Properties

Label 672.4.bq
Level $672$
Weight $4$
Character orbit 672.bq
Rep. character $\chi_{672}(85,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $576$
Sturm bound $512$

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Defining parameters

Level: \( N \) \(=\) \( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 672.bq (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(512\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(672, [\chi])\).

Total New Old
Modular forms 1552 576 976
Cusp forms 1520 576 944
Eisenstein series 32 0 32

Trace form

\( 576q + O(q^{10}) \) \( 576q + 240q^{10} - 96q^{12} - 120q^{16} - 72q^{18} + 392q^{22} + 656q^{23} + 912q^{24} + 80q^{26} + 2480q^{32} + 2000q^{34} - 3280q^{40} + 1616q^{43} - 1000q^{44} - 2880q^{46} - 2976q^{51} - 1728q^{52} + 1504q^{53} - 432q^{54} - 576q^{55} + 392q^{56} + 2448q^{60} - 3648q^{61} + 5856q^{62} + 1008q^{63} + 816q^{67} + 10064q^{68} - 2112q^{69} + 1008q^{70} - 2632q^{74} - 4416q^{75} - 10064q^{76} + 3808q^{77} - 12640q^{80} - 11680q^{82} - 4736q^{86} + 3120q^{88} + 2152q^{92} + 23600q^{94} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(672, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(672, [\chi])\) into lower level spaces

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