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Properties

Label 2550.2.bz
Level $2550$
Weight $2$
Character orbit 2550.bz
Rep. character $\chi_{2550}(259,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $736$
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.bz (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 425 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(1080\)

Dimensions

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

Total New Old
Modular forms 4384 736 3648
Cusp forms 4256 736 3520
Eisenstein series 128 0 128

Trace form

\( 736 q - 184 q^{4} + 8 q^{5} + O(q^{10}) \) \( 736 q - 184 q^{4} + 8 q^{5} + 24 q^{11} - 184 q^{16} + 8 q^{20} + 16 q^{21} + 40 q^{22} - 40 q^{23} - 16 q^{29} - 40 q^{33} + 48 q^{35} + 16 q^{41} - 16 q^{44} + 8 q^{45} + 24 q^{46} - 16 q^{50} - 16 q^{55} - 80 q^{61} - 40 q^{63} - 184 q^{64} + 48 q^{65} + 160 q^{67} + 48 q^{69} + 64 q^{71} - 160 q^{73} + 16 q^{74} + 16 q^{75} - 48 q^{79} + 8 q^{80} + 184 q^{81} + 16 q^{84} + 56 q^{85} + 96 q^{89} - 104 q^{91} + 32 q^{95} + 16 q^{99} + O(q^{100}) \)

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

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