↑

Properties

Label 320.2.q
Level $320$
Weight $2$
Character orbit 320.q
Rep. character $\chi_{320}(49,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $20$
Newform subspaces $3$
Sturm bound $96$
Trace bound $3$

Related objects

Downloads

Learn more

Defining parameters

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

\( 20 q - 2 q^{5} + 4 q^{11} + 4 q^{15} + 12 q^{19} - 16 q^{21} - 4 q^{29} - 16 q^{31} + 24 q^{35} + 14 q^{45} - 12 q^{49} - 12 q^{59} - 20 q^{61} - 12 q^{65} - 36 q^{75} - 48 q^{79} + 4 q^{81} + 8 q^{85}+ \cdots - 76 q^{99}+O(q^{100}) \) 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.q.a 320.q 80.q $2$ $2.555$ \(\Q(\sqrt{-1}) \) None 80.2.q.a \(0\) \(-2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-i-1)q^{3}+(2 i+1)q^{5}-i q^{9}+\cdots\)
320.2.q.b 320.q 80.q $2$ $2.555$ \(\Q(\sqrt{-1}) \) None 80.2.q.a \(0\) \(2\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(i+1)q^{3}+(i+2)q^{5}-i q^{9}+(3 i+3)q^{11}+\cdots\)
320.2.q.c 320.q 80.q $16$ $2.555$ 16.0.\(\cdots\).1 None 80.2.q.c \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{11}q^{3}+(-1-\beta _{6}-\beta _{10})q^{5}+(\beta _{3}+\cdots)q^{7}+\cdots\)

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

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