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Properties

Label 63.3.b
Level $63$
Weight $3$
Character orbit 63.b
Rep. character $\chi_{63}(8,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
Sturm bound $24$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 63.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(63, [\chi])\).

Total New Old
Modular forms 20 4 16
Cusp forms 12 4 8
Eisenstein series 8 0 8

Trace form

\( 4 q + O(q^{10}) \) \( 4 q - 32 q^{10} + 24 q^{13} - 36 q^{16} + 24 q^{19} + 76 q^{22} + 36 q^{25} + 28 q^{28} - 152 q^{31} + 24 q^{34} - 128 q^{37} - 72 q^{40} + 80 q^{43} + 132 q^{46} + 28 q^{49} - 112 q^{52} + 152 q^{55} + 148 q^{58} - 48 q^{61} - 32 q^{64} - 24 q^{67} + 56 q^{70} + 16 q^{73} - 280 q^{76} - 88 q^{79} - 256 q^{82} + 48 q^{85} + 108 q^{88} - 112 q^{91} + 216 q^{94} + 160 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(63, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
63.3.b.a 63.b 3.b $4$ $1.717$ \(\Q(\sqrt{-2}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+2\beta _{1}q^{5}+\beta _{2}q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(63, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(63, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)