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Properties

Label 2394.2.dk
Level $2394$
Weight $2$
Character orbit 2394.dk
Rep. character $\chi_{2394}(863,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $112$
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.dk (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 399 \)
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 992 112 880
Cusp forms 928 112 816
Eisenstein series 64 0 64

Trace form

\( 112 q - 56 q^{4} + O(q^{10}) \) \( 112 q - 56 q^{4} - 56 q^{16} + 8 q^{19} - 24 q^{22} + 64 q^{25} + 48 q^{31} + 24 q^{34} + 24 q^{37} - 24 q^{43} - 32 q^{49} + 16 q^{55} + 8 q^{58} + 16 q^{61} + 112 q^{64} + 48 q^{67} - 48 q^{70} + 48 q^{73} + 8 q^{76} - 24 q^{79} - 64 q^{82} + 16 q^{85} + 24 q^{88} + 72 q^{91} + 48 q^{94} + 24 q^{97} + O(q^{100}) \)

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

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