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Properties

Label 2394.4.p
Level $2394$
Weight $4$
Character orbit 2394.p
Rep. character $\chi_{2394}(961,\cdot)$
Character field $\Q(\zeta_{3})$
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.p (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1197 \)
Character field: \(\Q(\zeta_{3})\)
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

\( 960 q + 3840 q^{4} - 12 q^{7} + O(q^{10}) \) \( 960 q + 3840 q^{4} - 12 q^{7} - 24 q^{13} - 212 q^{15} + 15360 q^{16} + 96 q^{17} - 32 q^{18} - 120 q^{19} + 96 q^{21} - 52 q^{23} - 12000 q^{25} + 264 q^{27} - 48 q^{28} - 272 q^{30} + 30 q^{31} - 1104 q^{35} - 168 q^{37} + 664 q^{39} - 2624 q^{41} + 764 q^{42} - 42 q^{43} + 448 q^{45} + 66 q^{47} + 240 q^{49} - 152 q^{50} + 800 q^{51} - 96 q^{52} + 352 q^{53} + 60 q^{54} + 916 q^{59} - 848 q^{60} + 840 q^{61} + 922 q^{63} + 61440 q^{64} + 116 q^{65} + 544 q^{66} - 1176 q^{67} + 384 q^{68} + 800 q^{69} + 1084 q^{71} - 128 q^{72} + 1344 q^{73} - 420 q^{74} - 2500 q^{75} - 480 q^{76} - 2632 q^{77} + 712 q^{78} + 840 q^{79} + 1520 q^{81} + 384 q^{84} + 3208 q^{87} - 8544 q^{89} + 5824 q^{90} + 2010 q^{91} - 208 q^{92} - 1764 q^{93} + 178 q^{95} + 1056 q^{97} + 744 q^{98} + 8376 q^{99} + O(q^{100}) \)

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

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