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Properties

Label 63.4.p
Level $63$
Weight $4$
Character orbit 63.p
Rep. character $\chi_{63}(17,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
Newform subspaces $1$
Sturm bound $32$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
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: \(32\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(63, [\chi])\).

Total New Old
Modular forms 56 16 40
Cusp forms 40 16 24
Eisenstein series 16 0 16

Trace form

\( 16 q + 32 q^{4} + 56 q^{7} + O(q^{10}) \) \( 16 q + 32 q^{4} + 56 q^{7} - 72 q^{10} - 188 q^{16} - 612 q^{19} + 528 q^{22} - 20 q^{25} + 1036 q^{28} + 1128 q^{31} - 1196 q^{37} - 3204 q^{40} + 328 q^{43} - 1392 q^{46} + 784 q^{49} + 4452 q^{52} - 3372 q^{58} - 1632 q^{61} + 5432 q^{64} + 308 q^{67} + 3612 q^{70} + 4068 q^{73} - 2176 q^{79} - 10188 q^{82} - 4608 q^{85} + 708 q^{88} + 924 q^{91} - 2916 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(63, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
63.4.p.a 63.p 21.g $16$ $3.717$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(56\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(4+\beta _{2}-4\beta _{3}+\beta _{9})q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(63, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(63, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)