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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
63.2.f.a 63.f 9.c $6$ $0.503$ \(\Q(\zeta_{18})\) None 63.2.f.a \(-3\) \(0\) \(-3\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta_{5}+\beta_1-1)q^{2}+(\beta_{5}-\beta_{3})q^{3}+\cdots\)
63.2.f.b 63.f 9.c $6$ $0.503$ 6.0.309123.1 None 63.2.f.b \(1\) \(-4\) \(5\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{2}+(\beta _{2}+\beta _{3}+\cdots)q^{3}+\cdots\)