Properties

Label 122.2.a
Level 122
Weight 2
Character orbit a
Rep. character \(\chi_{122}(1,\cdot)\)
Character field \(\Q\)
Dimension 6
Newform subspaces 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: \(\Q\)
Newform subspaces: \( 3 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(122))\) into newform subspaces

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

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