Properties

Label 1368.1.bw
Level $1368$
Weight $1$
Character orbit 1368.bw
Rep. character $\chi_{1368}(125,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $8$
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.bw (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 456 \)
Character field: \(\Q(\zeta_{6})\)
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 24 8 16
Cusp forms 8 8 0
Eisenstein series 16 0 16

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 0 0 8 0

Trace form

\( 8 q - 8 q^{7} + O(q^{10}) \) \( 8 q - 8 q^{7} + 4 q^{16} + 4 q^{22} + 4 q^{25} + 8 q^{31} - 4 q^{34} - 8 q^{46} + 4 q^{52} - 8 q^{58} + 4 q^{73} + 4 q^{76} - 4 q^{79} + 8 q^{88} - 8 q^{94} - 8 q^{97} + O(q^{100}) \)

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.bw.a $8$ $0.683$ \(\Q(\zeta_{24})\) $S_{4}$ None None \(0\) \(0\) \(0\) \(-8\) \(q-\zeta_{24}^{5}q^{2}+\zeta_{24}^{10}q^{4}-q^{7}+\zeta_{24}^{3}q^{8}+\cdots\)