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Properties

Label 121.2.a
Level $121$
Weight $2$
Character orbit 121.a
Rep. character $\chi_{121}(1,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $4$
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: \(\Q\)
Newform subspaces: \( 4 \)
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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(121))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 11
121.2.a.a 121.a 1.a $1$ $0.966$ \(\Q\) None \(-1\) \(2\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}-q^{4}+q^{5}-2q^{6}+2q^{7}+\cdots\)
121.2.a.b 121.a 1.a $1$ $0.966$ \(\Q\) \(\Q(\sqrt{-11}) \) \(0\) \(-1\) \(-3\) \(0\) $+$ $N(\mathrm{U}(1))$ \(q-q^{3}-2q^{4}-3q^{5}-2q^{9}+2q^{12}+\cdots\)
121.2.a.c 121.a 1.a $1$ $0.966$ \(\Q\) None \(1\) \(2\) \(1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}-q^{4}+q^{5}+2q^{6}-2q^{7}+\cdots\)
121.2.a.d 121.a 1.a $1$ $0.966$ \(\Q\) None \(2\) \(-1\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}+q^{5}-2q^{6}+2q^{7}+\cdots\)

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

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