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Properties

Label 2394.2.fa
Level $2394$
Weight $2$
Character orbit 2394.fa
Rep. character $\chi_{2394}(53,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $312$
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.fa (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 399 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2394, [\chi])\).

Total New Old
Modular forms 2976 312 2664
Cusp forms 2784 312 2472
Eisenstein series 192 0 192

Trace form

\( 312 q + O(q^{10}) \) \( 312 q - 12 q^{13} + 12 q^{19} + 24 q^{22} + 24 q^{25} - 12 q^{28} - 24 q^{34} - 72 q^{37} + 60 q^{43} + 48 q^{49} + 12 q^{52} + 12 q^{61} - 156 q^{64} + 60 q^{67} + 96 q^{70} - 24 q^{73} + 144 q^{79} + 24 q^{85} + 24 q^{91} + 72 q^{94} + 48 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2394, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(399, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(798, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1197, [\chi])\)\(^{\oplus 2}\)