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Properties

Label 1120.2.cb
Level $1120$
Weight $2$
Character orbit 1120.cb
Rep. character $\chi_{1120}(81,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $64$
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.cb (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
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 64 352
Cusp forms 352 64 288
Eisenstein series 64 0 64

Trace form

\( 64 q + 32 q^{9} + O(q^{10}) \) \( 64 q + 32 q^{9} + 8 q^{23} + 32 q^{25} + 40 q^{47} + 16 q^{49} + 32 q^{55} - 32 q^{57} + 80 q^{63} + 48 q^{71} + 16 q^{73} - 40 q^{79} - 40 q^{81} - 48 q^{87} + 8 q^{89} - 64 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.cb.a 1120.cb 56.p $4$ $8.943$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{12}+\zeta_{12}^{3})q^{5}+(1+2\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)
1120.2.cb.b 1120.cb 56.p $60$ $8.943$ None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(1120, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 2}\)