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Properties

Label 63.2.s
Level $63$
Weight $2$
Character orbit 63.s
Rep. character $\chi_{63}(47,\cdot)$
Character field $\Q(\zeta_{6})$
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.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
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

\( 12 q - 3 q^{2} - 3 q^{3} + 5 q^{4} - 6 q^{5} - 6 q^{6} - 2 q^{7} + 3 q^{9} + O(q^{10}) \) \( 12 q - 3 q^{2} - 3 q^{3} + 5 q^{4} - 6 q^{5} - 6 q^{6} - 2 q^{7} + 3 q^{9} - 6 q^{10} - 3 q^{12} + 3 q^{13} + 3 q^{14} + 6 q^{15} - q^{16} - 9 q^{17} - 27 q^{18} - 6 q^{19} - 6 q^{20} + 24 q^{21} + 2 q^{22} + 24 q^{24} - 6 q^{25} + 6 q^{26} + 27 q^{27} - 2 q^{28} - 24 q^{29} - 18 q^{30} - 15 q^{31} + 39 q^{32} - 6 q^{33} - 6 q^{34} - 12 q^{36} - q^{37} + 54 q^{38} + 18 q^{39} - 6 q^{41} - 21 q^{42} + 2 q^{43} + 27 q^{44} + 6 q^{45} - 4 q^{46} + 15 q^{47} - 15 q^{48} - 12 q^{49} - 9 q^{50} - 24 q^{51} - 24 q^{53} + 36 q^{54} - 54 q^{56} - 27 q^{57} + 2 q^{58} - 18 q^{59} + 6 q^{60} + 36 q^{61} + 24 q^{62} + 6 q^{63} + 4 q^{64} + 6 q^{65} - 33 q^{66} - 6 q^{67} - 48 q^{68} - 12 q^{69} - 18 q^{70} + 27 q^{72} - 6 q^{73} - 33 q^{75} + 48 q^{77} + 15 q^{78} + 12 q^{79} - 45 q^{80} - 57 q^{81} - 30 q^{83} + 69 q^{84} + 9 q^{85} + 39 q^{87} + 22 q^{88} + 27 q^{89} + 51 q^{90} - 15 q^{91} + 30 q^{92} + 12 q^{93} - 3 q^{94} + 27 q^{95} + 12 q^{96} + 3 q^{97} + 21 q^{98} + 12 q^{99} + O(q^{100}) \)

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.s.a 63.s 63.s $2$ $0.503$ \(\Q(\sqrt{-3}) \) None \(-3\) \(-3\) \(-6\) \(-5\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
63.2.s.b 63.s 63.s $10$ $0.503$ 10.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(3\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{4}+\beta _{7}+\beta _{8})q^{2}+(-\beta _{1}+\beta _{2}-\beta _{4}+\cdots)q^{3}+\cdots\)