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Properties

Label 2394.2.j
Level $2394$
Weight $2$
Character orbit 2394.j
Rep. character $\chi_{2394}(121,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $320$
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.j (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1197 \)
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 976 320 656
Cusp forms 944 320 624
Eisenstein series 32 0 32

Trace form

\( 320 q - 160 q^{4} + 2 q^{7} + O(q^{10}) \) \( 320 q - 160 q^{4} + 2 q^{7} - 2 q^{13} + 16 q^{15} - 160 q^{16} + 6 q^{17} - 8 q^{18} - 4 q^{19} - 12 q^{21} + 8 q^{23} - 160 q^{25} + 12 q^{27} - 4 q^{28} + 4 q^{30} + 4 q^{31} + 12 q^{35} - 2 q^{37} - 2 q^{39} + 64 q^{41} + 44 q^{42} - 2 q^{43} - 32 q^{45} - 6 q^{47} + 2 q^{49} - 20 q^{50} - 16 q^{51} + 4 q^{52} + 16 q^{53} - 12 q^{54} + 24 q^{57} - 14 q^{59} - 2 q^{60} - 14 q^{61} - 20 q^{63} + 320 q^{64} + 8 q^{65} - 8 q^{66} - 14 q^{67} + 6 q^{68} - 40 q^{69} + 22 q^{71} - 8 q^{72} + 28 q^{73} + 12 q^{74} - 22 q^{75} - 4 q^{76} - 40 q^{77} + 4 q^{78} - 2 q^{79} + 32 q^{81} - 12 q^{84} - 56 q^{87} - 48 q^{89} - 32 q^{90} - 32 q^{91} - 4 q^{92} + 72 q^{93} + 76 q^{95} + 4 q^{97} - 12 q^{98} - 60 q^{99} + O(q^{100}) \)

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

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