Properties

Label 1008.4.cq
Level $1008$
Weight $4$
Character orbit 1008.cq
Rep. character $\chi_{1008}(431,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $96$
Newform subspaces $3$
Sturm bound $768$
Trace bound $7$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1008.cq (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 84 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(768\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1008, [\chi])\).

Total New Old
Modular forms 1200 96 1104
Cusp forms 1104 96 1008
Eisenstein series 96 0 96

Trace form

\( 96 q + O(q^{10}) \) \( 96 q + 144 q^{13} + 1704 q^{25} - 504 q^{37} - 1584 q^{49} + 2160 q^{61} - 5688 q^{73} - 7776 q^{85} - 1296 q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1008, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1008.4.cq.a 1008.cq 84.n $32$ $59.474$ None \(0\) \(0\) \(0\) \(-36\) $\mathrm{SU}(2)[C_{6}]$
1008.4.cq.b 1008.cq 84.n $32$ $59.474$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
1008.4.cq.c 1008.cq 84.n $32$ $59.474$ None \(0\) \(0\) \(0\) \(36\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{4}^{\mathrm{old}}(1008, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1008, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)