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Properties

Label 1650.2.cj
Level $1650$
Weight $2$
Character orbit 1650.cj
Rep. character $\chi_{1650}(113,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $960$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 1650 = 2 \cdot 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1650.cj (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 825 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1650, [\chi])\).

Total New Old
Modular forms 2944 960 1984
Cusp forms 2816 960 1856
Eisenstein series 128 0 128

Trace form

\( 960 q - 16 q^{3} + 8 q^{7} + 20 q^{9} + O(q^{10}) \) \( 960 q - 16 q^{3} + 8 q^{7} + 20 q^{9} + 12 q^{10} - 4 q^{12} + 24 q^{13} + 4 q^{15} - 960 q^{16} + 4 q^{22} + 8 q^{25} - 16 q^{27} - 12 q^{28} + 8 q^{33} + 48 q^{42} - 48 q^{43} + 32 q^{45} + 16 q^{48} + 140 q^{49} - 24 q^{52} - 60 q^{54} - 8 q^{55} - 48 q^{57} + 56 q^{58} - 4 q^{60} - 40 q^{63} + 32 q^{67} - 52 q^{70} + 56 q^{73} + 92 q^{75} - 16 q^{78} - 140 q^{79} + 60 q^{81} - 16 q^{82} - 16 q^{85} + 64 q^{87} + 24 q^{88} - 32 q^{90} - 72 q^{93} + 64 q^{97} - 160 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1650, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1650, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1650, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(825, [\chi])\)\(^{\oplus 2}\)