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Properties

Label 2394.2.er
Level $2394$
Weight $2$
Character orbit 2394.er
Rep. character $\chi_{2394}(29,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $720$
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.er (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
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 2928 720 2208
Cusp forms 2832 720 2112
Eisenstein series 96 0 96

Trace form

\( 720 q + 12 q^{3} + 12 q^{6} - 12 q^{9} + O(q^{10}) \) \( 720 q + 12 q^{3} + 12 q^{6} - 12 q^{9} - 12 q^{15} + 36 q^{18} + 18 q^{22} - 36 q^{23} - 6 q^{24} + 18 q^{27} - 96 q^{33} - 12 q^{36} + 48 q^{39} + 36 q^{45} + 6 q^{48} - 360 q^{49} + 144 q^{51} - 156 q^{57} + 12 q^{60} + 24 q^{63} - 360 q^{64} + 90 q^{66} - 36 q^{67} + 18 q^{68} + 6 q^{72} - 36 q^{73} - 48 q^{78} - 156 q^{81} + 18 q^{82} + 144 q^{83} + 48 q^{87} + 108 q^{89} - 108 q^{90} - 12 q^{93} - 36 q^{97} - 6 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2394, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 2}\)