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Properties

Label 2550.2.x
Level $2550$
Weight $2$
Character orbit 2550.x
Rep. character $\chi_{2550}(257,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $432$
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.x (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 255 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(1080\)

Dimensions

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

Total New Old
Modular forms 2256 432 1824
Cusp forms 2064 432 1632
Eisenstein series 192 0 192

Trace form

\( 432 q + 432 q^{4} + O(q^{10}) \) \( 432 q + 432 q^{4} + 16 q^{13} + 432 q^{16} + 16 q^{22} - 32 q^{31} + 32 q^{37} + 32 q^{39} + 48 q^{42} + 64 q^{49} - 32 q^{51} + 16 q^{52} + 16 q^{57} - 16 q^{58} - 80 q^{63} + 432 q^{64} + 16 q^{67} + 144 q^{73} + 160 q^{79} + 96 q^{82} + 16 q^{88} + 192 q^{91} + 144 q^{97} - 24 q^{99} + O(q^{100}) \)

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

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