Properties

Label 3332.1.bn
Level $3332$
Weight $1$
Character orbit 3332.bn
Rep. character $\chi_{3332}(979,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $32$
Newform subspaces $4$
Sturm bound $504$
Trace bound $18$

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Defining parameters

Level: \( N \) \(=\) \( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3332.bn (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 476 \)
Character field: \(\Q(\zeta_{16})\)
Newform subspaces: \( 4 \)
Sturm bound: \(504\)
Trace bound: \(18\)

Dimensions

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

Total New Old
Modular forms 160 96 64
Cusp forms 32 32 0
Eisenstein series 128 64 64

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 32 0 0 0

Trace form

\( 32 q + O(q^{10}) \) \( 32 q + 32 q^{74} + O(q^{100}) \)

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.bn.a 3332.bn 476.af $8$ $1.663$ \(\Q(\zeta_{16})\) $D_{16}$ \(\Q(\sqrt{-1}) \) None 3332.1.bn.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{5}q^{2}-\zeta_{16}^{2}q^{4}+(-\zeta_{16}^{2}+\zeta_{16}^{5}+\cdots)q^{5}+\cdots\)
3332.1.bn.b 3332.bn 476.af $8$ $1.663$ \(\Q(\zeta_{16})\) $D_{16}$ \(\Q(\sqrt{-1}) \) None 3332.1.bn.b \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}^{5}q^{2}-\zeta_{16}^{2}q^{4}+(-\zeta_{16}+\zeta_{16}^{6}+\cdots)q^{5}+\cdots\)
3332.1.bn.c 3332.bn 476.af $8$ $1.663$ \(\Q(\zeta_{16})\) $D_{16}$ \(\Q(\sqrt{-1}) \) None 3332.1.bn.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{5}q^{2}-\zeta_{16}^{2}q^{4}+(\zeta_{16}^{2}-\zeta_{16}^{5}+\cdots)q^{5}+\cdots\)
3332.1.bn.d 3332.bn 476.af $8$ $1.663$ \(\Q(\zeta_{16})\) $D_{16}$ \(\Q(\sqrt{-1}) \) None 3332.1.bn.b \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}^{5}q^{2}-\zeta_{16}^{2}q^{4}+(\zeta_{16}-\zeta_{16}^{6}+\cdots)q^{5}+\cdots\)