Properties

Label 1848.2.du
Level $1848$
Weight $2$
Character orbit 1848.du
Rep. character $\chi_{1848}(403,\cdot)$
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.du (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

\( 1536 q + 4 q^{4} + 192 q^{9} + O(q^{10}) \) \( 1536 q + 4 q^{4} + 192 q^{9} - 8 q^{11} - 16 q^{14} + 12 q^{16} + 10 q^{18} - 16 q^{20} + 48 q^{22} + 30 q^{24} - 192 q^{25} - 16 q^{26} + 112 q^{34} - 8 q^{36} + 12 q^{42} + 54 q^{44} + 70 q^{46} - 64 q^{56} - 10 q^{58} - 32 q^{59} + 12 q^{60} + 16 q^{64} - 12 q^{66} - 16 q^{67} + 24 q^{70} - 10 q^{72} + 72 q^{78} - 132 q^{80} + 192 q^{81} - 24 q^{82} - 60 q^{84} - 110 q^{86} + 18 q^{88} + 40 q^{91} + 188 q^{92} - 120 q^{94} - 32 q^{97} - 64 q^{99} + O(q^{100}) \)

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

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