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Properties

Label 2394.2.m
Level $2394$
Weight $2$
Character orbit 2394.m
Rep. character $\chi_{2394}(1369,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $120$
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.m (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 992 120 872
Cusp forms 928 120 808
Eisenstein series 64 0 64

Trace form

\( 120 q - 60 q^{4} - 6 q^{5} - 2 q^{7} + O(q^{10}) \) \( 120 q - 60 q^{4} - 6 q^{5} - 2 q^{7} + 4 q^{10} - 10 q^{11} + 8 q^{14} - 60 q^{16} - 4 q^{17} + 2 q^{19} + 12 q^{20} - 8 q^{22} + 10 q^{23} - 58 q^{25} - 4 q^{26} - 8 q^{28} + 24 q^{29} - 4 q^{31} - 14 q^{35} - 12 q^{37} - 6 q^{38} + 4 q^{40} - 40 q^{41} + 20 q^{43} - 10 q^{44} - 20 q^{46} + 20 q^{47} + 58 q^{49} - 32 q^{50} + 36 q^{53} + 20 q^{55} - 4 q^{56} + 8 q^{59} - 34 q^{61} + 32 q^{62} + 120 q^{64} + 12 q^{65} - 4 q^{68} - 48 q^{70} + 24 q^{71} - 14 q^{73} + 14 q^{74} - 4 q^{76} + 24 q^{77} + 32 q^{79} - 6 q^{80} + 16 q^{82} - 60 q^{83} - 104 q^{85} - 32 q^{86} + 4 q^{88} + 8 q^{89} - 36 q^{91} - 20 q^{92} + 24 q^{94} - 2 q^{95} + 112 q^{97} - 32 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2394, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(266, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(399, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(798, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1197, [\chi])\)\(^{\oplus 2}\)