Properties

Label 209.1.h
Level $209$
Weight $1$
Character orbit 209.h
Rep. character $\chi_{209}(87,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $1$
Sturm bound $20$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 209 = 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 209.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 209 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(20\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(209, [\chi])\).

Total New Old
Modular forms 8 8 0
Cusp forms 4 4 0
Eisenstein series 4 4 0

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 0 4 0 0

Trace form

\( 4 q - 2 q^{3} - 2 q^{5} + O(q^{10}) \) \( 4 q - 2 q^{3} - 2 q^{5} - 2 q^{15} + 2 q^{16} + 2 q^{22} - 2 q^{23} + 4 q^{26} - 4 q^{27} - 2 q^{34} - 2 q^{38} - 2 q^{47} + 2 q^{48} + 4 q^{49} + 2 q^{53} - 4 q^{58} - 2 q^{59} - 4 q^{64} + 2 q^{66} + 2 q^{67} + 4 q^{69} + 2 q^{71} - 2 q^{78} + 2 q^{80} + 2 q^{81} + 2 q^{82} - 2 q^{86} - 4 q^{88} + 2 q^{89} + 2 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(209, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
209.1.h.a $4$ $0.104$ \(\Q(\zeta_{12})\) $A_{4}$ None None \(0\) \(-2\) \(-2\) \(0\) \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{2}q^{3}-\zeta_{12}^{2}q^{5}+\cdots\)