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Properties

Label 504.2.t
Level $504$
Weight $2$
Character orbit 504.t
Rep. character $\chi_{504}(193,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $48$
Newform subspaces $4$
Sturm bound $192$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 504.t (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 4 \)
Sturm bound: \(192\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

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

\( 48 q - 8 q^{5} - 2 q^{9} + O(q^{10}) \) \( 48 q - 8 q^{5} - 2 q^{9} - 8 q^{15} + 8 q^{17} + 18 q^{21} + 8 q^{23} + 48 q^{25} - 6 q^{27} - 6 q^{29} + 6 q^{31} - 4 q^{33} + 12 q^{35} + 4 q^{39} + 18 q^{41} + 6 q^{43} + 22 q^{45} + 6 q^{47} + 12 q^{49} - 18 q^{51} + 4 q^{53} + 12 q^{55} - 20 q^{57} - 36 q^{59} + 6 q^{61} - 4 q^{63} + 12 q^{65} - 32 q^{69} - 40 q^{71} - 24 q^{75} + 4 q^{77} - 6 q^{79} - 26 q^{81} - 36 q^{83} + 46 q^{87} + 18 q^{89} - 6 q^{91} - 52 q^{93} - 10 q^{95} - 32 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.t.a 504.t 63.g $2$ $4.024$ \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(2\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\zeta_{6})q^{3}+q^{5}+(-2-\zeta_{6})q^{7}+\cdots\)
504.2.t.b 504.t 63.g $2$ $4.024$ \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(-2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\zeta_{6})q^{3}-q^{5}+(-2+3\zeta_{6})q^{7}+\cdots\)
504.2.t.c 504.t 63.g $22$ $4.024$ None \(0\) \(-2\) \(-2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$
504.2.t.d 504.t 63.g $22$ $4.024$ None \(0\) \(2\) \(-6\) \(7\) $\mathrm{SU}(2)[C_{3}]$

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

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