Properties

Label 3332.1.bp
Level $3332$
Weight $1$
Character orbit 3332.bp
Rep. character $\chi_{3332}(263,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $32$
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.bp (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 476 \)
Character field: \(\Q(\zeta_{24})\)
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 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

\( 32 q + O(q^{10}) \) \( 32 q + 16 q^{16} + 16 q^{53} - 16 q^{74} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3332.1.bp.a 3332.bp 476.ag $8$ $1.663$ \(\Q(\zeta_{24})\) $D_{8}$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(\zeta_{24}-\zeta_{24}^{4}+\cdots)q^{5}+\cdots\)
3332.1.bp.b 3332.bp 476.ag $8$ $1.663$ \(\Q(\zeta_{24})\) $D_{8}$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(-\zeta_{24}^{7}-\zeta_{24}^{10}+\cdots)q^{5}+\cdots\)
3332.1.bp.c 3332.bp 476.ag $8$ $1.663$ \(\Q(\zeta_{24})\) $D_{8}$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(\zeta_{24}^{7}+\zeta_{24}^{10}+\cdots)q^{5}+\cdots\)
3332.1.bp.d 3332.bp 476.ag $8$ $1.663$ \(\Q(\zeta_{24})\) $D_{8}$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(-\zeta_{24}+\zeta_{24}^{4}+\cdots)q^{5}+\cdots\)