Properties

Label 960.3.be
Level $960$
Weight $3$
Character orbit 960.be
Rep. character $\chi_{960}(337,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $96$
Newform subspaces $1$
Sturm bound $576$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 960.be (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(576\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(960, [\chi])\).

Total New Old
Modular forms 800 96 704
Cusp forms 736 96 640
Eisenstein series 64 0 64

Trace form

\( 96 q + 288 q^{9} + O(q^{10}) \) \( 96 q + 288 q^{9} - 32 q^{19} + 96 q^{35} - 96 q^{51} - 128 q^{59} + 32 q^{61} - 96 q^{69} + 96 q^{73} - 192 q^{75} + 864 q^{81} + 320 q^{83} + 384 q^{91} + 768 q^{95} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(960, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
960.3.be.a 960.be 80.t $96$ $26.158$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{3}^{\mathrm{old}}(960, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(960, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)