Properties

Label 1792.1.bt
Level $1792$
Weight $1$
Character orbit 1792.bt
Rep. character $\chi_{1792}(13,\cdot)$
Character field $\Q(\zeta_{64})$
Dimension $32$
Newform subspaces $1$
Sturm bound $256$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1792 = 2^{8} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1792.bt (of order \(64\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1792 \)
Character field: \(\Q(\zeta_{64})\)
Newform subspaces: \( 1 \)
Sturm bound: \(256\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1792, [\chi])\).

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

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 \(S_{1}^{\mathrm{new}}(1792, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1792.1.bt.a \(32\) \(0.894\) \(\Q(\zeta_{64})\) \(D_{64}\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{64}^{3}q^{2}+\zeta_{64}^{6}q^{4}-\zeta_{64}^{7}q^{7}+\cdots\)