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Properties

Label 1848.2.z
Level $1848$
Weight $2$
Character orbit 1848.z
Rep. character $\chi_{1848}(1651,\cdot)$
Character field $\Q$
Dimension $160$
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.z (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 392 160 232
Cusp forms 376 160 216
Eisenstein series 16 0 16

Trace form

\( 160 q + 24 q^{8} - 160 q^{9} + O(q^{10}) \) \( 160 q + 24 q^{8} - 160 q^{9} + 20 q^{14} - 16 q^{16} + 160 q^{25} + 8 q^{28} + 32 q^{30} + 40 q^{32} - 48 q^{35} + 20 q^{42} - 16 q^{44} - 80 q^{46} + 16 q^{49} + 96 q^{50} - 92 q^{56} + 32 q^{57} - 36 q^{58} - 52 q^{60} - 36 q^{64} + 96 q^{67} + 76 q^{70} - 24 q^{72} + 12 q^{78} + 160 q^{81} - 16 q^{84} - 40 q^{86} - 12 q^{88} + 32 q^{91} - 144 q^{92} - 32 q^{98} + O(q^{100}) \)

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

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