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Properties

Label 2394.2.cd
Level $2394$
Weight $2$
Character orbit 2394.cd
Rep. character $\chi_{2394}(353,\cdot)$
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.cd (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

\( 320 q + 160 q^{4} - 2 q^{7} + O(q^{10}) \) \( 320 q + 160 q^{4} - 2 q^{7} + 6 q^{13} - 16 q^{15} - 160 q^{16} + 18 q^{17} - 8 q^{18} - 12 q^{21} - 160 q^{25} - 4 q^{28} - 4 q^{30} + 2 q^{37} + 14 q^{39} - 20 q^{42} + 2 q^{43} + 24 q^{45} + 18 q^{47} + 2 q^{49} - 60 q^{50} - 16 q^{51} - 12 q^{57} + 30 q^{59} - 2 q^{60} - 42 q^{61} - 8 q^{63} - 320 q^{64} - 24 q^{66} - 14 q^{67} - 18 q^{68} + 18 q^{71} + 8 q^{72} - 30 q^{75} + 48 q^{77} + 4 q^{78} - 2 q^{79} - 32 q^{81} + 12 q^{84} + 48 q^{87} - 24 q^{91} - 12 q^{92} - 40 q^{93} + 48 q^{95} - 12 q^{97} - 36 q^{98} + 36 q^{99} + O(q^{100}) \)

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

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