Properties

Label 3072.1.p
Level $3072$
Weight $1$
Character orbit 3072.p
Rep. character $\chi_{3072}(641,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $32$
Newform subspaces $4$
Sturm bound $512$
Trace bound $37$

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Defining parameters

Level: \( N \) \(=\) \( 3072 = 2^{10} \cdot 3 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3072.p (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 96 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 4 \)
Sturm bound: \(512\)
Trace bound: \(37\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3072, [\chi])\).

Total New Old
Modular forms 224 32 192
Cusp forms 32 32 0
Eisenstein series 192 0 192

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

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

Decomposition of \(S_{1}^{\mathrm{new}}(3072, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3072.1.p.a \(8\) \(1.533\) \(\Q(\zeta_{16})\) \(D_{8}\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}q^{3}+(\zeta_{16}^{5}+\zeta_{16}^{7})q^{7}+\zeta_{16}^{2}q^{9}+\cdots\)
3072.1.p.b \(8\) \(1.533\) \(\Q(\zeta_{16})\) \(D_{8}\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}q^{3}+(\zeta_{16}-\zeta_{16}^{3})q^{7}+\zeta_{16}^{2}q^{9}+\cdots\)
3072.1.p.c \(8\) \(1.533\) \(\Q(\zeta_{16})\) \(D_{8}\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}q^{3}+(-\zeta_{16}+\zeta_{16}^{3})q^{7}+\zeta_{16}^{2}q^{9}+\cdots\)
3072.1.p.d \(8\) \(1.533\) \(\Q(\zeta_{16})\) \(D_{8}\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}q^{3}+(-\zeta_{16}^{5}-\zeta_{16}^{7})q^{7}+\zeta_{16}^{2}q^{9}+\cdots\)