Properties

Label 320.4.l
Level $320$
Weight $4$
Character orbit 320.l
Rep. character $\chi_{320}(81,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $48$
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.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
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 48 256
Cusp forms 272 48 224
Eisenstein series 32 0 32

Trace form

\( 48 q + O(q^{10}) \) \( 48 q + 40 q^{11} - 120 q^{15} - 24 q^{19} + 264 q^{27} + 400 q^{29} + 16 q^{37} - 808 q^{43} - 1880 q^{47} - 2352 q^{49} - 2144 q^{51} + 752 q^{53} + 2728 q^{59} - 912 q^{61} + 2520 q^{63} + 2040 q^{67} - 528 q^{69} + 1904 q^{77} - 2832 q^{79} - 3888 q^{81} - 2440 q^{83} - 240 q^{85} + 4448 q^{91} + 4272 q^{93} + 3040 q^{95} + 4456 q^{99} + O(q^{100}) \)

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.l.a 320.l 16.e $48$ $18.881$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

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

\( S_{4}^{\mathrm{old}}(320, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 3}\)