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Properties

Label 207.4.o
Level $207$
Weight $4$
Character orbit 207.o
Rep. character $\chi_{207}(5,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $1400$
Newform subspaces $1$
Sturm bound $96$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 207 = 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 207.o (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 207 \)
Character field: \(\Q(\zeta_{66})\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(207, [\chi])\).

Total New Old
Modular forms 1480 1480 0
Cusp forms 1400 1400 0
Eisenstein series 80 80 0

Trace form

\( 1400 q - 27 q^{2} - 22 q^{3} - 281 q^{4} - 33 q^{5} + 29 q^{6} - 11 q^{7} - 22 q^{9} - 44 q^{10} - 33 q^{11} + 86 q^{12} - 9 q^{13} - 33 q^{14} + 726 q^{15} + 999 q^{16} + 51 q^{18} - 44 q^{19} - 33 q^{20}+ \cdots - 9262 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(207, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
207.4.o.a 207.o 207.o $1400$ $12.213$ None 207.4.o.a \(-27\) \(-22\) \(-33\) \(-11\) $\mathrm{SU}(2)[C_{66}]$