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Properties

Label 2550.2.ce
Level $2550$
Weight $2$
Character orbit 2550.ce
Rep. character $\chi_{2550}(19,\cdot)$
Character field $\Q(\zeta_{40})$
Dimension $1408$
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.ce (of order \(40\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 425 \)
Character field: \(\Q(\zeta_{40})\)
Sturm bound: \(1080\)

Dimensions

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

Total New Old
Modular forms 8768 1408 7360
Cusp forms 8512 1408 7104
Eisenstein series 256 0 256

Trace form

\( 1408 q - 16 q^{5} + O(q^{10}) \) \( 1408 q - 16 q^{5} + 8 q^{10} + 48 q^{11} + 352 q^{16} - 32 q^{20} + 8 q^{25} - 48 q^{26} - 48 q^{29} + 80 q^{33} - 32 q^{35} + 48 q^{41} - 8 q^{45} - 48 q^{46} - 32 q^{49} + 32 q^{50} + 200 q^{53} + 32 q^{61} - 32 q^{65} - 32 q^{69} + 144 q^{70} + 160 q^{73} + 112 q^{74} + 32 q^{75} + 320 q^{77} - 96 q^{79} + 16 q^{80} + 160 q^{83} + 32 q^{84} - 8 q^{85} + 8 q^{90} - 64 q^{91} + 64 q^{94} + 112 q^{95} + 32 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2550, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(425, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(850, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1275, [\chi])\)\(^{\oplus 2}\)