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Properties

Label 850.2.v
Level $850$
Weight $2$
Character orbit 850.v
Rep. character $\chi_{850}(107,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $216$
Newform subspaces $6$
Sturm bound $270$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 850 = 2 \cdot 5^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 850.v (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 85 \)
Character field: \(\Q(\zeta_{16})\)
Newform subspaces: \( 6 \)
Sturm bound: \(270\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 1176 216 960
Cusp forms 984 216 768
Eisenstein series 192 0 192

Trace form

\( 216 q + O(q^{10}) \) \( 216 q - 48 q^{27} + 16 q^{28} + 64 q^{31} - 32 q^{33} - 64 q^{34} + 32 q^{37} + 128 q^{39} - 40 q^{41} + 48 q^{42} + 32 q^{52} - 32 q^{53} + 144 q^{57} - 112 q^{59} + 48 q^{62} + 48 q^{63} - 32 q^{67} - 64 q^{71} - 40 q^{72} - 120 q^{73} + 40 q^{74} - 48 q^{77} - 64 q^{78} + 64 q^{79} - 192 q^{81} - 64 q^{82} - 32 q^{83} - 64 q^{86} - 176 q^{87} - 32 q^{88} - 192 q^{91} - 16 q^{92} + 16 q^{93} + 32 q^{97} - 72 q^{98} - 192 q^{99} + O(q^{100}) \)

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.v.a 850.v 85.r $24$ $6.787$ None 850.2.s.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$
850.2.v.b 850.v 85.r $24$ $6.787$ None 850.2.s.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$
850.2.v.c 850.v 85.r $32$ $6.787$ None 170.2.o.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$
850.2.v.d 850.v 85.r $40$ $6.787$ None 170.2.o.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$
850.2.v.e 850.v 85.r $48$ $6.787$ None 850.2.s.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$
850.2.v.f 850.v 85.r $48$ $6.787$ None 850.2.s.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$

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

\( S_{2}^{\mathrm{old}}(850, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(170, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(425, [\chi])\)\(^{\oplus 2}\)