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Properties

Label 2550.2.l
Level $2550$
Weight $2$
Character orbit 2550.l
Rep. character $\chi_{2550}(443,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $192$
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.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Sturm bound: \(1080\)

Dimensions

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

Total New Old
Modular forms 1128 192 936
Cusp forms 1032 192 840
Eisenstein series 96 0 96

Trace form

\( 192 q - 8 q^{3} - 16 q^{6} - 8 q^{7} + O(q^{10}) \) \( 192 q - 8 q^{3} - 16 q^{6} - 8 q^{7} + 8 q^{12} + 8 q^{13} - 192 q^{16} + 16 q^{18} + 8 q^{22} - 8 q^{27} - 8 q^{28} + 16 q^{31} - 8 q^{33} + 16 q^{36} + 48 q^{37} + 32 q^{42} - 8 q^{43} + 96 q^{46} + 8 q^{48} - 8 q^{52} - 16 q^{57} - 56 q^{58} - 112 q^{61} + 24 q^{63} - 64 q^{66} - 40 q^{67} - 16 q^{72} + 8 q^{73} - 16 q^{76} - 32 q^{81} - 64 q^{87} + 8 q^{88} + 128 q^{91} - 88 q^{93} + 16 q^{96} - 56 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2550, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)