Properties

Label 320.2.o
Level $320$
Weight $2$
Character orbit 320.o
Rep. character $\chi_{320}(223,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $24$
Newform subspaces $6$
Sturm bound $96$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 320.o (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 6 \)
Sturm bound: \(96\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

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

Total New Old
Modular forms 120 24 96
Cusp forms 72 24 48
Eisenstein series 48 0 48

Trace form

\( 24 q + O(q^{10}) \) \( 24 q + 24 q^{17} - 24 q^{25} - 24 q^{65} - 24 q^{73} - 120 q^{81} - 120 q^{97} + O(q^{100}) \)

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.o.a 320.o 40.k $2$ $2.555$ \(\Q(\sqrt{-1}) \) None 320.2.o.a \(0\) \(-2\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+i)q^{3}+(-1-2i)q^{5}+(-1+\cdots)q^{7}+\cdots\)
320.2.o.b 320.o 40.k $2$ $2.555$ \(\Q(\sqrt{-1}) \) None 320.2.o.a \(0\) \(-2\) \(2\) \(2\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+i)q^{3}+(1+2i)q^{5}+(1-i)q^{7}+\cdots\)
320.2.o.c 320.o 40.k $2$ $2.555$ \(\Q(\sqrt{-1}) \) None 320.2.o.a \(0\) \(2\) \(-2\) \(2\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-i)q^{3}+(-1-2i)q^{5}+(1-i)q^{7}+\cdots\)
320.2.o.d 320.o 40.k $2$ $2.555$ \(\Q(\sqrt{-1}) \) None 320.2.o.a \(0\) \(2\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-i)q^{3}+(1+2i)q^{5}+(-1+i)q^{7}+\cdots\)
320.2.o.e 320.o 40.k $8$ $2.555$ 8.0.49787136.1 None 320.2.o.e \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-\beta _{2}-\beta _{7})q^{3}+\beta _{7}q^{5}-\beta _{6}q^{7}+\cdots\)
320.2.o.f 320.o 40.k $8$ $2.555$ 8.0.49787136.1 None 320.2.o.e \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-\beta _{2}-\beta _{7})q^{3}-\beta _{7}q^{5}+\beta _{6}q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(320, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)