Properties

Label 960.2.bl
Level $960$
Weight $2$
Character orbit 960.bl
Rep. character $\chi_{960}(49,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $48$
Newform subspaces $1$
Sturm bound $384$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 960.bl (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(384\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 416 48 368
Cusp forms 352 48 304
Eisenstein series 64 0 64

Trace form

\( 48 q + O(q^{10}) \) \( 48 q - 8 q^{19} + 48 q^{31} - 24 q^{35} + 48 q^{49} - 8 q^{51} + 32 q^{59} + 16 q^{61} + 16 q^{65} - 16 q^{69} + 16 q^{75} + 96 q^{79} - 48 q^{81} + 32 q^{91} + 48 q^{95} + O(q^{100}) \)

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.bl.a 960.bl 80.q $48$ $7.666$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

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

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