Properties

Label 63.2.p
Level $63$
Weight $2$
Character orbit 63.p
Rep. character $\chi_{63}(17,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $1$
Sturm bound $16$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 63.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(16\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(63, [\chi])\).

Total New Old
Modular forms 24 4 20
Cusp forms 8 4 4
Eisenstein series 16 0 16

Trace form

\( 4 q - 2 q^{7} + O(q^{10}) \) \( 4 q - 2 q^{7} - 12 q^{10} + 8 q^{16} + 6 q^{19} - 8 q^{22} - 2 q^{25} + 6 q^{31} + 2 q^{37} + 24 q^{40} - 4 q^{43} + 16 q^{46} - 26 q^{49} - 8 q^{58} - 12 q^{61} - 32 q^{64} - 22 q^{67} + 24 q^{70} + 6 q^{73} - 10 q^{79} - 36 q^{82} + 48 q^{85} + 8 q^{88} + 54 q^{91} + 60 q^{94} + O(q^{100}) \)

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.p.a 63.p 21.g $4$ $0.503$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(-\beta _{1}+2\beta _{3})q^{5}+(1-3\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(63, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(63, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)