Properties

Label 2394.4.cp
Level $2394$
Weight $4$
Character orbit 2394.cp
Rep. character $\chi_{2394}(65,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $960$
Sturm bound $1920$

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Defining parameters

Level: \( N \) \(=\) \( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2394.cp (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1197 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1920\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2394, [\chi])\).

Total New Old
Modular forms 2896 960 1936
Cusp forms 2864 960 1904
Eisenstein series 32 0 32

Trace form

\( 960 q + 3840 q^{4} + 12 q^{7} + O(q^{10}) \) \( 960 q + 3840 q^{4} + 12 q^{7} - 72 q^{13} + 132 q^{15} + 15360 q^{16} + 120 q^{19} + 156 q^{23} + 12000 q^{25} - 792 q^{27} + 48 q^{28} - 272 q^{30} + 90 q^{31} + 504 q^{37} - 664 q^{39} - 764 q^{42} - 42 q^{43} + 448 q^{45} + 198 q^{47} + 240 q^{49} + 1128 q^{50} - 288 q^{52} - 1056 q^{53} - 60 q^{54} - 1856 q^{57} + 1500 q^{59} + 528 q^{60} - 840 q^{61} + 1486 q^{63} + 61440 q^{64} - 348 q^{65} + 544 q^{66} + 2772 q^{71} + 1344 q^{73} - 1260 q^{74} + 480 q^{76} + 1608 q^{77} - 2136 q^{78} - 272 q^{81} + 1640 q^{87} + 5088 q^{90} + 990 q^{91} + 624 q^{92} + 1180 q^{93} + 882 q^{95} - 2232 q^{98} - 2440 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(2394, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(2394, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2394, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(1197, [\chi])\)\(^{\oplus 2}\)