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Properties

Label 2394.4.dr
Level $2394$
Weight $4$
Character orbit 2394.dr
Rep. character $\chi_{2394}(31,\cdot)$
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.dr (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

\( 960 q - 3840 q^{4} - 12 q^{7} + O(q^{10}) \) \( 960 q - 3840 q^{4} - 12 q^{7} + 72 q^{13} - 132 q^{15} + 15360 q^{16} - 52 q^{23} + 12000 q^{25} + 48 q^{28} + 272 q^{30} - 90 q^{31} - 1104 q^{35} - 504 q^{37} - 176 q^{39} + 452 q^{42} + 42 q^{43} + 2736 q^{45} - 198 q^{47} + 240 q^{49} - 1128 q^{50} - 288 q^{52} - 1056 q^{53} + 180 q^{54} + 112 q^{57} + 1500 q^{59} + 528 q^{60} - 2520 q^{61} + 598 q^{63} - 61440 q^{64} - 348 q^{65} - 2292 q^{71} - 420 q^{74} - 7500 q^{75} + 1720 q^{77} - 2136 q^{78} + 272 q^{81} - 1020 q^{87} - 990 q^{91} + 208 q^{92} + 1764 q^{93} + 5326 q^{95} + 2232 q^{98} + 504 q^{99} + O(q^{100}) \)

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

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