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Properties

Label 1848.2.cg
Level $1848$
Weight $2$
Character orbit 1848.cg
Rep. character $\chi_{1848}(1013,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $640$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 1848 = 2^{3} \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1848.cg (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 168 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1848, [\chi])\).

Total New Old
Modular forms 784 640 144
Cusp forms 752 640 112
Eisenstein series 32 0 32

Trace form

\( 640 q + O(q^{10}) \) \( 640 q + 30 q^{12} - 10 q^{18} + 320 q^{25} + 32 q^{28} - 20 q^{30} + 20 q^{36} + 60 q^{40} - 20 q^{46} + 16 q^{49} - 30 q^{54} - 28 q^{58} + 20 q^{60} + 80 q^{63} + 24 q^{64} - 30 q^{66} - 108 q^{70} - 48 q^{72} + 48 q^{73} + 40 q^{78} - 16 q^{81} - 60 q^{82} - 100 q^{84} + 12 q^{88} - 102 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1848, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1848, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1848, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)