Properties

Label 1120.1.p
Level $1120$
Weight $1$
Character orbit 1120.p
Rep. character $\chi_{1120}(769,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
Sturm bound $192$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1120 = 2^{5} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1120.p (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(192\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1120, [\chi])\).

Total New Old
Modular forms 32 4 28
Cusp forms 16 4 12
Eisenstein series 16 0 16

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\( 4 q + 4 q^{9} + O(q^{10}) \) \( 4 q + 4 q^{9} - 4 q^{21} - 4 q^{25} + 8 q^{29} - 4 q^{81} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1120, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1120.1.p.a $4$ $0.559$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{5}+\zeta_{8}^{3}q^{7}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1120, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1120, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 2}\)