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Properties

Label 61.2.a
Level $61$
Weight $2$
Character orbit 61.a
Rep. character $\chi_{61}(1,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $2$
Sturm bound $10$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 61.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(10\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(61))\).

Total New Old
Modular forms 5 5 0
Cusp forms 4 4 0
Eisenstein series 1 1 0

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

\(61\)Dim
\(+\)\(1\)
\(-\)\(3\)

Trace form

\( 4 q - 4 q^{5} - 2 q^{6} - 2 q^{7} + 6 q^{8} + 4 q^{9} + O(q^{10}) \) \( 4 q - 4 q^{5} - 2 q^{6} - 2 q^{7} + 6 q^{8} + 4 q^{9} - 6 q^{10} + 8 q^{11} - 8 q^{12} - 8 q^{13} - 4 q^{14} + 4 q^{15} - 4 q^{16} + 2 q^{17} + 4 q^{18} - 4 q^{19} + 4 q^{20} - 10 q^{21} + 16 q^{22} - 4 q^{23} - 10 q^{24} + 8 q^{25} + 12 q^{27} + 4 q^{28} - 2 q^{29} - 6 q^{30} - 2 q^{31} - 8 q^{32} + 14 q^{33} + 4 q^{34} + 8 q^{35} - 12 q^{36} + 2 q^{37} + 18 q^{38} + 4 q^{39} + 8 q^{41} - 22 q^{43} + 14 q^{44} - 24 q^{45} + 4 q^{46} + 12 q^{48} - 16 q^{49} - 16 q^{50} - 8 q^{51} - 16 q^{52} + 4 q^{53} + 16 q^{54} + 2 q^{55} + 8 q^{56} - 24 q^{57} + 16 q^{58} + 38 q^{59} + 16 q^{60} + 2 q^{61} - 32 q^{62} - 18 q^{63} - 4 q^{64} - 20 q^{65} - 32 q^{66} + 2 q^{67} - 6 q^{68} + 26 q^{69} + 4 q^{70} + 6 q^{71} - 10 q^{72} - 12 q^{73} + 4 q^{74} + 4 q^{75} + 36 q^{76} - 20 q^{77} + 26 q^{78} + 16 q^{79} - 16 q^{80} - 12 q^{81} - 12 q^{82} - 4 q^{83} + 22 q^{84} - 30 q^{85} + 12 q^{86} + 16 q^{87} - 4 q^{88} - 8 q^{89} + 10 q^{90} - 6 q^{91} + 6 q^{92} + 28 q^{93} + 16 q^{94} + 16 q^{95} + 34 q^{96} - 4 q^{97} + 2 q^{98} + 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(61))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 61
61.2.a.a 61.a 1.a $1$ $0.487$ \(\Q\) None \(-1\) \(-2\) \(-3\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}-q^{4}-3q^{5}+2q^{6}+q^{7}+\cdots\)
61.2.a.b 61.a 1.a $3$ $0.487$ 3.3.148.1 None \(1\) \(2\) \(-1\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)