Properties

Label 63.2.h
Level $63$
Weight $2$
Character orbit 63.h
Rep. character $\chi_{63}(25,\cdot)$
Character field $\Q(\zeta_{3})$
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.h (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

\( 12q - 2q^{2} - q^{3} + 6q^{4} + 5q^{5} - 2q^{6} - 12q^{8} + 5q^{9} + O(q^{10}) \) \( 12q - 2q^{2} - q^{3} + 6q^{4} + 5q^{5} - 2q^{6} - 12q^{8} + 5q^{9} - 6q^{10} - q^{11} - 20q^{12} - 3q^{13} - 16q^{14} - 16q^{15} - 6q^{16} + 9q^{17} - 2q^{18} + 4q^{20} + 19q^{21} - 6q^{22} + 6q^{24} + 3q^{25} + 16q^{26} - 7q^{27} - 6q^{28} + 8q^{29} + 19q^{30} + 6q^{31} + 14q^{32} + 29q^{33} + 4q^{35} + 40q^{36} - 3q^{37} + 19q^{38} - 13q^{39} - 6q^{40} + 10q^{41} + 2q^{42} - 6q^{43} - 5q^{44} - 19q^{45} - 54q^{47} - 5q^{48} - 6q^{49} + 23q^{50} - 18q^{51} - 15q^{52} - 12q^{53} + q^{54} - 6q^{55} + 6q^{56} - q^{57} - 9q^{58} - 60q^{59} + 7q^{60} - 12q^{62} - 71q^{63} - 36q^{64} + 32q^{65} + 34q^{66} + 12q^{67} + 30q^{68} + 6q^{69} + 39q^{70} - 30q^{71} - 18q^{72} + 12q^{73} - 39q^{74} - 26q^{75} + 6q^{76} - 14q^{77} - 35q^{78} + 24q^{79} + 19q^{80} + 41q^{81} + 18q^{83} + 29q^{84} - 3q^{85} - 7q^{86} + 5q^{87} - 3q^{88} + 41q^{89} + 25q^{90} + 21q^{91} + 30q^{92} - 6q^{93} + 6q^{94} + 26q^{95} + 59q^{96} - 3q^{97} + 61q^{98} + 50q^{99} + O(q^{100}) \)

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.h.a \(2\) \(0.503\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(1\) \(4\) \(q+q^{2}+(1-2\zeta_{6})q^{3}-q^{4}+\zeta_{6}q^{5}+\cdots\)
63.2.h.b \(10\) \(0.503\) 10.0.\(\cdots\).1 None \(-4\) \(-1\) \(4\) \(-4\) \(q+(-\beta _{1}+\beta _{5})q^{2}-\beta _{8}q^{3}+(1-\beta _{4}+\cdots)q^{4}+\cdots\)