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Properties

Label 1848.2.cx
Level $1848$
Weight $2$
Character orbit 1848.cx
Rep. character $\chi_{1848}(13,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $768$
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.cx (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 616 \)
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 768 800
Cusp forms 1504 768 736
Eisenstein series 64 0 64

Trace form

\( 768 q - 4 q^{4} - 192 q^{9} + O(q^{10}) \) \( 768 q - 4 q^{4} - 192 q^{9} + 8 q^{14} - 20 q^{16} + 10 q^{18} - 52 q^{22} + 16 q^{23} - 192 q^{25} - 4 q^{36} + 12 q^{42} - 58 q^{44} + 70 q^{46} + 32 q^{56} - 14 q^{58} - 12 q^{60} + 32 q^{64} + 88 q^{70} + 88 q^{71} - 10 q^{72} - 72 q^{78} + 40 q^{79} - 192 q^{81} + 60 q^{84} - 78 q^{86} + 36 q^{88} - 86 q^{92} + O(q^{100}) \)

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

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