Properties

Label 62.2.g
Level 62
Weight 2
Character orbit g
Rep. character \(\chi_{62}(7,\cdot)\)
Character field \(\Q(\zeta_{15})\)
Dimension 16
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.g (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 31 \)
Character field: \(\Q(\zeta_{15})\)
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 80 16 64
Cusp forms 48 16 32
Eisenstein series 32 0 32

Trace form

\( 16q + 4q^{3} - 4q^{4} - 2q^{5} - 8q^{6} - 14q^{7} + 4q^{9} + O(q^{10}) \) \( 16q + 4q^{3} - 4q^{4} - 2q^{5} - 8q^{6} - 14q^{7} + 4q^{9} + 4q^{10} - 10q^{11} + 4q^{12} - 12q^{14} - 10q^{15} - 4q^{16} - 4q^{17} + 8q^{18} - 2q^{20} - 30q^{21} + 14q^{22} + 18q^{23} + 2q^{24} + 10q^{25} - 20q^{26} - 8q^{27} + 16q^{28} + 24q^{29} + 28q^{30} - 8q^{33} + 40q^{34} + 40q^{35} + 4q^{36} + 14q^{37} - 6q^{38} - 20q^{39} - 6q^{40} - 6q^{41} + 12q^{42} - 26q^{43} + 2q^{45} - 12q^{46} + 10q^{47} - 6q^{48} - 14q^{49} - 28q^{50} + 12q^{51} - 34q^{53} - 28q^{54} + 8q^{55} - 2q^{56} + 24q^{57} - 12q^{58} - 10q^{59} - 10q^{60} + 28q^{61} - 38q^{62} - 28q^{63} - 4q^{64} - 20q^{65} - 16q^{66} - 6q^{67} - 14q^{68} + 28q^{69} - 8q^{70} + 16q^{71} + 8q^{72} - 46q^{73} - 2q^{74} - 18q^{75} - 30q^{76} - 2q^{77} - 20q^{78} - 10q^{79} + 18q^{80} + 28q^{82} + 46q^{83} + 30q^{84} + 12q^{85} + 34q^{86} + 12q^{87} + 4q^{88} + 36q^{89} + 30q^{90} + 40q^{91} + 8q^{92} + 76q^{93} + 32q^{94} + 54q^{95} + 2q^{96} - 22q^{97} + 28q^{98} - 4q^{99} + O(q^{100}) \)

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.g.a \(8\) \(0.495\) \(\Q(\zeta_{15})\) None \(-2\) \(3\) \(1\) \(2\) \(q+\zeta_{15}^{6}q^{2}+(\zeta_{15}+\zeta_{15}^{4}+\zeta_{15}^{7})q^{3}+\cdots\)
62.2.g.b \(8\) \(0.495\) \(\Q(\zeta_{15})\) None \(2\) \(1\) \(-3\) \(-16\) \(q-\zeta_{15}^{6}q^{2}+(\zeta_{15}-\zeta_{15}^{4}+\zeta_{15}^{7})q^{3}+\cdots\)

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

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