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Properties

Label 2394.2.bl
Level $2394$
Weight $2$
Character orbit 2394.bl
Rep. character $\chi_{2394}(425,\cdot)$
Character field $\Q(\zeta_{6})$
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.bl (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1197 \)
Character field: \(\Q(\zeta_{6})\)
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

\( 320 q + 160 q^{4} - 2 q^{7} + O(q^{10}) \) \( 320 q + 160 q^{4} - 2 q^{7} + 2 q^{15} - 160 q^{16} - 18 q^{17} + 16 q^{18} - 12 q^{21} - 12 q^{23} - 160 q^{25} - 4 q^{28} + 8 q^{30} - 6 q^{31} + 2 q^{37} - 16 q^{39} - 38 q^{42} - 4 q^{43} + 36 q^{45} + 36 q^{47} + 2 q^{49} - 60 q^{50} + 32 q^{51} - 6 q^{52} + 60 q^{59} - 14 q^{60} - 26 q^{63} - 320 q^{64} + 12 q^{65} + 24 q^{66} - 14 q^{67} - 36 q^{68} - 18 q^{71} + 8 q^{72} + 18 q^{74} + 24 q^{77} + 4 q^{78} - 2 q^{79} + 40 q^{81} - 24 q^{84} + 30 q^{87} + 72 q^{90} - 24 q^{91} - 40 q^{93} + 30 q^{95} + 36 q^{98} - 42 q^{99} + O(q^{100}) \)

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

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