Properties

Label 1792.1.bf
Level $1792$
Weight $1$
Character orbit 1792.bf
Rep. character $\chi_{1792}(209,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $8$
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.bf (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 448 \)
Character field: \(\Q(\zeta_{16})\)
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 24 72
Cusp forms 32 8 24
Eisenstein series 64 16 48

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 0 0

Trace form

\( 8q + O(q^{10}) \) \( 8q + 8q^{63} + 8q^{67} + O(q^{100}) \)

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.bf.a \(8\) \(0.894\) \(\Q(\zeta_{16})\) \(D_{16}\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}^{7}q^{7}+\zeta_{16}q^{9}+(-\zeta_{16}^{2}-\zeta_{16}^{5}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1792, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1792, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 3}\)