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Properties

Label 63.6.p
Level $63$
Weight $6$
Character orbit 63.p
Rep. character $\chi_{63}(17,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $28$
Newform subspaces $2$
Sturm bound $48$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 63.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(48\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(63, [\chi])\).

Total New Old
Modular forms 88 28 60
Cusp forms 72 28 44
Eisenstein series 16 0 16

Trace form

\( 28 q + 256 q^{4} + 54 q^{7} + O(q^{10}) \) \( 28 q + 256 q^{4} + 54 q^{7} + 1488 q^{10} - 4284 q^{16} - 2202 q^{19} + 896 q^{22} - 17894 q^{25} - 48580 q^{28} + 30798 q^{31} + 20142 q^{37} + 160284 q^{40} + 20988 q^{43} + 368 q^{46} - 72854 q^{49} - 98700 q^{52} + 180332 q^{58} - 11892 q^{61} - 354504 q^{64} + 95930 q^{67} - 58860 q^{70} - 518478 q^{73} + 244526 q^{79} + 1080180 q^{82} - 206832 q^{85} + 399076 q^{88} - 215322 q^{91} - 1716756 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(63, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
63.6.p.a 63.p 21.g $4$ $10.104$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(490\) $\mathrm{SU}(2)[C_{6}]$ \(q+2\beta _{1}q^{2}-24\beta _{2}q^{4}+(-21\beta _{1}+42\beta _{3})q^{5}+\cdots\)
63.6.p.b 63.p 21.g $24$ $10.104$ None \(0\) \(0\) \(0\) \(-436\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{6}^{\mathrm{old}}(63, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(63, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)