Properties

Label 1650.2.cy
Level $1650$
Weight $2$
Character orbit 1650.cy
Rep. character $\chi_{1650}(137,\cdot)$
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.cy (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

\( 960 q + 4 q^{3} + 8 q^{7} + O(q^{10}) \) \( 960 q + 4 q^{3} + 8 q^{7} - 8 q^{10} - 4 q^{12} + 24 q^{13} - 16 q^{15} + 240 q^{16} + 40 q^{19} + 24 q^{22} + 8 q^{25} + 4 q^{27} - 12 q^{28} + 8 q^{33} - 40 q^{37} + 100 q^{39} + 48 q^{42} + 112 q^{43} + 32 q^{45} - 4 q^{48} - 20 q^{49} + 16 q^{52} + 60 q^{54} + 12 q^{55} - 48 q^{57} - 84 q^{58} - 4 q^{60} - 40 q^{63} - 8 q^{67} + 20 q^{69} - 32 q^{70} - 264 q^{73} + 112 q^{75} - 76 q^{78} - 40 q^{81} - 16 q^{82} - 56 q^{85} - 96 q^{87} + 4 q^{88} - 32 q^{90} + 88 q^{93} - 136 q^{97} + O(q^{100}) \)

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

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