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Properties

Label 2394.4.fv
Level $2394$
Weight $4$
Character orbit 2394.fv
Rep. character $\chi_{2394}(17,\cdot)$
Character field $\Q(\zeta_{18})$
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.fv (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 399 \)
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 8736 960 7776
Cusp forms 8544 960 7584
Eisenstein series 192 0 192

Trace form

\( 960 q + O(q^{10}) \) \( 960 q + 108 q^{13} + 972 q^{19} - 432 q^{22} - 432 q^{25} + 624 q^{28} - 2160 q^{34} - 504 q^{37} + 84 q^{43} - 1296 q^{46} + 576 q^{49} + 144 q^{52} - 720 q^{61} + 30720 q^{64} + 1932 q^{67} - 3168 q^{70} + 2592 q^{73} + 8484 q^{79} - 2952 q^{85} + 2652 q^{91} + 5616 q^{94} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(2394, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(399, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(798, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(1197, [\chi])\)\(^{\oplus 2}\)