Properties

Label 672.2.bd
Level 672
Weight 2
Character orbit bd
Rep. character \(\chi_{672}(431,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 56
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.bd (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 168 \)
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 72 216
Cusp forms 224 56 168
Eisenstein series 64 16 48

Trace form

\( 56q + 2q^{3} - 2q^{9} + O(q^{10}) \) \( 56q + 2q^{3} - 2q^{9} + 4q^{19} - 16q^{25} + 8q^{27} - 14q^{33} + 16q^{43} - 16q^{49} + 34q^{51} + 4q^{57} + 36q^{67} + 4q^{73} - 10q^{81} - 72q^{91} - 32q^{97} + 44q^{99} + O(q^{100}) \)

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.bd.a \(56\) \(5.366\) None \(0\) \(2\) \(0\) \(0\)

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database