Properties

Label 3344.1.bc
Level $3344$
Weight $1$
Character orbit 3344.bc
Rep. character $\chi_{3344}(2463,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $2$
Sturm bound $480$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 3344 = 2^{4} \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3344.bc (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 836 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(480\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3344, [\chi])\).

Total New Old
Modular forms 28 4 24
Cusp forms 4 4 0
Eisenstein series 24 0 24

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\( 4 q - 2 q^{5} + 2 q^{9} + O(q^{10}) \) \( 4 q - 2 q^{5} + 2 q^{9} - 4 q^{45} - 6 q^{53} - 4 q^{77} - 2 q^{81} + 6 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3344, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3344.1.bc.a 3344.bc 836.m $2$ $1.669$ \(\Q(\sqrt{-3}) \) $D_{6}$ None \(\Q(\sqrt{11}) \) 3344.1.bc.a \(0\) \(0\) \(-1\) \(-2\) \(q+\zeta_{6}^{2}q^{5}-q^{7}+\zeta_{6}q^{9}+q^{11}-\zeta_{6}^{2}q^{19}+\cdots\)
3344.1.bc.b 3344.bc 836.m $2$ $1.669$ \(\Q(\sqrt{-3}) \) $D_{6}$ None \(\Q(\sqrt{11}) \) 3344.1.bc.a \(0\) \(0\) \(-1\) \(2\) \(q+\zeta_{6}^{2}q^{5}+q^{7}+\zeta_{6}q^{9}-q^{11}+\zeta_{6}^{2}q^{19}+\cdots\)