Properties

Label 287.1.d
Level $287$
Weight $1$
Character orbit 287.d
Rep. character $\chi_{287}(286,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $2$
Sturm bound $28$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 287 = 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 287.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 287 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(28\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(287, [\chi])\).

Total New Old
Modular forms 8 8 0
Cusp forms 6 6 0
Eisenstein series 2 2 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 6 0 0 0

Trace form

\( 6 q - 2 q^{2} + 4 q^{4} - 4 q^{8} + 4 q^{9} + O(q^{10}) \) \( 6 q - 2 q^{2} + 4 q^{4} - 4 q^{8} + 4 q^{9} + 2 q^{16} - 6 q^{18} - 2 q^{21} - 2 q^{23} + 6 q^{25} - 6 q^{32} - 2 q^{36} - 2 q^{37} - 4 q^{39} - 4 q^{42} - 2 q^{43} - 4 q^{46} + 6 q^{49} - 2 q^{50} - 4 q^{51} - 4 q^{57} + 2 q^{72} + 10 q^{74} + 6 q^{78} + 2 q^{81} + 8 q^{84} - 4 q^{86} - 2 q^{91} + 8 q^{92} - 2 q^{98} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(287, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
287.1.d.a 287.d 287.d $3$ $0.143$ \(\Q(\zeta_{14})^+\) $D_{7}$ \(\Q(\sqrt{-287}) \) None \(-1\) \(-1\) \(0\) \(3\) \(q+(-1+\beta _{1}-\beta _{2})q^{2}-\beta _{1}q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
287.1.d.b 287.d 287.d $3$ $0.143$ \(\Q(\zeta_{14})^+\) $D_{7}$ \(\Q(\sqrt{-287}) \) None \(-1\) \(1\) \(0\) \(-3\) \(q+(-1+\beta _{1}-\beta _{2})q^{2}+\beta _{1}q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)