Properties

Label 320.4.s
Level $320$
Weight $4$
Character orbit 320.s
Rep. character $\chi_{320}(207,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $68$
Newform subspaces $1$
Sturm bound $192$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 320.s (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(192\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(320, [\chi])\).

Total New Old
Modular forms 304 76 228
Cusp forms 272 68 204
Eisenstein series 32 8 24

Trace form

\( 68 q + 4 q^{3} - 2 q^{5} + 4 q^{7} + 540 q^{9} + O(q^{10}) \) \( 68 q + 4 q^{3} - 2 q^{5} + 4 q^{7} + 540 q^{9} + 4 q^{11} + 108 q^{15} - 4 q^{17} - 24 q^{19} - 4 q^{21} + 4 q^{23} + 112 q^{27} - 4 q^{33} - 20 q^{35} - 306 q^{45} - 408 q^{47} - 740 q^{51} - 4 q^{53} + 4 q^{55} - 108 q^{57} + 688 q^{59} - 916 q^{61} + 108 q^{63} - 4 q^{65} + 420 q^{69} + 232 q^{71} + 296 q^{73} + 2812 q^{75} - 1376 q^{77} + 2908 q^{81} + 2684 q^{83} + 248 q^{85} + 1292 q^{87} - 844 q^{91} + 1240 q^{95} - 4 q^{97} + 2764 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(320, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
320.4.s.a 320.s 80.s $68$ $18.881$ None \(0\) \(4\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{4}^{\mathrm{old}}(320, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(320, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 3}\)