Properties

Label 3332.1.w
Level $3332$
Weight $1$
Character orbit 3332.w
Rep. character $\chi_{3332}(491,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $16$
Newform subspaces $4$
Sturm bound $504$
Trace bound $20$

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Defining parameters

Level: \( N \) \(=\) \( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3332.w (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 68 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 4 \)
Sturm bound: \(504\)
Trace bound: \(20\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3332, [\chi])\).

Total New Old
Modular forms 80 56 24
Cusp forms 16 16 0
Eisenstein series 64 40 24

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 16 0 0 0

Trace form

\( 16 q - 16 q^{16} - 16 q^{53} + 16 q^{74}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(3332, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3332.1.w.a 3332.w 68.g $4$ $1.663$ \(\Q(\zeta_{8})\) $D_{8}$ \(\Q(\sqrt{-1}) \) None 3332.1.w.a \(0\) \(0\) \(-4\) \(0\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-1-\zeta_{8}^{3})q^{5}+\cdots\)
3332.1.w.b 3332.w 68.g $4$ $1.663$ \(\Q(\zeta_{8})\) $D_{8}$ \(\Q(\sqrt{-1}) \) None 3332.1.w.b \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(\zeta_{8}+\zeta_{8}^{2})q^{5}+\cdots\)
3332.1.w.c 3332.w 68.g $4$ $1.663$ \(\Q(\zeta_{8})\) $D_{8}$ \(\Q(\sqrt{-1}) \) None 3332.1.w.b \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}-\zeta_{8}^{2})q^{5}+\cdots\)
3332.1.w.d 3332.w 68.g $4$ $1.663$ \(\Q(\zeta_{8})\) $D_{8}$ \(\Q(\sqrt{-1}) \) None 3332.1.w.a \(0\) \(0\) \(4\) \(0\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(1+\zeta_{8}^{3})q^{5}-\zeta_{8}^{3}q^{8}+\cdots\)