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Properties

Label 1848.2.ef
Level $1848$
Weight $2$
Character orbit 1848.ef
Rep. character $\chi_{1848}(37,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1536$
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.ef (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 616 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 3136 1536 1600
Cusp forms 3008 1536 1472
Eisenstein series 128 0 128

Trace form

\( 1536 q - 4 q^{2} + 4 q^{4} + 8 q^{8} - 192 q^{9} + O(q^{10}) \) \( 1536 q - 4 q^{2} + 4 q^{4} + 8 q^{8} - 192 q^{9} - 16 q^{14} + 12 q^{16} - 6 q^{18} + 16 q^{20} - 48 q^{22} + 16 q^{23} - 18 q^{24} - 192 q^{25} - 16 q^{26} + 12 q^{28} + 16 q^{32} + 112 q^{34} + 8 q^{36} - 12 q^{42} + 58 q^{44} + 38 q^{46} - 56 q^{50} - 12 q^{52} - 64 q^{56} - 2 q^{58} + 12 q^{60} - 128 q^{64} - 12 q^{66} + 44 q^{68} - 24 q^{70} + 16 q^{71} - 6 q^{72} - 20 q^{74} + 96 q^{76} + 120 q^{78} + 24 q^{79} - 132 q^{80} + 192 q^{81} + 24 q^{82} - 60 q^{84} - 126 q^{86} + 192 q^{87} - 38 q^{88} + 172 q^{92} - 60 q^{94} + 32 q^{97} - 64 q^{98} + O(q^{100}) \)

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

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