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Properties

Label 207.2.g
Level $207$
Weight $2$
Character orbit 207.g
Rep. character $\chi_{207}(68,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $44$
Newform subspaces $2$
Sturm bound $48$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 207 = 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 207.g (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 207 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(48\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(207, [\chi])\).

Total New Old
Modular forms 52 52 0
Cusp forms 44 44 0
Eisenstein series 8 8 0

Trace form

\( 44 q - 6 q^{2} - 6 q^{3} + 18 q^{4} + 3 q^{6} - 6 q^{9} + O(q^{10}) \) \( 44 q - 6 q^{2} - 6 q^{3} + 18 q^{4} + 3 q^{6} - 6 q^{9} - 2 q^{13} - 14 q^{16} - 27 q^{18} - 6 q^{23} + 36 q^{24} - 22 q^{25} + 24 q^{27} - 60 q^{29} - 8 q^{31} - 45 q^{36} + 18 q^{39} - 42 q^{41} - 8 q^{46} + 54 q^{47} + 12 q^{48} + 20 q^{49} - 30 q^{50} + 27 q^{52} - 42 q^{54} - q^{58} - 24 q^{59} - 22 q^{64} + 30 q^{69} + 48 q^{70} + 96 q^{72} - 8 q^{73} + 24 q^{75} - 72 q^{77} - 69 q^{78} + 114 q^{81} - 34 q^{82} - 12 q^{85} + 42 q^{87} - 96 q^{92} + 12 q^{93} - 13 q^{94} + 60 q^{95} - 105 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(207, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
207.2.g.a 207.g 207.g $12$ $1.653$ 12.0.\(\cdots\).2 \(\Q(\sqrt{-23}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+\beta _{10}q^{2}+\beta _{7}q^{3}+(2-\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
207.2.g.b 207.g 207.g $32$ $1.653$ None \(-6\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$