Properties

Label 1120.2.bq
Level $1120$
Weight $2$
Character orbit 1120.bq
Rep. character $\chi_{1120}(719,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $88$
Newform subspaces $2$
Sturm bound $384$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1120 = 2^{5} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1120.bq (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 280 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(384\)
Trace bound: \(1\)
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

\( 88 q - 40 q^{9} + O(q^{10}) \) \( 88 q - 40 q^{9} + 4 q^{11} + 12 q^{19} - 2 q^{25} + 2 q^{35} - 8 q^{49} - 20 q^{51} + 60 q^{59} + 8 q^{65} + 6 q^{75} - 36 q^{81} - 36 q^{89} - 32 q^{91} - 80 q^{99} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1120.2.bq.a 1120.bq 280.aa $8$ $8.943$ 8.0.3317760000.3 \(\Q(\sqrt{-10}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+\beta _{1}q^{5}+(\beta _{1}-\beta _{2}-\beta _{6})q^{7}+3\beta _{3}q^{9}+\cdots\)
1120.2.bq.b 1120.bq 280.aa $80$ $8.943$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

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

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