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Properties

Label 2550.2.bn
Level $2550$
Weight $2$
Character orbit 2550.bn
Rep. character $\chi_{2550}(401,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $912$
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.bn (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 51 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(1080\)

Dimensions

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

Total New Old
Modular forms 4512 912 3600
Cusp forms 4128 912 3216
Eisenstein series 384 0 384

Trace form

\( 912 q + O(q^{10}) \) \( 912 q - 8 q^{12} - 32 q^{18} + 48 q^{21} - 8 q^{24} + 32 q^{31} - 32 q^{37} - 32 q^{39} - 48 q^{42} - 16 q^{43} + 32 q^{46} - 64 q^{49} + 64 q^{51} - 32 q^{52} + 104 q^{54} - 88 q^{57} + 32 q^{58} + 32 q^{61} + 96 q^{63} + 8 q^{66} - 32 q^{69} + 128 q^{73} + 64 q^{79} - 8 q^{81} + 128 q^{82} + 48 q^{87} + 32 q^{88} + 128 q^{91} + 64 q^{93} + 64 q^{94} + 96 q^{97} + 104 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2550, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(102, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(255, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(510, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1275, [\chi])\)\(^{\oplus 2}\)