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Properties

Label 2394.4.e
Level $2394$
Weight $4$
Character orbit 2394.e
Rep. character $\chi_{2394}(1063,\cdot)$
Character field $\Q$
Dimension $200$
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.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 133 \)
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 200 1256
Cusp forms 1424 200 1224
Eisenstein series 32 0 32

Trace form

\( 200 q - 800 q^{4} - 56 q^{7} + O(q^{10}) \) \( 200 q - 800 q^{4} - 56 q^{7} + 3200 q^{16} - 308 q^{23} - 4976 q^{25} + 224 q^{28} - 158 q^{35} - 696 q^{43} - 548 q^{49} + 672 q^{58} - 12800 q^{64} - 2760 q^{74} - 2762 q^{77} + 1988 q^{85} + 1232 q^{92} - 1008 q^{95} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(2394, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(266, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(399, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(798, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(1197, [\chi])\)\(^{\oplus 2}\)