Properties

Label 320.2.n
Level $320$
Weight $2$
Character orbit 320.n
Rep. character $\chi_{320}(63,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $20$
Newform subspaces $9$
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.n (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 9 \)
Sturm bound: \(96\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(7\), \(13\)

Dimensions

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

Total New Old
Modular forms 120 28 92
Cusp forms 72 20 52
Eisenstein series 48 8 40

Trace form

\( 20 q + 4 q^{5} + 4 q^{13} - 12 q^{17} + 8 q^{21} - 12 q^{25} + 8 q^{33} + 4 q^{37} - 8 q^{41} - 16 q^{45} + 52 q^{53} - 16 q^{57} - 24 q^{61} + 4 q^{65} - 12 q^{73} - 72 q^{77} + 36 q^{81} - 44 q^{85} - 56 q^{93}+ \cdots - 28 q^{97}+O(q^{100}) \) 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.n.a 320.n 20.e $2$ $2.555$ \(\Q(\sqrt{-1}) \) None 160.2.n.a \(0\) \(-4\) \(4\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-2 i-2)q^{3}+(-i+2)q^{5}+(-2 i+2)q^{7}+\cdots\)
320.2.n.b 320.n 20.e $2$ $2.555$ \(\Q(\sqrt{-1}) \) None 160.2.n.c \(0\) \(-2\) \(-2\) \(-6\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-i-1)q^{3}+(-2 i-1)q^{5}+(3 i-3)q^{7}+\cdots\)
320.2.n.c 320.n 20.e $2$ $2.555$ \(\Q(\sqrt{-1}) \) None 160.2.n.b \(0\) \(-2\) \(-2\) \(2\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-i-1)q^{3}+(2 i-1)q^{5}+(-i+1)q^{7}+\cdots\)
320.2.n.d 320.n 20.e $2$ $2.555$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) 80.2.n.a \(0\) \(0\) \(-4\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-i-2)q^{5}-3 i q^{9}+(-5 i+5)q^{13}+\cdots\)
320.2.n.e 320.n 20.e $2$ $2.555$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) 20.2.e.a \(0\) \(0\) \(4\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-i+2)q^{5}-3 i q^{9}+(-i+1)q^{13}+\cdots\)
320.2.n.f 320.n 20.e $2$ $2.555$ \(\Q(\sqrt{-1}) \) None 160.2.n.b \(0\) \(2\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{4}]$ \(q+(i+1)q^{3}+(2 i-1)q^{5}+(i-1)q^{7}+\cdots\)
320.2.n.g 320.n 20.e $2$ $2.555$ \(\Q(\sqrt{-1}) \) None 160.2.n.c \(0\) \(2\) \(-2\) \(6\) $\mathrm{SU}(2)[C_{4}]$ \(q+(i+1)q^{3}+(-2 i-1)q^{5}+(-3 i+3)q^{7}+\cdots\)
320.2.n.h 320.n 20.e $2$ $2.555$ \(\Q(\sqrt{-1}) \) None 160.2.n.a \(0\) \(4\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(2 i+2)q^{3}+(-i+2)q^{5}+(2 i-2)q^{7}+\cdots\)
320.2.n.i 320.n 20.e $4$ $2.555$ \(\Q(\zeta_{12})\) None 80.2.n.b \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta_{2} q^{3}+(2\beta_1+1)q^{5}-\beta_{3} q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(320, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)