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Properties

Label 2394.2.ep
Level $2394$
Weight $2$
Character orbit 2394.ep
Rep. character $\chi_{2394}(529,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $960$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2394.ep (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1197 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2394, [\chi])\).

Total New Old
Modular forms 2928 960 1968
Cusp forms 2832 960 1872
Eisenstein series 96 0 96

Trace form

\( 960 q + O(q^{10}) \) \( 960 q + 6 q^{13} + 6 q^{15} + 36 q^{17} + 12 q^{18} + 24 q^{19} + 12 q^{23} + 12 q^{28} + 72 q^{35} + 18 q^{39} - 12 q^{43} - 18 q^{45} + 24 q^{50} - 12 q^{52} + 24 q^{53} + 54 q^{57} + 60 q^{59} + 42 q^{60} + 42 q^{61} - 18 q^{63} - 480 q^{64} - 48 q^{66} + 42 q^{67} - 12 q^{71} - 84 q^{73} + 24 q^{78} + 6 q^{79} - 120 q^{81} + 18 q^{84} + 60 q^{87} + 96 q^{90} - 6 q^{91} + 12 q^{92} - 120 q^{93} + 30 q^{95} + 36 q^{98} + 30 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2394, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(2394, [\chi])\) into lower level spaces

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