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Properties

Label 122.2.a
Level $122$
Weight $2$
Character orbit 122.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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 61
122.2.a.a 122.a 1.a $1$ $0.974$ \(\Q\) None \(-1\) \(-2\) \(1\) \(-5\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}+q^{4}+q^{5}+2q^{6}-5q^{7}+\cdots\)
122.2.a.b 122.a 1.a $2$ $0.974$ \(\Q(\sqrt{13}) \) None \(-2\) \(1\) \(0\) \(5\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-\beta )q^{3}+q^{4}+(-1+\beta )q^{6}+\cdots\)
122.2.a.c 122.a 1.a $3$ $0.974$ 3.3.229.1 None \(3\) \(-1\) \(1\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{2}q^{3}+q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\cdots\)

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

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