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

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

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

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
287.1.d.a \(3\) \(0.143\) \(\Q(\zeta_{14})^+\) \(D_{7}\) \(\Q(\sqrt{-287}) \) 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 \(3\) \(0.143\) \(\Q(\zeta_{14})^+\) \(D_{7}\) \(\Q(\sqrt{-287}) \) None \(-1\) \(1\) \(0\) \(-3\) \(q+(-1+\beta _{1}-\beta _{2})q^{2}+\beta _{1}q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)