Properties

Label 297.1.h
Level $297$
Weight $1$
Character orbit 297.h
Rep. character $\chi_{297}(10,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $2$
Newform subspaces $1$
Sturm bound $36$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 297 = 3^{3} \cdot 11 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 297.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 99 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(36\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(297, [\chi])\).

Total New Old
Modular forms 18 6 12
Cusp forms 6 2 4
Eisenstein series 12 4 8

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2 q - q^{4} - q^{5} + O(q^{10}) \) \( 2 q - q^{4} - q^{5} + q^{11} - q^{16} - q^{20} + 2 q^{23} + q^{31} - 2 q^{37} - 2 q^{44} - q^{47} - q^{49} + 2 q^{53} - 2 q^{55} - q^{59} + 2 q^{64} + q^{67} + 2 q^{71} + 2 q^{80} - 4 q^{89} + 2 q^{92} + q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(297, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
297.1.h.a $2$ $0.148$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(-1\) \(0\) \(q+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{11}-\zeta_{6}q^{16}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(297, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(297, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 2}\)