Properties

Label 1216.4.bd
Level $1216$
Weight $4$
Character orbit 1216.bd
Rep. character $\chi_{1216}(77,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $3456$
Sturm bound $640$

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Defining parameters

Level: \( N \) \(=\) \( 1216 = 2^{6} \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1216.bd (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 64 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(640\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1216, [\chi])\).

Total New Old
Modular forms 3856 3456 400
Cusp forms 3824 3456 368
Eisenstein series 32 0 32

Trace form

\( 3456q + O(q^{10}) \) \( 3456q - 944q^{22} - 2000q^{24} + 4640q^{30} + 1760q^{36} - 6320q^{42} - 2000q^{44} + 6624q^{52} - 1152q^{55} - 784q^{56} - 4752q^{58} + 5504q^{59} - 2928q^{62} + 10080q^{63} + 8160q^{67} - 2064q^{68} + 896q^{71} + 1296q^{72} + 5264q^{74} - 8832q^{75} + 3984q^{78} - 9280q^{80} - 13920q^{82} - 8288q^{84} + 1040q^{86} + 25232q^{92} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1216, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1216, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1216, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)