Properties

Label 336.1.bn
Level $336$
Weight $1$
Character orbit 336.bn
Rep. character $\chi_{336}(65,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $2$
Newform subspaces $1$
Sturm bound $64$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 336.bn (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(64\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(336, [\chi])\).

Total New Old
Modular forms 32 6 26
Cusp forms 8 2 6
Eisenstein series 24 4 20

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

\( 2 q + q^{3} + q^{7} - q^{9} + O(q^{10}) \) \( 2 q + q^{3} + q^{7} - q^{9} - 2 q^{13} - q^{19} + 2 q^{21} - q^{25} - 2 q^{27} - q^{31} + q^{37} - q^{39} + 2 q^{43} - q^{49} - 2 q^{57} - 2 q^{61} + q^{63} - q^{67} + q^{73} + q^{75} - q^{79} - q^{81} - q^{91} + q^{93} + 4 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(336, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
336.1.bn.a 336.bn 21.h $2$ $0.168$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(1\) \(q-\zeta_{6}^{2}q^{3}+\zeta_{6}q^{7}-\zeta_{6}q^{9}-q^{13}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(336, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(336, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 3}\)