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Properties

Label 320.2.s
Level $320$
Weight $2$
Character orbit 320.s
Rep. character $\chi_{320}(207,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $20$
Newform subspaces $2$
Sturm bound $96$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 320.s (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(320, [\chi])\).

Total New Old
Modular forms 112 28 84
Cusp forms 80 20 60
Eisenstein series 32 8 24

Trace form

\( 20 q + 4 q^{3} - 2 q^{5} + 4 q^{7} + 12 q^{9} + 4 q^{11} + 12 q^{15} - 4 q^{17} + 8 q^{19} - 4 q^{21} + 4 q^{23} + 16 q^{27} - 4 q^{33} - 20 q^{35} - 18 q^{45} - 24 q^{47} - 4 q^{51} - 4 q^{53} + 4 q^{55}+ \cdots - 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(320, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
320.2.s.a 320.s 80.s $2$ $2.555$ \(\Q(\sqrt{-1}) \) None 80.2.j.a \(0\) \(4\) \(-4\) \(6\) $\mathrm{SU}(2)[C_{4}]$ \(q+2 q^{3}+(i-2)q^{5}+(3 i+3)q^{7}+\cdots\)
320.2.s.b 320.s 80.s $18$ $2.555$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None 80.2.j.b \(0\) \(0\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{1}q^{3}+\beta _{7}q^{5}+\beta _{10}q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(320, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(320, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 3}\)