Properties

Label 62.2.c
Level 62
Weight 2
Character orbit c
Rep. character \(\chi_{62}(5,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 4
Newforms 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: \(\Q(\zeta_{3})\)
Newforms: \( 2 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(62, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
62.2.c.a \(2\) \(0.495\) \(\Q(\sqrt{-3}) \) None \(-2\) \(-1\) \(3\) \(1\) \(q-q^{2}+(-1+\zeta_{6})q^{3}+q^{4}+3\zeta_{6}q^{5}+\cdots\)
62.2.c.b \(2\) \(0.495\) \(\Q(\sqrt{-3}) \) None \(2\) \(-3\) \(-1\) \(3\) \(q+q^{2}+(-3+3\zeta_{6})q^{3}+q^{4}-\zeta_{6}q^{5}+\cdots\)

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

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