Properties

Label 1215.1.h
Level $1215$
Weight $1$
Character orbit 1215.h
Rep. character $\chi_{1215}(404,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $12$
Newform subspaces $2$
Sturm bound $162$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1215 = 3^{5} \cdot 5 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1215.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(162\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1215, [\chi])\).

Total New Old
Modular forms 56 12 44
Cusp forms 20 12 8
Eisenstein series 36 0 36

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 12 0 0 0

Trace form

\( 12 q - 6 q^{4} + O(q^{10}) \) \( 12 q - 6 q^{4} - 6 q^{16} - 6 q^{25} + 6 q^{34} + 6 q^{40} - 12 q^{46} - 6 q^{49} + 6 q^{76} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1215, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1215.1.h.a 1215.h 45.h $6$ $0.606$ \(\Q(\zeta_{18})\) $D_{9}$ \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(-3\) \(0\) \(q+(\zeta_{18}^{4}+\zeta_{18}^{8})q^{2}+(-\zeta_{18}^{3}-\zeta_{18}^{7}+\cdots)q^{4}+\cdots\)
1215.1.h.b 1215.h 45.h $6$ $0.606$ \(\Q(\zeta_{18})\) $D_{9}$ \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(3\) \(0\) \(q+(\zeta_{18}-\zeta_{18}^{2})q^{2}+(\zeta_{18}^{2}-\zeta_{18}^{3}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1215, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1215, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(405, [\chi])\)\(^{\oplus 2}\)