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Properties

Label 550.2.bk
Level $550$
Weight $2$
Character orbit 550.bk
Rep. character $\chi_{550}(123,\cdot)$
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.bk (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

\( 240 q - 4 q^{3} - 8 q^{5} + O(q^{10}) \) \( 240 q - 4 q^{3} - 8 q^{5} + 4 q^{12} - 40 q^{13} + 24 q^{15} + 60 q^{16} - 20 q^{17} + 40 q^{19} - 4 q^{20} - 24 q^{22} - 8 q^{23} + 20 q^{25} + 8 q^{27} - 40 q^{28} + 16 q^{33} + 60 q^{36} + 20 q^{37} + 24 q^{38} - 100 q^{39} + 60 q^{42} - 100 q^{43} - 44 q^{45} + 4 q^{48} - 20 q^{49} + 40 q^{50} + 40 q^{53} + 60 q^{54} + 16 q^{55} - 200 q^{57} + 48 q^{58} + 60 q^{59} + 20 q^{60} + 60 q^{62} - 180 q^{63} + 20 q^{65} + 20 q^{67} + 20 q^{69} - 36 q^{70} - 40 q^{71} - 60 q^{73} - 96 q^{75} + 104 q^{77} + 76 q^{78} - 12 q^{80} + 20 q^{81} + 40 q^{85} - 140 q^{87} - 4 q^{88} + 100 q^{89} - 12 q^{92} + 16 q^{93} + 180 q^{95} - 128 q^{97} + O(q^{100}) \)

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.bk.a 550.bk 275.an $240$ $4.392$ None \(0\) \(-4\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{20}]$

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

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