Properties

Label 504.2.q
Level $504$
Weight $2$
Character orbit 504.q
Rep. character $\chi_{504}(25,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $48$
Newform subspaces $4$
Sturm bound $192$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 504.q (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: \(5\)
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

\( 48q + 4q^{5} + 4q^{9} + O(q^{10}) \) \( 48q + 4q^{5} + 4q^{9} - 8q^{15} + 8q^{17} - 4q^{23} - 24q^{25} - 6q^{27} - 6q^{29} - 12q^{31} + 8q^{33} + 12q^{35} - 26q^{39} + 18q^{41} + 6q^{43} - 2q^{45} - 12q^{47} - 6q^{49} + 36q^{51} + 4q^{53} + 12q^{55} - 20q^{57} + 72q^{59} - 12q^{61} + 26q^{63} - 24q^{65} - 32q^{69} - 40q^{71} + 30q^{75} + 28q^{77} + 12q^{79} - 8q^{81} - 36q^{83} - 68q^{87} + 18q^{89} - 6q^{91} + 8q^{93} + 20q^{95} - 32q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
504.2.q.a \(2\) \(4.024\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(4\) \(q+(1-2\zeta_{6})q^{3}-\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
504.2.q.b \(2\) \(4.024\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(-4\) \(q+(-1+2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-1-2\zeta_{6})q^{7}+\cdots\)
504.2.q.c \(22\) \(4.024\) None \(0\) \(-2\) \(1\) \(5\)
504.2.q.d \(22\) \(4.024\) None \(0\) \(2\) \(3\) \(-5\)

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

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