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Properties

Label 62.2.c
Level $62$
Weight $2$
Character orbit 62.c
Rep. character $\chi_{62}(5,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $4$
Newform subspaces $2$
Sturm bound $16$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 62 = 2 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 62.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 31 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(16\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(62, [\chi])\).

Total New Old
Modular forms 20 4 16
Cusp forms 12 4 8
Eisenstein series 8 0 8

Trace form

\( 4 q - 4 q^{3} + 4 q^{4} + 2 q^{5} - 2 q^{6} + 4 q^{7} - 4 q^{9} + O(q^{10}) \) \( 4 q - 4 q^{3} + 4 q^{4} + 2 q^{5} - 2 q^{6} + 4 q^{7} - 4 q^{9} - 4 q^{10} - 4 q^{12} - 10 q^{13} + 2 q^{14} + 4 q^{16} - 6 q^{17} - 8 q^{18} + 2 q^{20} + 10 q^{21} + 6 q^{22} - 8 q^{23} - 2 q^{24} + 8 q^{27} + 4 q^{28} + 16 q^{29} + 12 q^{30} - 12 q^{33} - 4 q^{36} + 6 q^{37} - 14 q^{38} + 40 q^{39} - 4 q^{40} + 6 q^{41} + 8 q^{42} - 4 q^{43} - 12 q^{45} - 8 q^{46} - 40 q^{47} - 4 q^{48} + 4 q^{49} + 8 q^{50} - 12 q^{51} - 10 q^{52} - 6 q^{53} + 28 q^{54} + 12 q^{55} + 2 q^{56} - 14 q^{57} - 8 q^{58} - 8 q^{61} + 8 q^{62} - 32 q^{63} + 4 q^{64} + 10 q^{65} - 24 q^{66} + 16 q^{67} - 6 q^{68} + 12 q^{69} - 12 q^{70} + 4 q^{71} - 8 q^{72} + 6 q^{73} - 8 q^{74} + 8 q^{75} + 12 q^{77} + 20 q^{78} + 2 q^{80} - 10 q^{81} + 12 q^{82} + 4 q^{83} + 10 q^{84} - 12 q^{85} + 6 q^{86} - 12 q^{87} + 6 q^{88} + 24 q^{89} - 40 q^{91} - 8 q^{92} + 14 q^{93} + 8 q^{94} + 56 q^{95} - 2 q^{96} + 32 q^{97} - 8 q^{98} + 24 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(62, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
62.2.c.a 62.c 31.c $2$ $0.495$ \(\Q(\sqrt{-3}) \) None \(-2\) \(-1\) \(3\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(-1+\zeta_{6})q^{3}+q^{4}+3\zeta_{6}q^{5}+\cdots\)
62.2.c.b 62.c 31.c $2$ $0.495$ \(\Q(\sqrt{-3}) \) None \(2\) \(-3\) \(-1\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(-3+3\zeta_{6})q^{3}+q^{4}-\zeta_{6}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(62, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(62, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 2}\)