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Properties

Label 2394.4.ei
Level $2394$
Weight $4$
Character orbit 2394.ei
Rep. character $\chi_{2394}(709,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $2880$
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.ei (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1197 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(1920\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2394, [\chi])\).

Total New Old
Modular forms 8688 2880 5808
Cusp forms 8592 2880 5712
Eisenstein series 96 0 96

Trace form

\( 2880 q + O(q^{10}) \) \( 2880 q + 72 q^{13} + 636 q^{15} - 288 q^{17} + 48 q^{18} + 720 q^{19} + 156 q^{23} - 288 q^{28} + 3312 q^{35} + 1260 q^{39} + 126 q^{43} - 1368 q^{45} + 672 q^{50} + 288 q^{52} - 1056 q^{53} - 2016 q^{57} + 1500 q^{59} - 480 q^{60} + 5040 q^{61} - 1692 q^{63} - 92160 q^{64} + 816 q^{66} - 1764 q^{67} + 5064 q^{71} + 2016 q^{73} + 4272 q^{78} + 1260 q^{79} - 3648 q^{81} + 288 q^{84} + 4200 q^{87} - 5088 q^{90} - 990 q^{91} - 1248 q^{92} - 3288 q^{93} - 3732 q^{95} - 2232 q^{98} - 5352 q^{99} + O(q^{100}) \)

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

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