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Properties

Label 1650.2.p
Level $1650$
Weight $2$
Character orbit 1650.p
Rep. character $\chi_{1650}(421,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $240$
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.p (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 275 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 1472 240 1232
Cusp forms 1408 240 1168
Eisenstein series 64 0 64

Trace form

\( 240 q - 60 q^{4} - 12 q^{5} - 16 q^{6} + 14 q^{7} - 60 q^{9} + O(q^{10}) \) \( 240 q - 60 q^{4} - 12 q^{5} - 16 q^{6} + 14 q^{7} - 60 q^{9} + 4 q^{10} + 8 q^{11} + 16 q^{13} - 18 q^{15} - 60 q^{16} - 24 q^{17} + 24 q^{19} - 12 q^{20} + 8 q^{21} - 8 q^{22} - 4 q^{23} + 4 q^{24} - 12 q^{25} + 14 q^{28} + 8 q^{30} - 2 q^{31} + 12 q^{33} - 20 q^{35} + 240 q^{36} - 96 q^{37} + 4 q^{40} - 12 q^{41} - 2 q^{42} - 8 q^{43} + 8 q^{44} + 8 q^{45} - 48 q^{46} + 56 q^{47} - 46 q^{49} + 16 q^{50} + 8 q^{51} + 16 q^{52} + 48 q^{53} + 4 q^{54} + 20 q^{55} - 12 q^{57} + 8 q^{58} + 48 q^{59} + 12 q^{60} + 32 q^{61} + 80 q^{62} + 4 q^{63} - 60 q^{64} - 36 q^{65} + 108 q^{67} + 16 q^{68} - 4 q^{69} + 48 q^{70} - 24 q^{71} + 72 q^{73} - 16 q^{75} - 56 q^{76} + 36 q^{77} - 12 q^{79} + 8 q^{80} - 60 q^{81} + 8 q^{82} + 64 q^{83} - 32 q^{84} + 28 q^{85} - 12 q^{86} - 16 q^{87} + 12 q^{88} - 6 q^{90} - 36 q^{91} - 4 q^{92} - 24 q^{93} - 128 q^{94} - 68 q^{95} + 4 q^{96} + 88 q^{97} + 64 q^{98} + 8 q^{99} + O(q^{100}) \)

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

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