Properties

Label 63.3.q
Level $63$
Weight $3$
Character orbit 63.q
Rep. character $\chi_{63}(44,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $12$
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.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
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 40 12 28
Cusp forms 24 12 12
Eisenstein series 16 0 16

Trace form

\( 12 q + 16 q^{4} - 2 q^{7} + O(q^{10}) \) \( 12 q + 16 q^{4} - 2 q^{7} - 16 q^{10} - 52 q^{13} - 44 q^{16} + 26 q^{19} + 32 q^{22} + 106 q^{25} + 84 q^{28} + 22 q^{31} - 528 q^{34} - 146 q^{37} + 300 q^{40} + 108 q^{43} + 168 q^{46} + 114 q^{49} + 252 q^{52} + 16 q^{55} + 92 q^{58} - 136 q^{61} + 312 q^{64} + 2 q^{67} - 620 q^{70} - 482 q^{73} - 504 q^{76} + 42 q^{79} - 212 q^{82} - 288 q^{85} - 180 q^{88} + 222 q^{91} + 612 q^{94} + 568 q^{97} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
63.3.q.a $12$ $1.717$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(-2\) \(q+\beta _{1}q^{2}+(-3\beta _{8}+\beta _{9})q^{4}-\beta _{6}q^{5}+\cdots\)

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

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