Properties

Label 672.2.bq
Level 672
Weight 2
Character orbit bq
Rep. character \(\chi_{672}(85,\cdot)\)
Character field \(\Q(\zeta_{8})\)
Dimension 192
Newform subspaces 2
Sturm bound 256
Trace bound 1

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Defining parameters

Level: \( N \) = \( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 672.bq (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 2 \)
Sturm bound: \(256\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 528 192 336
Cusp forms 496 192 304
Eisenstein series 32 0 32

Trace form

\( 192q + O(q^{10}) \) \( 192q + 16q^{10} + 32q^{12} + 8q^{16} + 8q^{18} + 24q^{22} + 16q^{23} + 16q^{24} - 80q^{26} - 80q^{32} - 80q^{34} - 80q^{40} + 16q^{43} - 8q^{44} + 64q^{46} - 32q^{51} + 64q^{52} + 32q^{53} - 16q^{54} - 64q^{55} - 56q^{56} - 48q^{60} + 64q^{61} - 96q^{62} - 16q^{63} - 16q^{67} + 16q^{68} + 64q^{69} - 48q^{70} - 56q^{74} - 64q^{75} + 112q^{76} + 32q^{77} + 160q^{80} + 160q^{82} + 128q^{86} - 80q^{88} + 8q^{92} + 16q^{94} + O(q^{100}) \)

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.bq.a \(88\) \(5.366\) None \(0\) \(0\) \(0\) \(0\)
672.2.bq.b \(104\) \(5.366\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(672, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database