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Properties

Label 1848.2.bk
Level $1848$
Weight $2$
Character orbit 1848.bk
Rep. character $\chi_{1848}(901,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $384$
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.bk (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 616 \)
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 784 384 400
Cusp forms 752 384 368
Eisenstein series 32 0 32

Trace form

\( 384 q - 4 q^{4} - 192 q^{9} + O(q^{10}) \) \( 384 q - 4 q^{4} - 192 q^{9} - 16 q^{14} + 4 q^{16} + 20 q^{22} + 16 q^{23} - 192 q^{25} + 8 q^{36} + 12 q^{42} + 12 q^{44} + 16 q^{56} - 4 q^{58} - 12 q^{60} - 40 q^{64} - 36 q^{66} + 4 q^{70} + 96 q^{71} - 48 q^{78} - 192 q^{81} + 72 q^{82} + 96 q^{86} - 66 q^{88} - 128 q^{92} + O(q^{100}) \)

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

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