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Properties

Label 960.4.s
Level $960$
Weight $4$
Character orbit 960.s
Rep. character $\chi_{960}(241,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $96$
Newform subspaces $2$
Sturm bound $768$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 960.s (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(768\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(960, [\chi])\).

Total New Old
Modular forms 1184 96 1088
Cusp forms 1120 96 1024
Eisenstein series 64 0 64

Trace form

\( 96 q + O(q^{10}) \) \( 96 q - 80 q^{11} + 120 q^{15} + 24 q^{19} - 800 q^{29} - 32 q^{37} + 1616 q^{43} - 4704 q^{49} + 744 q^{51} - 1504 q^{53} - 1376 q^{59} + 912 q^{61} - 1008 q^{63} - 816 q^{67} + 528 q^{69} - 3808 q^{77} + 2832 q^{79} - 7776 q^{81} + 240 q^{85} - 5296 q^{91} - 720 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(960, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
960.4.s.a 960.s 16.e $44$ $56.642$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
960.4.s.b 960.s 16.e $52$ $56.642$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{4}^{\mathrm{old}}(960, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(960, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)