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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

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

Display 100 coefficients 10 coefficients

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

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