Properties

Label 504.2.cx
Level $504$
Weight $2$
Character orbit 504.cx
Rep. character $\chi_{504}(185,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $48$
Newform subspaces $1$
Sturm bound $192$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 504.cx (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(192\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(504, [\chi])\).

Total New Old
Modular forms 208 48 160
Cusp forms 176 48 128
Eisenstein series 32 0 32

Trace form

\( 48 q + 2 q^{9} + O(q^{10}) \) \( 48 q + 2 q^{9} + 8 q^{15} - 10 q^{21} + 48 q^{25} + 18 q^{27} + 18 q^{29} + 18 q^{31} + 12 q^{33} - 4 q^{39} - 6 q^{41} - 6 q^{43} - 18 q^{45} + 18 q^{47} - 12 q^{49} + 6 q^{51} - 12 q^{53} + 4 q^{57} + 18 q^{61} - 32 q^{63} - 36 q^{65} - 12 q^{77} + 6 q^{79} + 6 q^{81} - 54 q^{87} - 18 q^{89} + 6 q^{91} + 4 q^{93} - 54 q^{95} - 64 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(504, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
504.2.cx.a 504.cx 63.s $48$ $4.024$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(504, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(504, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)