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Properties

Label 648.2.y
Level $648$
Weight $2$
Character orbit 648.y
Rep. character $\chi_{648}(25,\cdot)$
Character field $\Q(\zeta_{27})$
Dimension $486$
Newform subspaces $2$
Sturm bound $216$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 648 = 2^{3} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 648.y (of order \(27\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 81 \)
Character field: \(\Q(\zeta_{27})\)
Newform subspaces: \( 2 \)
Sturm bound: \(216\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(648, [\chi])\).

Total New Old
Modular forms 2016 486 1530
Cusp forms 1872 486 1386
Eisenstein series 144 0 144

Trace form

\( 486 q + O(q^{10}) \) \( 486 q + 18 q^{41} + 54 q^{45} + 54 q^{47} + 63 q^{51} + 54 q^{53} + 54 q^{57} + 63 q^{59} + 54 q^{63} + 54 q^{65} + 18 q^{69} - 27 q^{89} - 54 q^{93} - 162 q^{95} - 162 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(648, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
648.2.y.a 648.y 81.g $234$ $5.174$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{27}]$
648.2.y.b 648.y 81.g $252$ $5.174$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{27}]$

Decomposition of \(S_{2}^{\mathrm{old}}(648, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(648, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(162, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 2}\)