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Properties

Label 2394.4.gj
Level $2394$
Weight $4$
Character orbit 2394.gj
Rep. character $\chi_{2394}(5,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $2880$
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.gj (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1197 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(1920\)

Dimensions

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

Total New Old
Modular forms 8688 2880 5808
Cusp forms 8592 2880 5712
Eisenstein series 96 0 96

Trace form

\( 2880 q + O(q^{10}) \) \( 2880 q + 216 q^{13} - 636 q^{15} + 432 q^{17} - 24 q^{18} + 144 q^{28} - 630 q^{39} - 126 q^{43} + 4104 q^{45} + 864 q^{52} + 3168 q^{53} + 1344 q^{57} - 9000 q^{59} + 960 q^{60} + 7560 q^{61} + 846 q^{63} + 92160 q^{64} - 1764 q^{67} + 4272 q^{78} + 1260 q^{79} + 3648 q^{81} + 576 q^{84} + 990 q^{91} + 7188 q^{93} + 2646 q^{95} - 6696 q^{98} + 4056 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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