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Properties

Label 2394.2.eo
Level $2394$
Weight $2$
Character orbit 2394.eo
Rep. character $\chi_{2394}(415,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $396$
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.eo (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 133 \)
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 2976 396 2580
Cusp forms 2784 396 2388
Eisenstein series 192 0 192

Trace form

\( 396 q + 12 q^{7} + O(q^{10}) \) \( 396 q + 12 q^{7} - 12 q^{11} - 6 q^{13} - 6 q^{14} - 30 q^{17} - 18 q^{19} - 12 q^{20} + 18 q^{22} + 36 q^{23} + 36 q^{25} + 12 q^{26} - 24 q^{29} - 12 q^{34} + 18 q^{35} + 12 q^{37} + 6 q^{41} + 12 q^{43} - 12 q^{44} + 24 q^{46} + 24 q^{50} - 6 q^{52} + 30 q^{53} + 6 q^{56} - 54 q^{59} - 48 q^{61} - 12 q^{62} - 198 q^{64} - 6 q^{65} + 102 q^{67} - 12 q^{68} - 60 q^{70} + 36 q^{71} + 84 q^{73} + 30 q^{74} + 6 q^{76} - 48 q^{77} - 54 q^{79} + 6 q^{83} + 36 q^{85} - 12 q^{86} + 60 q^{89} - 42 q^{91} + 36 q^{92} - 54 q^{94} + 24 q^{95} + 42 q^{97} + 36 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2394, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(266, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(399, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(798, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1197, [\chi])\)\(^{\oplus 2}\)