Properties

Label 504.4.bl
Level $504$
Weight $4$
Character orbit 504.bl
Rep. character $\chi_{504}(17,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $48$
Newform subspaces $1$
Sturm bound $384$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 504.bl (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(384\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(504, [\chi])\).

Total New Old
Modular forms 608 48 560
Cusp forms 544 48 496
Eisenstein series 64 0 64

Trace form

\( 48q - 24q^{7} + O(q^{10}) \) \( 48q - 24q^{7} + 540q^{19} - 924q^{25} + 648q^{31} - 132q^{37} - 792q^{43} + 672q^{49} - 12q^{67} + 2412q^{73} + 1680q^{79} + 480q^{85} + 1404q^{91} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(504, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
504.4.bl.a \(48\) \(29.737\) None \(0\) \(0\) \(0\) \(-24\)

Decomposition of \(S_{4}^{\mathrm{old}}(504, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(504, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)