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Properties

Label 2394.2.bd
Level $2394$
Weight $2$
Character orbit 2394.bd
Rep. character $\chi_{2394}(1019,\cdot)$
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.bd (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

\( 320 q - 160 q^{4} - 2 q^{7} + O(q^{10}) \) \( 320 q - 160 q^{4} - 2 q^{7} + 6 q^{15} - 160 q^{16} + 4 q^{19} + 12 q^{23} - 320 q^{25} + 36 q^{27} - 2 q^{28} + 4 q^{30} + 6 q^{37} + 2 q^{39} + 22 q^{42} + 4 q^{43} - 32 q^{45} - 18 q^{47} + 2 q^{49} - 12 q^{50} + 6 q^{52} - 24 q^{53} - 6 q^{54} + 16 q^{57} + 30 q^{59} + 12 q^{60} + 14 q^{61} + 46 q^{63} + 320 q^{64} + 24 q^{65} - 8 q^{66} - 42 q^{67} - 18 q^{68} - 18 q^{71} - 56 q^{73} - 18 q^{74} + 30 q^{75} - 8 q^{76} - 48 q^{77} - 12 q^{78} + 6 q^{79} + 40 q^{81} + 44 q^{87} + 6 q^{91} + 4 q^{93} - 48 q^{95} - 36 q^{98} - 106 q^{99} + O(q^{100}) \)

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

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