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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 $1$

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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
63.2.g.a 63.g 63.g $2$ $0.503$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-3\) \(-2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
63.2.g.b 63.g 63.g $10$ $0.503$ 10.0.\(\cdots\).1 None \(2\) \(2\) \(-8\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(\beta _{2}-\beta _{7})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)