Properties

Label 672.2.bu
Level 672
Weight 2
Character orbit bu
Rep. character \(\chi_{672}(139,\cdot)\)
Character field \(\Q(\zeta_{8})\)
Dimension 256
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.bu (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 224 \)
Character field: \(\Q(\zeta_{8})\)
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 528 256 272
Cusp forms 496 256 240
Eisenstein series 32 0 32

Trace form

\( 256q + O(q^{10}) \) \( 256q + 32q^{14} - 8q^{16} + 8q^{18} - 8q^{22} + 16q^{23} + 40q^{28} - 48q^{35} + 16q^{43} - 8q^{44} - 48q^{50} - 32q^{53} + 64q^{58} + 48q^{60} - 144q^{64} + 16q^{67} + 72q^{70} - 128q^{71} + 232q^{74} - 48q^{78} + 176q^{88} + 48q^{91} - 152q^{92} - 32q^{98} + O(q^{100}) \)

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.bu.a \(256\) \(5.366\) None \(0\) \(0\) \(0\) \(0\)

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database