Properties

Label 207.2.c
Level $207$
Weight $2$
Character orbit 207.c
Rep. character $\chi_{207}(206,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $1$
Sturm bound $48$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 207 = 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 207.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 69 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(48\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 28 8 20
Cusp forms 20 8 12
Eisenstein series 8 0 8

Trace form

\( 8 q + O(q^{10}) \) \( 8 q - 8 q^{13} - 8 q^{16} + 32 q^{25} - 32 q^{31} - 32 q^{46} - 16 q^{49} + 24 q^{52} + 8 q^{58} + 32 q^{64} + 72 q^{70} + 16 q^{73} - 88 q^{82} - 72 q^{85} + 104 q^{94} + O(q^{100}) \)

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.c.a 207.c 69.c $8$ $1.653$ 8.0.3057647616.5 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{5}q^{4}-\beta _{7}q^{5}+\beta _{6}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(207, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(207, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 2}\)