Properties

Label 1216.4.bs
Level $1216$
Weight $4$
Character orbit 1216.bs
Rep. character $\chi_{1216}(15,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $1416$
Sturm bound $640$

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Defining parameters

Level: \( N \) \(=\) \( 1216 = 2^{6} \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1216.bs (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 304 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(640\)

Dimensions

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

Total New Old
Modular forms 5856 1464 4392
Cusp forms 5664 1416 4248
Eisenstein series 192 48 144

Trace form

\( 1416q + 12q^{3} - 12q^{5} + 12q^{7} + O(q^{10}) \) \( 1416q + 12q^{3} - 12q^{5} + 12q^{7} + 6q^{11} - 12q^{13} - 24q^{17} + 12q^{19} + 150q^{21} + 24q^{23} + 18q^{27} - 12q^{29} - 24q^{33} - 738q^{35} + 48q^{39} + 12q^{43} - 6q^{45} - 31176q^{49} - 2220q^{51} - 12q^{53} + 24q^{55} + 12q^{59} - 12q^{61} - 36q^{65} + 12q^{67} - 4770q^{69} + 24q^{71} + 4092q^{77} - 24q^{81} + 6q^{83} - 1452q^{85} + 12q^{87} - 2046q^{91} + 150q^{93} - 24q^{97} + 4386q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1216, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 3}\)