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Properties

Label 850.2.p
Level $850$
Weight $2$
Character orbit 850.p
Rep. character $\chi_{850}(169,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $176$
Newform subspaces $1$
Sturm bound $270$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 850 = 2 \cdot 5^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 850.p (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 425 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(270\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(850, [\chi])\).

Total New Old
Modular forms 560 176 384
Cusp forms 528 176 352
Eisenstein series 32 0 32

Trace form

\( 176 q + 44 q^{4} - 40 q^{9} + O(q^{10}) \) \( 176 q + 44 q^{4} - 40 q^{9} - 16 q^{15} - 44 q^{16} - 10 q^{17} - 8 q^{19} + 32 q^{21} + 24 q^{25} + 40 q^{26} - 20 q^{30} + 20 q^{33} + 16 q^{35} + 40 q^{36} - 100 q^{47} + 104 q^{49} - 4 q^{50} - 32 q^{51} + 40 q^{53} + 16 q^{60} + 44 q^{64} - 16 q^{66} + 80 q^{67} - 108 q^{69} + 36 q^{70} + 8 q^{76} - 80 q^{77} - 28 q^{81} - 180 q^{83} + 28 q^{84} - 96 q^{85} + 20 q^{86} + 180 q^{87} - 36 q^{89} - 16 q^{94} + 80 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(850, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
850.2.p.a 850.p 425.q $176$ $6.787$ None 850.2.p.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{2}^{\mathrm{old}}(850, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(850, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(425, [\chi])\)\(^{\oplus 2}\)