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Properties

Label 1848.2.cn
Level $1848$
Weight $2$
Character orbit 1848.cn
Rep. character $\chi_{1848}(29,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $1152$
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.cn (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 264 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 1568 1152 416
Cusp forms 1504 1152 352
Eisenstein series 64 0 64

Trace form

\( 1152 q + O(q^{10}) \) \( 1152 q + 40 q^{16} - 288 q^{25} + 40 q^{28} - 8 q^{33} + 48 q^{36} + 288 q^{49} + 40 q^{52} + 32 q^{55} - 20 q^{58} + 60 q^{60} - 12 q^{64} - 58 q^{66} + 12 q^{70} + 150 q^{72} - 52 q^{78} + 160 q^{79} - 16 q^{81} - 84 q^{82} - 220 q^{88} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1848, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 2}\)