Properties

Label 672.2.bk
Level 672
Weight 2
Character orbit bk
Rep. character \(\chi_{672}(529,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 32
Newform subspaces 1
Sturm bound 256
Trace bound 0

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Defining parameters

Level: \( N \) = \( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 672.bk (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 56 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(256\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(672, [\chi])\).

Total New Old
Modular forms 288 32 256
Cusp forms 224 32 192
Eisenstein series 64 0 64

Trace form

\( 32q + 16q^{9} + O(q^{10}) \) \( 32q + 16q^{9} + 8q^{23} + 16q^{25} + 24q^{31} + 24q^{47} + 8q^{49} + 64q^{55} - 16q^{57} + 80q^{71} + 8q^{73} - 8q^{79} - 16q^{81} - 24q^{87} - 24q^{95} - 48q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(672, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
672.2.bk.a \(32\) \(5.366\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(672, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(672, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database