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Properties

Label 1650.2.cm
Level $1650$
Weight $2$
Character orbit 1650.cm
Rep. character $\chi_{1650}(337,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $480$
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.cm (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 275 \)
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 480 2464
Cusp forms 2816 480 2336
Eisenstein series 128 0 128

Trace form

\( 480 q - 24 q^{5} - 20 q^{7} + O(q^{10}) \) \( 480 q - 24 q^{5} - 20 q^{7} - 20 q^{10} - 8 q^{15} + 120 q^{16} + 40 q^{17} + 40 q^{19} + 4 q^{22} - 16 q^{23} + 20 q^{28} + 12 q^{33} + 120 q^{36} + 88 q^{37} + 8 q^{42} + 32 q^{47} - 60 q^{49} - 72 q^{53} - 36 q^{55} + 8 q^{58} + 120 q^{59} + 16 q^{60} + 80 q^{62} - 120 q^{67} + 40 q^{68} + 40 q^{69} - 8 q^{70} - 140 q^{73} - 16 q^{75} + 240 q^{77} + 20 q^{79} - 16 q^{80} - 480 q^{81} + 64 q^{82} + 40 q^{85} - 36 q^{88} - 24 q^{92} + 24 q^{93} + 104 q^{97} + 160 q^{98} + 40 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1650, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(550, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(825, [\chi])\)\(^{\oplus 2}\)