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Properties

Label 1650.2.bu
Level $1650$
Weight $2$
Character orbit 1650.bu
Rep. character $\chi_{1650}(101,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $304$
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.bu (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
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 1536 304 1232
Cusp forms 1344 304 1040
Eisenstein series 192 0 192

Trace form

\( 304 q - 76 q^{4} - 5 q^{6} + 12 q^{9} + O(q^{10}) \) \( 304 q - 76 q^{4} - 5 q^{6} + 12 q^{9} + 10 q^{12} - 76 q^{16} - 5 q^{18} - 30 q^{19} + 5 q^{24} + 6 q^{27} - 10 q^{28} - 2 q^{31} - 31 q^{33} + 36 q^{34} - 3 q^{36} + 4 q^{37} + 50 q^{39} + 28 q^{42} + 20 q^{46} + 108 q^{49} + 25 q^{51} + 20 q^{52} - 45 q^{57} + 38 q^{58} + 60 q^{61} + 10 q^{63} - 76 q^{64} + 22 q^{66} - 20 q^{67} - 26 q^{69} - 20 q^{72} + 30 q^{73} - 80 q^{78} - 20 q^{79} + 8 q^{81} + 22 q^{82} - 40 q^{84} - 80 q^{91} + 82 q^{93} - 80 q^{94} + 66 q^{97} - 28 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1650, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(330, [\chi])\)\(^{\oplus 2}\)