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Properties

Label 1848.2.cs
Level $1848$
Weight $2$
Character orbit 1848.cs
Rep. character $\chi_{1848}(643,\cdot)$
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.cs (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

\( 768 q - 4 q^{2} - 4 q^{4} - 4 q^{8} + 192 q^{9} + O(q^{10}) \) \( 768 q - 4 q^{2} - 4 q^{4} - 4 q^{8} + 192 q^{9} + 8 q^{11} + 8 q^{14} - 20 q^{16} - 6 q^{18} + 52 q^{22} - 192 q^{25} + 12 q^{28} + 16 q^{32} + 4 q^{36} - 12 q^{42} + 16 q^{43} - 54 q^{44} + 46 q^{46} - 28 q^{50} + 32 q^{56} - 22 q^{58} - 12 q^{60} - 88 q^{64} - 16 q^{67} - 88 q^{70} - 6 q^{72} + 64 q^{74} - 24 q^{78} - 192 q^{81} + 60 q^{84} - 46 q^{86} + 100 q^{88} - 40 q^{91} - 94 q^{92} + 120 q^{98} + 32 q^{99} + O(q^{100}) \)

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

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