Properties

Label 1848.2.di
Level $1848$
Weight $2$
Character orbit 1848.di
Rep. character $\chi_{1848}(211,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $576$
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.di (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 88 \)
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 576 992
Cusp forms 1504 576 928
Eisenstein series 64 0 64

Trace form

\( 576 q + 4 q^{4} - 144 q^{9} + O(q^{10}) \) \( 576 q + 4 q^{4} - 144 q^{9} - 8 q^{11} - 16 q^{12} + 6 q^{14} - 20 q^{16} + 10 q^{18} - 60 q^{20} - 28 q^{22} + 144 q^{25} + 60 q^{26} - 10 q^{28} + 40 q^{30} + 40 q^{34} + 4 q^{36} + 4 q^{38} + 140 q^{40} + 62 q^{44} + 70 q^{46} - 32 q^{48} - 144 q^{49} + 140 q^{50} + 140 q^{52} - 28 q^{56} - 114 q^{58} + 12 q^{60} + 40 q^{64} + 8 q^{66} - 16 q^{67} + 12 q^{70} - 10 q^{72} - 100 q^{74} + 96 q^{75} - 88 q^{78} - 96 q^{80} - 144 q^{81} - 124 q^{82} + 400 q^{83} - 74 q^{86} - 16 q^{88} - 40 q^{90} - 30 q^{92} + 140 q^{94} - 100 q^{96} + 32 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1848, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(616, [\chi])\)\(^{\oplus 2}\)