\mathstrut 14q^{62} \) \(\mathstrut -\mathstrut 4q^{63} \) \(\mathstrut -\mathstrut 2q^{64} \) \(\mathstrut -\mathstrut 4q^{65} \) \(\mathstrut +\mathstrut 10q^{67} \) \(\mathstrut +\mathstrut 4q^{68} \) \(\mathstrut +\mathstrut 18q^{69} \) \(\mathstrut +\mathstrut 18q^{71} \) \(\mathstrut -\mathstrut 4q^{73} \) \(\mathstrut +\mathstrut 6q^{74} \) \(\mathstrut -\mathstrut 16q^{75} \) \(\mathstrut +\mathstrut 12q^{78} \) \(\mathstrut +\mathstrut 10q^{79} \) \(\mathstrut -\mathstrut 18q^{80} \) \(\mathstrut -\mathstrut 20q^{81} \) \(\mathstrut +\mathstrut 6q^{82} \) \(\mathstrut +\mathstrut 6q^{83} \) \(\mathstrut -\mathstrut 4q^{84} \) \(\mathstrut +\mathstrut 2q^{85} \) \(\mathstrut +\mathstrut 12q^{86} \) \(\mathstrut -\mathstrut 12q^{89} \) \(\mathstrut -\mathstrut 4q^{90} \) \(\mathstrut -\mathstrut 12q^{91} \) \(\mathstrut +\mathstrut 12q^{92} \) \(\mathstrut -\mathstrut 10q^{93} \) \(\mathstrut +\mathstrut 16q^{94} \) \(\mathstrut +\mathstrut 8q^{96} \) \(\mathstrut -\mathstrut 16q^{97} \) \(\mathstrut -\mathstrut 6q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(121))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 11
121.2.a.a \(1\) \(0.966\) \(\Q\) None \(-1\) \(2\) \(1\) \(2\) \(-\) \(q-q^{2}+2q^{3}-q^{4}+q^{5}-2q^{6}+2q^{7}+\cdots\)
121.2.a.b \(1\) \(0.966\) \(\Q\) \(\Q(\sqrt{-11}) \) \(0\) \(-1\) \(-3\) \(0\) \(+\) \(q-q^{3}-2q^{4}-3q^{5}-2q^{9}+2q^{12}+\cdots\)
121.2.a.c \(1\) \(0.966\) \(\Q\) None \(1\) \(2\) \(1\) \(-2\) \(-\) \(q+q^{2}+2q^{3}-q^{4}+q^{5}+2q^{6}-2q^{7}+\cdots\)
121.2.a.d \(1\) \(0.966\) \(\Q\) None \(2\) \(-1\) \(1\) \(2\) \(-\) \(q+2q^{2}-q^{3}+2q^{4}+q^{5}-2q^{6}+2q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(121))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(121)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)