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Properties

Label 1650.2.ck
Level $1650$
Weight $2$
Character orbit 1650.ck
Rep. character $\chi_{1650}(373,\cdot)$
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.ck (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

\( 480 q + 16 q^{5} + O(q^{10}) \) \( 480 q + 16 q^{5} - 8 q^{15} + 120 q^{16} - 36 q^{22} - 16 q^{23} - 28 q^{33} + 120 q^{36} - 32 q^{37} + 8 q^{42} + 192 q^{47} + 48 q^{53} + 44 q^{55} + 8 q^{58} + 16 q^{60} + 160 q^{67} - 88 q^{70} - 16 q^{75} - 16 q^{80} + 120 q^{81} - 96 q^{82} + 4 q^{88} + 16 q^{92} + 64 q^{93} - 16 q^{97} + O(q^{100}) \)

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

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