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Properties

Label 2394.4.gm
Level $2394$
Weight $4$
Character orbit 2394.gm
Rep. character $\chi_{2394}(317,\cdot)$
Character field $\Q(\zeta_{18})$
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.gm (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1197 \)
Character field: \(\Q(\zeta_{18})\)
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

\( 2880 q + O(q^{10}) \) \( 2880 q - 72 q^{13} + 372 q^{15} - 720 q^{19} - 468 q^{23} + 288 q^{28} - 1260 q^{39} + 126 q^{43} - 1368 q^{45} - 2016 q^{50} + 288 q^{52} - 3168 q^{53} - 2016 q^{57} + 4500 q^{59} + 1536 q^{60} - 5040 q^{61} + 1692 q^{63} - 92160 q^{64} + 816 q^{66} - 1764 q^{67} + 2016 q^{73} - 4272 q^{78} - 1260 q^{79} + 1728 q^{81} - 864 q^{84} - 4200 q^{87} + 5088 q^{90} + 990 q^{91} + 14376 q^{93} - 6696 q^{98} - 12456 q^{99} + O(q^{100}) \)

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

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