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Properties

Label 200.4.o
Level $200$
Weight $4$
Character orbit 200.o
Rep. character $\chi_{200}(29,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $352$
Newform subspaces $1$
Sturm bound $120$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 200 = 2^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 200.o (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 200 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(120\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(200, [\chi])\).

Total New Old
Modular forms 368 368 0
Cusp forms 352 352 0
Eisenstein series 16 16 0

Trace form

\( 352 q - 5 q^{2} - 3 q^{4} + 13 q^{6} - 110 q^{8} - 762 q^{9} + 43 q^{10} - 5 q^{12} - 45 q^{14} + 46 q^{15} - 111 q^{16} - 10 q^{17} + 191 q^{20} + 320 q^{22} - 10 q^{23} + 32 q^{24} + 14 q^{25} + 18 q^{26}+ \cdots - 5120 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(200, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
200.4.o.a 200.o 200.o $352$ $11.800$ None 200.4.o.a \(-5\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$