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Properties

Label 1650.2.be
Level $1650$
Weight $2$
Character orbit 1650.be
Rep. character $\chi_{1650}(29,\cdot)$
Character field $\Q(\zeta_{10})$
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.be (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 825 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 1472 480 992
Cusp forms 1408 480 928
Eisenstein series 64 0 64

Trace form

\( 480 q + 120 q^{4} + 10 q^{7} - 4 q^{9} + O(q^{10}) \) \( 480 q + 120 q^{4} + 10 q^{7} - 4 q^{9} + 10 q^{12} - 6 q^{15} - 120 q^{16} + 20 q^{19} - 10 q^{22} - 22 q^{25} + 20 q^{28} + 30 q^{30} - 12 q^{31} - 50 q^{33} - 6 q^{36} - 50 q^{39} - 160 q^{43} + 48 q^{45} - 20 q^{46} - 54 q^{49} + 30 q^{54} + 16 q^{55} - 4 q^{60} + 120 q^{64} - 16 q^{66} + 80 q^{67} - 14 q^{69} + 12 q^{70} - 108 q^{75} - 30 q^{78} - 4 q^{81} - 100 q^{85} + 20 q^{88} - 16 q^{91} - 60 q^{93} + 70 q^{97} + 52 q^{99} + O(q^{100}) \)

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

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