Properties

Label 1216.4.m
Level $1216$
Weight $4$
Character orbit 1216.m
Rep. character $\chi_{1216}(303,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $236$
Sturm bound $640$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 976 244 732
Cusp forms 944 236 708
Eisenstein series 32 8 24

Trace form

\( 236 q - 4 q^{5} + 8 q^{7} + O(q^{10}) \) \( 236 q - 4 q^{5} + 8 q^{7} + 4 q^{11} - 8 q^{17} + 26 q^{19} + 8 q^{23} + 960 q^{35} + 8 q^{39} + 4 q^{43} + 388 q^{45} + 10380 q^{49} + 8 q^{55} - 1828 q^{61} - 1376 q^{77} - 16532 q^{81} + 2684 q^{83} - 984 q^{85} - 2568 q^{87} - 112 q^{93} - 364 q^{99} + O(q^{100}) \)

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

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