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Properties

Label 2550.2.bf
Level $2550$
Weight $2$
Character orbit 2550.bf
Rep. character $\chi_{2550}(271,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $352$
Sturm bound $1080$

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Defining parameters

Level: \( N \) \(=\) \( 2550 = 2 \cdot 3 \cdot 5^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2550.bf (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 425 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1080\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2550, [\chi])\).

Total New Old
Modular forms 2192 352 1840
Cusp forms 2128 352 1776
Eisenstein series 64 0 64

Trace form

\( 352 q - 4 q^{2} - 88 q^{4} - 4 q^{8} + 88 q^{9} + O(q^{10}) \) \( 352 q - 4 q^{2} - 88 q^{4} - 4 q^{8} + 88 q^{9} - 4 q^{15} - 88 q^{16} + 16 q^{17} - 16 q^{18} + 4 q^{19} + 8 q^{21} + 20 q^{25} + 24 q^{26} + 32 q^{30} + 16 q^{32} - 12 q^{33} + 18 q^{34} - 32 q^{35} + 88 q^{36} + 16 q^{38} + 40 q^{43} - 16 q^{47} - 272 q^{49} - 12 q^{50} - 60 q^{53} - 8 q^{55} + 24 q^{59} - 4 q^{60} - 88 q^{64} - 16 q^{66} - 136 q^{67} - 4 q^{68} + 24 q^{69} - 80 q^{70} + 4 q^{72} + 24 q^{76} - 96 q^{77} - 88 q^{81} - 112 q^{83} + 8 q^{84} + 78 q^{85} + 60 q^{87} + 84 q^{89} - 32 q^{93} + 148 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2550, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(2550, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2550, [\chi]) \cong \)