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Properties

Label 1120.2.w
Level $1120$
Weight $2$
Character orbit 1120.w
Rep. character $\chi_{1120}(433,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $88$
Newform subspaces $3$
Sturm bound $384$
Trace bound $15$

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Defining parameters

Level: \( N \) \(=\) \( 1120 = 2^{5} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1120.w (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 280 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(384\)
Trace bound: \(15\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1120, [\chi])\).

Total New Old
Modular forms 416 104 312
Cusp forms 352 88 264
Eisenstein series 64 16 48

Trace form

\( 88 q + 4 q^{7} + 8 q^{15} + 8 q^{23} - 8 q^{25} + 16 q^{57} - 12 q^{63} - 8 q^{65} + 80 q^{71} - 72 q^{81} - 80 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(1120, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1120.2.w.a 1120.w 280.s $8$ $8.943$ 8.0.\(\cdots\).8 \(\Q(\sqrt{-14}) \) 280.2.s.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-\beta _{5}-\beta _{6})q^{3}+(\beta _{1}-\beta _{5}-\beta _{6})q^{5}+\cdots\)
1120.2.w.b 1120.w 280.s $8$ $8.943$ 8.0.\(\cdots\).8 \(\Q(\sqrt{-14}) \) 280.2.s.b \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+\beta _{1}q^{3}+\beta _{5}q^{5}+\beta _{7}q^{7}+(-\beta _{3}-5\beta _{4}+\cdots)q^{9}+\cdots\)
1120.2.w.c 1120.w 280.s $72$ $8.943$ None 280.2.s.c \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1120, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1120, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 3}\)