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Properties

Label 550.2.i
Level $550$
Weight $2$
Character orbit 550.i
Rep. character $\chi_{550}(31,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $120$
Newform subspaces $5$
Sturm bound $180$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 550 = 2 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 550.i (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 275 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 5 \)
Sturm bound: \(180\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 376 120 256
Cusp forms 344 120 224
Eisenstein series 32 0 32

Trace form

\( 120 q + 6 q^{3} + 120 q^{4} - 6 q^{5} - 4 q^{6} + 4 q^{7} - 24 q^{9} + O(q^{10}) \) \( 120 q + 6 q^{3} + 120 q^{4} - 6 q^{5} - 4 q^{6} + 4 q^{7} - 24 q^{9} + 6 q^{10} - 4 q^{11} + 6 q^{12} + 24 q^{13} - 16 q^{15} + 120 q^{16} + 2 q^{17} - 6 q^{20} - 8 q^{21} - 2 q^{22} - 12 q^{23} - 4 q^{24} - 6 q^{27} + 4 q^{28} + 48 q^{29} - 20 q^{30} - 10 q^{31} + 6 q^{33} - 10 q^{35} - 24 q^{36} - 2 q^{37} - 24 q^{38} - 40 q^{39} + 6 q^{40} - 40 q^{41} + 10 q^{42} - 56 q^{43} - 4 q^{44} + 22 q^{45} - 4 q^{46} + 18 q^{47} + 6 q^{48} - 18 q^{49} + 16 q^{50} - 8 q^{51} + 24 q^{52} - 58 q^{53} - 10 q^{54} - 14 q^{55} + 20 q^{57} - 32 q^{58} - 28 q^{59} - 16 q^{60} - 2 q^{61} - 10 q^{62} + 78 q^{63} + 120 q^{64} - 4 q^{65} - 16 q^{66} + 62 q^{67} + 2 q^{68} - 40 q^{69} - 18 q^{70} - 28 q^{71} - 42 q^{73} - 20 q^{74} + 120 q^{75} - 86 q^{77} - 14 q^{78} + 8 q^{79} - 6 q^{80} + 4 q^{81} - 12 q^{82} + 48 q^{83} - 8 q^{84} + 20 q^{85} - 24 q^{86} - 88 q^{87} - 2 q^{88} - 60 q^{89} - 52 q^{90} - 10 q^{91} - 12 q^{92} + 8 q^{93} - 16 q^{94} - 80 q^{95} - 4 q^{96} + 24 q^{97} + 8 q^{98} + 58 q^{99} + O(q^{100}) \)

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.i.a 550.i 275.l $4$ $4.392$ \(\Q(\zeta_{10})\) None \(-4\) \(-3\) \(5\) \(-6\) $\mathrm{SU}(2)[C_{5}]$ \(q-q^{2}+(-1+\zeta_{10}^{3})q^{3}+q^{4}+(2-\zeta_{10}+\cdots)q^{5}+\cdots\)
550.2.i.b 550.i 275.l $4$ $4.392$ \(\Q(\zeta_{10})\) None \(-4\) \(-1\) \(-5\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q-q^{2}+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+\cdots\)
550.2.i.c 550.i 275.l $4$ $4.392$ \(\Q(\zeta_{10})\) None \(-4\) \(1\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{5}]$ \(q-q^{2}+(-1+2\zeta_{10}-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+\cdots\)
550.2.i.d 550.i 275.l $48$ $4.392$ None \(-48\) \(8\) \(-6\) \(11\) $\mathrm{SU}(2)[C_{5}]$
550.2.i.e 550.i 275.l $60$ $4.392$ None \(60\) \(1\) \(0\) \(2\) $\mathrm{SU}(2)[C_{5}]$

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

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