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Properties

Label 2394.2.cg
Level $2394$
Weight $2$
Character orbit 2394.cg
Rep. character $\chi_{2394}(419,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $288$
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.cg (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
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 976 288 688
Cusp forms 944 288 656
Eisenstein series 32 0 32

Trace form

\( 288 q + 144 q^{4} - 24 q^{9} + O(q^{10}) \) \( 288 q + 144 q^{4} - 24 q^{9} + 24 q^{11} + 12 q^{14} + 8 q^{15} - 144 q^{16} + 16 q^{18} - 12 q^{21} + 72 q^{23} - 144 q^{25} + 24 q^{29} + 56 q^{30} - 24 q^{36} + 68 q^{39} - 14 q^{42} - 48 q^{46} + 12 q^{49} - 40 q^{51} + 12 q^{56} + 24 q^{58} - 8 q^{60} - 92 q^{63} - 288 q^{64} - 144 q^{65} - 16 q^{72} - 36 q^{74} - 12 q^{77} + 64 q^{78} - 8 q^{81} - 24 q^{84} + 24 q^{85} + 48 q^{86} + 72 q^{92} + 32 q^{93} - 24 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2394, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1197, [\chi])\)\(^{\oplus 2}\)