Properties

Label 63.2.i
Level 63
Weight 2
Character orbit i
Rep. character \(\chi_{63}(5,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 12
Newform subspaces 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.i (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
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

\( 12q - 3q^{3} - 10q^{4} - 3q^{5} + 6q^{6} - 2q^{7} - 3q^{9} + O(q^{10}) \) \( 12q - 3q^{3} - 10q^{4} - 3q^{5} + 6q^{6} - 2q^{7} - 3q^{9} - 6q^{10} - 9q^{11} - 12q^{12} - 3q^{13} + 18q^{14} + 6q^{15} + 2q^{16} + 9q^{17} + 24q^{18} - 6q^{19} + 6q^{20} - 3q^{21} + 2q^{22} - 6q^{23} - 6q^{24} + 3q^{25} - 6q^{26} - 27q^{27} - 2q^{28} - 24q^{29} + 15q^{30} - 3q^{33} + 6q^{34} - 12q^{36} - q^{37} + 27q^{38} + 15q^{39} + 24q^{40} + 6q^{41} - 24q^{42} + 2q^{43} - 27q^{44} + 39q^{45} - 4q^{46} + 30q^{47} + 15q^{48} + 6q^{49} - 9q^{50} + 30q^{51} - 15q^{52} + 24q^{53} + 27q^{54} - 24q^{56} - 27q^{57} - q^{58} - 36q^{59} - 57q^{60} - 24q^{62} - 27q^{63} + 4q^{64} - 48q^{66} + 12q^{67} - 24q^{68} + 12q^{69} + 15q^{70} - 30q^{72} - 6q^{73} - 51q^{74} - 6q^{75} + 48q^{77} + 15q^{78} - 24q^{79} + 45q^{80} + 33q^{81} + 30q^{83} + 87q^{84} + 9q^{85} + 57q^{86} - 3q^{87} - 11q^{88} - 27q^{89} - 51q^{90} - 15q^{91} + 30q^{92} + 24q^{93} + 51q^{96} - 3q^{97} - 21q^{98} + 12q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(63, [\chi])\) into newform subspaces

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