Properties

Label 504.2.r
Level $504$
Weight $2$
Character orbit 504.r
Rep. character $\chi_{504}(169,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $36$
Newform subspaces $6$
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.r (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 6 \)
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 36 172
Cusp forms 176 36 140
Eisenstein series 32 0 32

Trace form

\( 36q - 2q^{3} + 6q^{9} + O(q^{10}) \) \( 36q - 2q^{3} + 6q^{9} + 14q^{11} + 20q^{15} + 12q^{17} - 12q^{19} + 4q^{23} - 18q^{25} - 20q^{27} - 12q^{29} - 18q^{33} - 24q^{35} - 28q^{39} - 6q^{41} + 6q^{43} + 36q^{45} - 12q^{47} - 18q^{49} + 38q^{51} + 48q^{53} + 30q^{57} + 14q^{59} - 4q^{63} - 16q^{65} + 6q^{67} - 16q^{69} + 24q^{71} + 36q^{73} - 22q^{75} - 8q^{77} + 6q^{81} + 16q^{83} - 24q^{85} + 40q^{87} - 48q^{89} - 44q^{93} + 12q^{95} - 42q^{97} + 36q^{99} + O(q^{100}) \)

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.r.a \(2\) \(4.024\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(-1\) \(q+(-1+2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}-\zeta_{6}q^{7}+\cdots\)
504.2.r.b \(2\) \(4.024\) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(-2\) \(-1\) \(q+(2-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{5}-\zeta_{6}q^{7}+\cdots\)
504.2.r.c \(6\) \(4.024\) \(\Q(\zeta_{18})\) None \(0\) \(0\) \(3\) \(-3\) \(q+(-\zeta_{18}^{2}-\zeta_{18}^{5})q^{3}+(1-\zeta_{18}+\zeta_{18}^{2}+\cdots)q^{5}+\cdots\)
504.2.r.d \(8\) \(4.024\) 8.0.508277025.1 None \(0\) \(-4\) \(4\) \(-4\) \(q+(-\beta _{4}-\beta _{6})q^{3}+(1+\beta _{1}+2\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots\)
504.2.r.e \(8\) \(4.024\) 8.0.2091141441.1 None \(0\) \(-1\) \(-3\) \(4\) \(q+\beta _{4}q^{3}+(\beta _{2}+\beta _{4}+\beta _{6})q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots\)
504.2.r.f \(10\) \(4.024\) 10.0.\(\cdots\).1 None \(0\) \(0\) \(-3\) \(5\) \(q+\beta _{6}q^{3}+(-\beta _{2}-\beta _{7})q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(504, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)