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Properties

Label 1848.2.bw
Level $1848$
Weight $2$
Character orbit 1848.bw
Rep. character $\chi_{1848}(859,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $320$
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.bw (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
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 784 320 464
Cusp forms 752 320 432
Eisenstein series 32 0 32

Trace form

\( 320 q - 24 q^{8} + 160 q^{9} + O(q^{10}) \) \( 320 q - 24 q^{8} + 160 q^{9} + 36 q^{10} + 4 q^{14} - 8 q^{16} - 160 q^{25} + 60 q^{26} + 40 q^{28} + 16 q^{30} + 20 q^{32} + 48 q^{35} + 36 q^{38} + 60 q^{40} - 20 q^{42} - 8 q^{44} - 40 q^{46} - 16 q^{49} - 96 q^{50} - 108 q^{52} - 16 q^{56} - 32 q^{57} + 96 q^{59} - 8 q^{60} + 48 q^{67} - 60 q^{68} - 16 q^{70} - 12 q^{72} + 48 q^{73} + 24 q^{78} - 72 q^{80} - 160 q^{81} - 32 q^{84} - 20 q^{86} + 12 q^{88} - 32 q^{91} + 144 q^{92} - 108 q^{94} - 60 q^{96} - 52 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1848, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(616, [\chi])\)\(^{\oplus 2}\)