Properties

Label 62.2.a
Level $62$
Weight $2$
Character orbit 62.a
Rep. character $\chi_{62}(1,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $2$
Sturm bound $16$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 62 = 2 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 62.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(16\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(62))\).

Total New Old
Modular forms 10 3 7
Cusp forms 7 3 4
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.

\(2\)\(31\)FrickeDim.
\(+\)\(-\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(3\)

Trace form

\( 3 q - q^{2} + 2 q^{3} + 3 q^{4} - 2 q^{5} - 2 q^{6} + 4 q^{7} - q^{8} - q^{9} + O(q^{10}) \) \( 3 q - q^{2} + 2 q^{3} + 3 q^{4} - 2 q^{5} - 2 q^{6} + 4 q^{7} - q^{8} - q^{9} - 2 q^{10} - 6 q^{11} + 2 q^{12} - 4 q^{14} - 12 q^{15} + 3 q^{16} - 6 q^{17} - 5 q^{18} - 4 q^{19} - 2 q^{20} + 4 q^{21} + 6 q^{22} + 8 q^{23} - 2 q^{24} + 13 q^{25} + 4 q^{26} + 8 q^{27} + 4 q^{28} - 4 q^{29} + 12 q^{30} + q^{31} - q^{32} - 6 q^{34} - q^{36} + 20 q^{37} + 12 q^{38} - 20 q^{39} - 2 q^{40} + 6 q^{41} - 4 q^{42} + 6 q^{43} - 6 q^{44} - 18 q^{45} + 8 q^{46} + 4 q^{47} + 2 q^{48} - 13 q^{49} - 15 q^{50} + 12 q^{51} - 8 q^{54} - 12 q^{55} - 4 q^{56} - 8 q^{57} + 8 q^{58} - 24 q^{59} - 12 q^{60} - 8 q^{61} - 3 q^{62} + 4 q^{63} + 3 q^{64} + 32 q^{65} + 4 q^{67} - 6 q^{68} + 8 q^{71} - 5 q^{72} - 10 q^{73} + 14 q^{75} - 4 q^{76} - 12 q^{77} + 20 q^{78} - 4 q^{79} - 2 q^{80} + 11 q^{81} - 18 q^{82} + 14 q^{83} + 4 q^{84} - 12 q^{85} + 10 q^{86} + 12 q^{87} + 6 q^{88} + 6 q^{89} + 30 q^{90} - 4 q^{91} + 8 q^{92} + 2 q^{93} - 20 q^{94} - 8 q^{95} - 2 q^{96} + 6 q^{97} - q^{98} + 6 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(62))\) 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 31
62.2.a.a 62.a 1.a $1$ $0.495$ \(\Q\) None \(1\) \(0\) \(-2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{5}+q^{8}-3q^{9}-2q^{10}+\cdots\)
62.2.a.b 62.a 1.a $2$ $0.495$ \(\Q(\sqrt{3}) \) None \(-2\) \(2\) \(0\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta )q^{3}+q^{4}-2\beta q^{5}+(-1+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(62))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(62)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 2}\)