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Properties

Label 550.2.bp
Level $550$
Weight $2$
Character orbit 550.bp
Rep. character $\chi_{550}(63,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $240$
Newform subspaces $1$
Sturm bound $180$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 550 = 2 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 550.bp (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 275 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 1 \)
Sturm bound: \(180\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(550, [\chi])\).

Total New Old
Modular forms 752 240 512
Cusp forms 688 240 448
Eisenstein series 64 0 64

Trace form

\( 240 q + 16 q^{3} - 8 q^{5} + 20 q^{9} + O(q^{10}) \) \( 240 q + 16 q^{3} - 8 q^{5} + 20 q^{9} - 20 q^{10} + 4 q^{12} + 40 q^{13} + 4 q^{15} - 240 q^{16} - 20 q^{17} - 4 q^{20} - 4 q^{22} + 12 q^{23} + 20 q^{25} + 28 q^{27} - 4 q^{33} + 60 q^{35} + 60 q^{36} + 60 q^{37} + 24 q^{38} + 40 q^{42} - 44 q^{45} + 60 q^{47} - 16 q^{48} - 120 q^{49} - 80 q^{50} - 40 q^{52} - 80 q^{53} - 60 q^{54} - 64 q^{55} - 40 q^{57} - 32 q^{58} - 20 q^{60} - 60 q^{62} + 80 q^{63} + 60 q^{67} + 44 q^{70} - 40 q^{71} - 76 q^{75} - 16 q^{77} + 16 q^{78} - 80 q^{79} + 8 q^{80} + 120 q^{81} + 100 q^{85} - 24 q^{88} - 12 q^{92} - 144 q^{93} + 72 q^{97} + 80 q^{98} + 260 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(550, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
550.2.bp.a 550.bp 275.af $240$ $4.392$ None \(0\) \(16\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{20}]$

Decomposition of \(S_{2}^{\mathrm{old}}(550, [\chi])\) into lower level spaces

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