Properties

Label 504.2.bs
Level 504
Weight 2
Character orbit bs
Rep. character \(\chi_{504}(257,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 48
Newform subspaces 1
Sturm bound 192
Trace bound 0

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Defining parameters

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

\( 48q - 4q^{9} + O(q^{10}) \) \( 48q - 4q^{9} + 8q^{15} + 8q^{21} - 12q^{23} - 24q^{25} - 18q^{27} + 18q^{29} - 10q^{39} + 6q^{41} - 6q^{43} + 6q^{45} + 36q^{47} + 6q^{49} - 12q^{51} + 12q^{53} + 4q^{57} + 46q^{63} - 54q^{75} - 36q^{77} - 12q^{79} - 24q^{87} + 18q^{89} + 6q^{91} + 16q^{93} - 64q^{99} + O(q^{100}) \)

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.bs.a \(48\) \(4.024\) None \(0\) \(0\) \(0\) \(0\)

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database