Properties

Label 122.2.a
Level 122
Weight 2
Character orbit a
Rep. character \(\chi_{122}(1,\cdot)\)
Character field \(\Q\)
Dimension 6
Newforms 3
Sturm bound 31
Trace bound 1

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Defining parameters

Level: \( N \) = \( 122 = 2 \cdot 61 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 122.a (trivial)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(31\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(122))\).

Total New Old
Modular forms 17 6 11
Cusp forms 14 6 8
Eisenstein series 3 0 3

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

\(2\)\(61\)FrickeDim.
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(3\)
Plus space\(+\)\(1\)
Minus space\(-\)\(5\)

Trace form

\(6q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 6q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(6q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 6q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 4q^{9} \) \(\mathstrut -\mathstrut 8q^{11} \) \(\mathstrut -\mathstrut 2q^{12} \) \(\mathstrut +\mathstrut 2q^{13} \) \(\mathstrut +\mathstrut 4q^{14} \) \(\mathstrut -\mathstrut 16q^{15} \) \(\mathstrut +\mathstrut 6q^{16} \) \(\mathstrut -\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut +\mathstrut 2q^{20} \) \(\mathstrut -\mathstrut 6q^{22} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut -\mathstrut 4q^{25} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut -\mathstrut 8q^{27} \) \(\mathstrut +\mathstrut 4q^{28} \) \(\mathstrut -\mathstrut 4q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut -\mathstrut 4q^{31} \) \(\mathstrut +\mathstrut 4q^{33} \) \(\mathstrut -\mathstrut 4q^{34} \) \(\mathstrut -\mathstrut 12q^{35} \) \(\mathstrut +\mathstrut 4q^{36} \) \(\mathstrut -\mathstrut 8q^{37} \) \(\mathstrut -\mathstrut 4q^{38} \) \(\mathstrut +\mathstrut 4q^{39} \) \(\mathstrut -\mathstrut 8q^{41} \) \(\mathstrut -\mathstrut 12q^{42} \) \(\mathstrut +\mathstrut 20q^{43} \) \(\mathstrut -\mathstrut 8q^{44} \) \(\mathstrut +\mathstrut 18q^{45} \) \(\mathstrut +\mathstrut 12q^{47} \) \(\mathstrut -\mathstrut 2q^{48} \) \(\mathstrut +\mathstrut 38q^{49} \) \(\mathstrut +\mathstrut 24q^{50} \) \(\mathstrut +\mathstrut 8q^{51} \) \(\mathstrut +\mathstrut 2q^{52} \) \(\mathstrut +\mathstrut 8q^{53} \) \(\mathstrut -\mathstrut 24q^{54} \) \(\mathstrut -\mathstrut 8q^{55} \) \(\mathstrut +\mathstrut 4q^{56} \) \(\mathstrut +\mathstrut 24q^{57} \) \(\mathstrut +\mathstrut 6q^{58} \) \(\mathstrut -\mathstrut 32q^{59} \) \(\mathstrut -\mathstrut 16q^{60} \) \(\mathstrut -\mathstrut 2q^{61} \) \(\mathstrut -\mathstrut 2q^{62} \) \(\mathstrut +\mathstrut 16q^{63} \) \(\mathstrut +\mathstrut 6q^{64} \) \(\mathstrut -\mathstrut 6q^{65} \) \(\mathstrut +\mathstrut 16q^{66} \) \(\mathstrut +\mathstrut 28q^{67} \) \(\mathstrut -\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 44q^{69} \) \(\mathstrut -\mathstrut 2q^{70} \) \(\mathstrut +\mathstrut 20q^{71} \) \(\mathstrut +\mathstrut 20q^{73} \) \(\mathstrut +\mathstrut 22q^{74} \) \(\mathstrut -\mathstrut 2q^{75} \) \(\mathstrut -\mathstrut 2q^{76} \) \(\mathstrut +\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 12q^{78} \) \(\mathstrut -\mathstrut 8q^{79} \) \(\mathstrut +\mathstrut 2q^{80} \) \(\mathstrut -\mathstrut 18q^{81} \) \(\mathstrut +\mathstrut 16q^{82} \) \(\mathstrut -\mathstrut 14q^{83} \) \(\mathstrut +\mathstrut 20q^{85} \) \(\mathstrut +\mathstrut 4q^{86} \) \(\mathstrut -\mathstrut 6q^{88} \) \(\mathstrut -\mathstrut 12q^{89} \) \(\mathstrut +\mathstrut 16q^{90} \) \(\mathstrut +\mathstrut 24q^{91} \) \(\mathstrut +\mathstrut 4q^{92} \) \(\mathstrut +\mathstrut 20q^{93} \) \(\mathstrut -\mathstrut 28q^{94} \) \(\mathstrut -\mathstrut 12q^{95} \) \(\mathstrut +\mathstrut 14q^{97} \) \(\mathstrut -\mathstrut 8q^{98} \) \(\mathstrut -\mathstrut 40q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(122))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 61
122.2.a.a \(1\) \(0.974\) \(\Q\) None \(-1\) \(-2\) \(1\) \(-5\) \(+\) \(+\) \(q-q^{2}-2q^{3}+q^{4}+q^{5}+2q^{6}-5q^{7}+\cdots\)
122.2.a.b \(2\) \(0.974\) \(\Q(\sqrt{13}) \) None \(-2\) \(1\) \(0\) \(5\) \(+\) \(-\) \(q-q^{2}+(1-\beta )q^{3}+q^{4}+(-1+\beta )q^{6}+\cdots\)
122.2.a.c \(3\) \(0.974\) 3.3.229.1 None \(3\) \(-1\) \(1\) \(4\) \(-\) \(+\) \(q+q^{2}+\beta _{2}q^{3}+q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(122))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(122)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(61))\)\(^{\oplus 2}\)