Properties

Label 63.2.f
Level $63$
Weight $2$
Character orbit 63.f
Rep. character $\chi_{63}(22,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $12$
Newform subspaces $2$
Sturm bound $16$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 63.f (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(16\)
Trace bound: \(2\)
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 12 8
Cusp forms 12 12 0
Eisenstein series 8 0 8

Trace form

\( 12q - 2q^{2} - 4q^{3} - 6q^{4} + 2q^{5} - 8q^{6} - 4q^{9} + O(q^{10}) \) \( 12q - 2q^{2} - 4q^{3} - 6q^{4} + 2q^{5} - 8q^{6} - 4q^{9} - 4q^{11} + 16q^{12} - 4q^{14} + 2q^{15} - 6q^{16} - 12q^{17} + 22q^{18} - 12q^{19} + 22q^{20} - 2q^{21} + 6q^{22} - 12q^{23} - 12q^{24} - 8q^{26} + 20q^{27} - 10q^{29} - 8q^{30} + 6q^{31} + 8q^{32} + 8q^{33} - 6q^{34} + 16q^{35} - 38q^{36} - 12q^{37} - 14q^{38} - 16q^{39} - 12q^{40} + 22q^{41} + 20q^{42} + 6q^{43} + 76q^{44} + 14q^{45} + 24q^{46} + 6q^{47} - 14q^{48} - 6q^{49} - 4q^{50} + 18q^{51} + 18q^{52} - 24q^{53} - 44q^{54} - 12q^{55} - 12q^{56} + 2q^{57} + 18q^{58} + 12q^{59} - 20q^{60} - 96q^{62} - 8q^{63} - 10q^{65} + 34q^{66} + 12q^{67} - 12q^{68} - 48q^{69} + 36q^{71} - 60q^{72} - 36q^{73} + 24q^{74} + 22q^{75} + 6q^{76} - 8q^{77} + 64q^{78} + 6q^{79} - 8q^{80} + 32q^{81} + 30q^{83} + 2q^{84} - 18q^{85} - 40q^{86} + 8q^{87} - 6q^{88} + 20q^{89} + 100q^{90} - 12q^{91} - 18q^{92} + 6q^{93} - 6q^{94} - 4q^{95} + 32q^{96} + 4q^{98} - 28q^{99} + O(q^{100}) \)

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.f.a \(6\) \(0.503\) \(\Q(\zeta_{18})\) None \(-3\) \(0\) \(-3\) \(-3\) \(q+(-1+\zeta_{18}+\zeta_{18}^{5})q^{2}+(-\zeta_{18}^{3}+\cdots)q^{3}+\cdots\)
63.2.f.b \(6\) \(0.503\) 6.0.309123.1 None \(1\) \(-4\) \(5\) \(3\) \(q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{2}+(\beta _{2}+\beta _{3}+\cdots)q^{3}+\cdots\)