Properties

Label 672.2.cj
Level 672
Weight 2
Character orbit cj
Rep. character \(\chi_{672}(37,\cdot)\)
Character field \(\Q(\zeta_{24})\)
Dimension 512
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.cj (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 224 \)
Character field: \(\Q(\zeta_{24})\)
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 1056 512 544
Cusp forms 992 512 480
Eisenstein series 64 0 64

Trace form

\( 512q + O(q^{10}) \) \( 512q - 64q^{14} + 8q^{16} + 8q^{18} + 64q^{20} + 16q^{22} + 16q^{23} - 40q^{28} + 96q^{31} + 48q^{35} - 80q^{38} + 64q^{40} - 32q^{43} - 8q^{44} - 48q^{50} + 24q^{52} + 32q^{53} - 32q^{58} + 64q^{59} - 48q^{60} - 48q^{64} + 48q^{66} - 16q^{67} + 72q^{70} - 128q^{71} - 144q^{74} - 48q^{78} + 24q^{80} + 40q^{82} - 88q^{88} + 48q^{91} + 128q^{92} - 24q^{94} - 40q^{96} - 88q^{98} + O(q^{100}) \)

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.cj.a \(512\) \(5.366\) 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