Properties

Label 1368.1.eh
Level $1368$
Weight $1$
Character orbit 1368.eh
Rep. character $\chi_{1368}(595,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $6$
Newform subspaces $1$
Sturm bound $240$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1368.eh (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 152 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(240\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1368, [\chi])\).

Total New Old
Modular forms 72 18 54
Cusp forms 24 6 18
Eisenstein series 48 12 36

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

\( 6 q + 3 q^{8} + O(q^{10}) \) \( 6 q + 3 q^{8} + 6 q^{22} + 3 q^{38} + 3 q^{41} - 6 q^{44} - 3 q^{49} + 3 q^{50} + 3 q^{59} - 3 q^{64} - 3 q^{67} - 3 q^{68} + 6 q^{73} - 3 q^{82} - 3 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1368, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1368.1.eh.a $6$ $0.683$ \(\Q(\zeta_{18})\) $D_{9}$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{18}^{5}q^{2}-\zeta_{18}q^{4}-\zeta_{18}^{6}q^{8}+(-\zeta_{18}^{4}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1368, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1368, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 3}\)