Properties

Label 672.2.bs
Level 672
Weight 2
Character orbit bs
Rep. character \(\chi_{672}(155,\cdot)\)
Character field \(\Q(\zeta_{8})\)
Dimension 384
Newform subspaces 2
Sturm bound 256
Trace bound 4

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Defining parameters

Level: \( N \) = \( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 672.bs (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 96 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 2 \)
Sturm bound: \(256\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 528 384 144
Cusp forms 496 384 112
Eisenstein series 32 0 32

Trace form

\( 384q + O(q^{10}) \) \( 384q + 16q^{10} + 32q^{16} + 32q^{22} + 48q^{27} - 40q^{30} - 64q^{36} + 48q^{39} - 64q^{46} - 104q^{48} - 64q^{52} - 64q^{55} - 144q^{58} - 56q^{60} + 64q^{61} + 64q^{66} - 64q^{67} - 48q^{70} + 120q^{72} - 112q^{76} + 24q^{78} - 64q^{79} - 112q^{87} + 80q^{88} + 120q^{90} + 96q^{94} + 64q^{96} - 128q^{99} + O(q^{100}) \)

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.bs.a \(192\) \(5.366\) None \(0\) \(0\) \(0\) \(0\)
672.2.bs.b \(192\) \(5.366\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(672, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database