Properties

Label 672.2.cf
Level 672
Weight 2
Character orbit cf
Rep. character \(\chi_{672}(19,\cdot)\)
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.cf (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

\( 512q + O(q^{10}) \) \( 512q + 64q^{14} + 8q^{16} - 8q^{18} - 16q^{22} - 16q^{23} - 40q^{28} + 48q^{35} + 32q^{43} + 8q^{44} + 48q^{50} - 72q^{52} + 32q^{53} + 32q^{58} - 192q^{59} - 48q^{60} + 144q^{64} - 144q^{66} - 16q^{67} - 72q^{70} + 128q^{71} + 32q^{74} + 48q^{78} - 72q^{80} - 120q^{82} + 88q^{88} - 48q^{91} + 128q^{92} - 72q^{94} - 120q^{96} - 136q^{98} + O(q^{100}) \)

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.cf.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