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Properties

Label 2394.4.ds
Level $2394$
Weight $4$
Character orbit 2394.ds
Rep. character $\chi_{2394}(559,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $400$
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.ds (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 133 \)
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 400 2512
Cusp forms 2848 400 2448
Eisenstein series 64 0 64

Trace form

\( 400 q + 800 q^{4} + 44 q^{7} + O(q^{10}) \) \( 400 q + 800 q^{4} + 44 q^{7} - 168 q^{11} - 12 q^{14} - 3200 q^{16} + 48 q^{22} - 112 q^{23} + 4676 q^{25} + 88 q^{28} + 468 q^{29} + 92 q^{35} + 360 q^{43} - 336 q^{44} - 736 q^{49} + 1644 q^{53} - 672 q^{58} - 25600 q^{64} - 2724 q^{67} - 696 q^{70} + 4200 q^{71} - 120 q^{74} + 6332 q^{77} - 3192 q^{79} - 1856 q^{85} + 264 q^{86} - 3660 q^{91} + 448 q^{92} + 6144 q^{95} - 864 q^{98} + O(q^{100}) \)

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

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