Properties

Label 960.2.t
Level $960$
Weight $2$
Character orbit 960.t
Rep. character $\chi_{960}(239,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $88$
Newform subspaces $2$
Sturm bound $384$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 960.t (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 240 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(384\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(960, [\chi])\).

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

Trace form

\( 88 q + O(q^{10}) \) \( 88 q + 8 q^{21} + 8 q^{39} - 12 q^{45} - 56 q^{49} + 16 q^{51} + 40 q^{55} + 8 q^{61} - 16 q^{69} + 36 q^{75} - 8 q^{81} - 24 q^{85} - 48 q^{91} + 8 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(960, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
960.2.t.a 960.t 240.t $8$ $7.666$ 8.0.3317760000.5 \(\Q(\sqrt{-15}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+3\beta _{3}q^{9}+\beta _{7}q^{15}+\cdots\)
960.2.t.b 960.t 240.t $80$ $7.666$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(960, [\chi])\) into lower level spaces

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