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Properties

Label 2550.2.bw
Level $2550$
Weight $2$
Character orbit 2550.bw
Rep. character $\chi_{2550}(361,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $704$
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.bw (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 704 3680
Cusp forms 4256 704 3552
Eisenstein series 128 0 128

Trace form

\( 704 q + 176 q^{4} + 4 q^{5} - 16 q^{7} + O(q^{10}) \) \( 704 q + 176 q^{4} + 4 q^{5} - 16 q^{7} + 4 q^{10} - 24 q^{11} - 16 q^{13} - 176 q^{16} - 8 q^{17} + 32 q^{18} - 24 q^{20} - 16 q^{21} + 24 q^{22} + 24 q^{23} + 16 q^{28} + 24 q^{29} - 24 q^{33} + 80 q^{35} + 28 q^{37} - 32 q^{38} - 4 q^{40} + 24 q^{41} - 16 q^{44} - 4 q^{45} - 24 q^{46} + 16 q^{50} + 16 q^{52} + 16 q^{57} - 40 q^{58} + 40 q^{61} + 24 q^{63} + 176 q^{64} - 4 q^{65} + 112 q^{67} + 8 q^{68} + 48 q^{69} - 64 q^{71} + 8 q^{72} + 24 q^{73} + 56 q^{74} - 16 q^{75} + 32 q^{78} - 48 q^{79} + 4 q^{80} + 176 q^{81} + 136 q^{82} + 16 q^{84} - 52 q^{85} + 16 q^{88} + 96 q^{89} + 4 q^{90} + 104 q^{91} + 16 q^{92} + 48 q^{95} + 72 q^{97} + 40 q^{98} + 16 q^{99} + O(q^{100}) \)

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

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