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Properties

Label 2394.4.y
Level $2394$
Weight $4$
Character orbit 2394.y
Rep. character $\chi_{2394}(1357,\cdot)$
Character field $\Q(\zeta_{6})$
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.y (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1197 \)
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 2896 960 1936
Cusp forms 2864 960 1904
Eisenstein series 32 0 32

Trace form

\( 960 q + 1920 q^{4} - 12 q^{7} + O(q^{10}) \) \( 960 q + 1920 q^{4} - 12 q^{7} - 132 q^{15} - 7680 q^{16} - 52 q^{23} - 24000 q^{25} + 48 q^{28} - 136 q^{30} + 552 q^{35} - 176 q^{39} + 452 q^{42} - 84 q^{43} + 240 q^{49} - 1128 q^{50} + 1056 q^{53} + 280 q^{57} + 2016 q^{60} - 1862 q^{63} - 61440 q^{64} + 348 q^{65} + 3528 q^{67} + 6024 q^{71} + 840 q^{74} - 1544 q^{77} - 2136 q^{78} + 2520 q^{79} - 1000 q^{81} + 990 q^{91} + 208 q^{92} + 120 q^{93} + 1660 q^{95} + 2232 q^{98} + 1008 q^{99} + O(q^{100}) \)

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

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