Properties

Label 63.2.s
Level 63
Weight 2
Character orbit s
Rep. character \(\chi_{63}(47,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 12
Newforms 2
Sturm bound 16
Trace bound 1

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Defining parameters

Level: \( N \) = \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 63.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newforms: \( 2 \)
Sturm bound: \(16\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(63, [\chi])\).

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

Trace form

\(12q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 5q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 5q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 3q^{9} \) \(\mathstrut -\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 3q^{12} \) \(\mathstrut +\mathstrut 3q^{13} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut +\mathstrut 6q^{15} \) \(\mathstrut -\mathstrut q^{16} \) \(\mathstrut -\mathstrut 9q^{17} \) \(\mathstrut -\mathstrut 27q^{18} \) \(\mathstrut -\mathstrut 6q^{19} \) \(\mathstrut -\mathstrut 6q^{20} \) \(\mathstrut +\mathstrut 24q^{21} \) \(\mathstrut +\mathstrut 2q^{22} \) \(\mathstrut +\mathstrut 24q^{24} \) \(\mathstrut -\mathstrut 6q^{25} \) \(\mathstrut +\mathstrut 6q^{26} \) \(\mathstrut +\mathstrut 27q^{27} \) \(\mathstrut -\mathstrut 2q^{28} \) \(\mathstrut -\mathstrut 24q^{29} \) \(\mathstrut -\mathstrut 18q^{30} \) \(\mathstrut -\mathstrut 15q^{31} \) \(\mathstrut +\mathstrut 39q^{32} \) \(\mathstrut -\mathstrut 6q^{33} \) \(\mathstrut -\mathstrut 6q^{34} \) \(\mathstrut -\mathstrut 12q^{36} \) \(\mathstrut -\mathstrut q^{37} \) \(\mathstrut +\mathstrut 54q^{38} \) \(\mathstrut +\mathstrut 18q^{39} \) \(\mathstrut -\mathstrut 6q^{41} \) \(\mathstrut -\mathstrut 21q^{42} \) \(\mathstrut +\mathstrut 2q^{43} \) \(\mathstrut +\mathstrut 27q^{44} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut -\mathstrut 4q^{46} \) \(\mathstrut +\mathstrut 15q^{47} \) \(\mathstrut -\mathstrut 15q^{48} \) \(\mathstrut -\mathstrut 12q^{49} \) \(\mathstrut -\mathstrut 9q^{50} \) \(\mathstrut -\mathstrut 24q^{51} \) \(\mathstrut -\mathstrut 24q^{53} \) \(\mathstrut +\mathstrut 36q^{54} \) \(\mathstrut -\mathstrut 54q^{56} \) \(\mathstrut -\mathstrut 27q^{57} \) \(\mathstrut +\mathstrut 2q^{58} \) \(\mathstrut -\mathstrut 18q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut +\mathstrut 36q^{61} \) \(\mathstrut +\mathstrut 24q^{62} \) \(\mathstrut +\mathstrut 6q^{63} \) \(\mathstrut +\mathstrut 4q^{64} \) \(\mathstrut +\mathstrut 6q^{65} \) \(\mathstrut -\mathstrut 33q^{66} \) \(\mathstrut -\mathstrut 6q^{67} \) \(\mathstrut -\mathstrut 48q^{68} \) \(\mathstrut -\mathstrut 12q^{69} \) \(\mathstrut -\mathstrut 18q^{70} \) \(\mathstrut +\mathstrut 27q^{72} \) \(\mathstrut -\mathstrut 6q^{73} \) \(\mathstrut -\mathstrut 33q^{75} \) \(\mathstrut +\mathstrut 48q^{77} \) \(\mathstrut +\mathstrut 15q^{78} \) \(\mathstrut +\mathstrut 12q^{79} \) \(\mathstrut -\mathstrut 45q^{80} \) \(\mathstrut -\mathstrut 57q^{81} \) \(\mathstrut -\mathstrut 30q^{83} \) \(\mathstrut +\mathstrut 69q^{84} \) \(\mathstrut +\mathstrut 9q^{85} \) \(\mathstrut +\mathstrut 39q^{87} \) \(\mathstrut +\mathstrut 22q^{88} \) \(\mathstrut +\mathstrut 27q^{89} \) \(\mathstrut +\mathstrut 51q^{90} \) \(\mathstrut -\mathstrut 15q^{91} \) \(\mathstrut +\mathstrut 30q^{92} \) \(\mathstrut +\mathstrut 12q^{93} \) \(\mathstrut -\mathstrut 3q^{94} \) \(\mathstrut +\mathstrut 27q^{95} \) \(\mathstrut +\mathstrut 12q^{96} \) \(\mathstrut +\mathstrut 3q^{97} \) \(\mathstrut +\mathstrut 21q^{98} \) \(\mathstrut +\mathstrut 12q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(63, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
63.2.s.a \(2\) \(0.503\) \(\Q(\sqrt{-3}) \) None \(-3\) \(-3\) \(-6\) \(-5\) \(q+(-1-\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
63.2.s.b \(10\) \(0.503\) 10.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(3\) \(q+(\beta _{4}+\beta _{7}+\beta _{8})q^{2}+(-\beta _{1}+\beta _{2}-\beta _{4}+\cdots)q^{3}+\cdots\)