Properties

Label 1216.4.z
Level $1216$
Weight $4$
Character orbit 1216.z
Rep. character $\chi_{1216}(49,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $472$
Sturm bound $640$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 1952 488 1464
Cusp forms 1888 472 1416
Eisenstein series 64 16 48

Trace form

\( 472q + 2q^{3} - 2q^{5} + O(q^{10}) \) \( 472q + 2q^{3} - 2q^{5} + 8q^{11} - 2q^{13} - 236q^{15} - 4q^{17} - 20q^{19} + 52q^{21} + 116q^{27} - 2q^{29} - 1472q^{31} - 4q^{33} + 208q^{35} - 8q^{37} + 2q^{43} - 400q^{45} + 4q^{47} - 20792q^{49} + 638q^{51} - 2q^{53} + 2q^{59} - 1826q^{61} - 1368q^{63} - 16q^{65} + 1850q^{67} + 1996q^{69} + 6224q^{75} + 2736q^{77} - 8820q^{79} + 16520q^{81} - 2672q^{83} + 738q^{85} - 684q^{91} - 56q^{93} + 3872q^{95} - 4q^{97} + 1092q^{99} + O(q^{100}) \)

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

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