Properties

Label 63.2.g
Level $63$
Weight $2$
Character orbit 63.g
Rep. character $\chi_{63}(4,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $12$
Newform subspaces $2$
Sturm bound $16$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 63.g (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
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

\( 12q + q^{2} - q^{3} - 3q^{4} - 10q^{5} - 2q^{6} - 12q^{8} - q^{9} + O(q^{10}) \) \( 12q + q^{2} - q^{3} - 3q^{4} - 10q^{5} - 2q^{6} - 12q^{8} - q^{9} - 6q^{10} + 2q^{11} + 19q^{12} - 3q^{13} + 11q^{14} - 16q^{15} + 3q^{16} + 9q^{17} + q^{18} + 4q^{20} - 8q^{21} - 6q^{22} + 12q^{24} - 6q^{25} + 16q^{26} - 7q^{27} - 6q^{28} + 8q^{29} - 26q^{30} - 3q^{31} - 7q^{32} - 16q^{33} + 4q^{35} + 40q^{36} - 3q^{37} - 38q^{38} + 20q^{39} + 12q^{40} + 10q^{41} + 41q^{42} - 6q^{43} - 5q^{44} - 4q^{45} + 27q^{47} - 5q^{48} + 12q^{49} + 23q^{50} + 24q^{51} + 30q^{52} - 12q^{53} - 62q^{54} - 6q^{55} - 48q^{56} - q^{57} + 18q^{58} + 30q^{59} - 38q^{60} - 12q^{62} - 20q^{63} - 36q^{64} - 16q^{65} - 41q^{66} - 6q^{67} - 60q^{68} + 6q^{69} - 24q^{70} - 30q^{71} + 39q^{72} + 12q^{73} + 78q^{74} + 43q^{75} + 6q^{76} - 26q^{77} - 35q^{78} - 12q^{79} + 19q^{80} - q^{81} + 18q^{83} + 5q^{84} - 3q^{85} + 14q^{86} + 29q^{87} + 6q^{88} + 41q^{89} + 25q^{90} + 21q^{91} + 30q^{92} - 12q^{93} - 3q^{94} - 13q^{95} + 14q^{96} - 3q^{97} + 61q^{98} + 50q^{99} + O(q^{100}) \)

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.g.a \(2\) \(0.503\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-3\) \(-2\) \(1\) \(q-\zeta_{6}q^{2}+(-1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
63.2.g.b \(10\) \(0.503\) 10.0.\(\cdots\).1 None \(2\) \(2\) \(-8\) \(-1\) \(q+\beta _{1}q^{2}+(\beta _{2}-\beta _{7})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)