Properties

Label 1650.2.u
Level $1650$
Weight $2$
Character orbit 1650.u
Rep. character $\chi_{1650}(529,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $192$
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.u (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
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 192 1280
Cusp forms 1408 192 1216
Eisenstein series 64 0 64

Trace form

\( 192 q + 48 q^{4} + 48 q^{9} + O(q^{10}) \) \( 192 q + 48 q^{4} + 48 q^{9} - 48 q^{16} + 80 q^{23} + 16 q^{25} - 16 q^{26} + 64 q^{29} - 40 q^{34} + 32 q^{35} - 48 q^{36} - 16 q^{41} - 128 q^{49} + 32 q^{50} + 48 q^{59} - 16 q^{61} + 48 q^{64} + 32 q^{65} + 8 q^{66} - 16 q^{69} + 64 q^{70} - 16 q^{74} + 8 q^{75} + 16 q^{79} - 48 q^{81} - 120 q^{83} - 32 q^{85} - 72 q^{89} - 40 q^{91} - 32 q^{94} - 120 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1650, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(550, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(825, [\chi])\)\(^{\oplus 2}\)