Properties

Label 1848.2.w
Level $1848$
Weight $2$
Character orbit 1848.w
Rep. character $\chi_{1848}(1693,\cdot)$
Character field $\Q$
Dimension $192$
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.w (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 616 \)
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 392 192 200
Cusp forms 376 192 184
Eisenstein series 16 0 16

Trace form

\( 192 q + 4 q^{4} + 192 q^{9} + O(q^{10}) \) \( 192 q + 4 q^{4} + 192 q^{9} - 8 q^{14} + 20 q^{16} - 8 q^{22} - 16 q^{23} + 192 q^{25} + 4 q^{36} - 12 q^{42} - 12 q^{44} + 8 q^{56} + 4 q^{58} + 12 q^{60} + 88 q^{64} - 28 q^{70} - 48 q^{71} + 12 q^{78} + 192 q^{81} - 72 q^{86} - 36 q^{88} - 64 q^{92} + O(q^{100}) \)

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

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