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Properties

Label 2394.4.ef
Level $2394$
Weight $4$
Character orbit 2394.ef
Rep. character $\chi_{2394}(1151,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $320$
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.ef (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 399 \)
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 2912 320 2592
Cusp forms 2848 320 2528
Eisenstein series 64 0 64

Trace form

\( 320 q - 1280 q^{4} + 52 q^{7} + O(q^{10}) \) \( 320 q - 1280 q^{4} + 52 q^{7} + 84 q^{13} + 5120 q^{16} + 684 q^{19} + 144 q^{22} + 8144 q^{25} - 208 q^{28} + 420 q^{31} + 720 q^{34} - 748 q^{37} - 196 q^{43} + 864 q^{46} + 140 q^{49} - 336 q^{52} - 336 q^{58} + 3264 q^{61} - 20480 q^{64} + 1624 q^{67} - 2112 q^{70} + 7380 q^{73} - 2736 q^{76} + 3976 q^{79} - 1080 q^{85} - 576 q^{88} - 3408 q^{91} - 3456 q^{94} - 13416 q^{97} + O(q^{100}) \)

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

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