Properties

Label 2394.4.b
Level $2394$
Weight $4$
Character orbit 2394.b
Rep. character $\chi_{2394}(1709,\cdot)$
Character field $\Q$
Dimension $120$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q\)
Sturm bound: \(1920\)

Dimensions

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

Total New Old
Modular forms 1456 120 1336
Cusp forms 1424 120 1304
Eisenstein series 32 0 32

Trace form

\( 120 q + 480 q^{4} + O(q^{10}) \) \( 120 q + 480 q^{4} + 1920 q^{16} + 96 q^{19} - 3912 q^{25} - 2496 q^{43} + 5880 q^{49} - 5856 q^{55} - 864 q^{58} - 3024 q^{61} + 7680 q^{64} - 144 q^{73} + 384 q^{76} - 2400 q^{82} + 12864 q^{85} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(2394, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(399, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(798, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(1197, [\chi])\)\(^{\oplus 2}\)