Properties

Label 320.3.h
Level $320$
Weight $3$
Character orbit 320.h
Rep. character $\chi_{320}(319,\cdot)$
Character field $\Q$
Dimension $22$
Newform subspaces $7$
Sturm bound $144$
Trace bound $5$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 320.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(144\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(320, [\chi])\).

Total New Old
Modular forms 108 26 82
Cusp forms 84 22 62
Eisenstein series 24 4 20

Trace form

\( 22 q + 2 q^{5} + 50 q^{9} + O(q^{10}) \) \( 22 q + 2 q^{5} + 50 q^{9} + 40 q^{21} - 26 q^{25} + 4 q^{29} - 84 q^{41} + 22 q^{45} + 66 q^{49} - 28 q^{61} + 424 q^{69} + 46 q^{81} - 192 q^{85} + 12 q^{89} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(320, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
320.3.h.a 320.h 20.d $1$ $8.719$ \(\Q\) \(\Q(\sqrt{-5}) \) \(0\) \(-4\) \(5\) \(-4\) $\mathrm{U}(1)[D_{2}]$ \(q-4q^{3}+5q^{5}-4q^{7}+7q^{9}-20q^{15}+\cdots\)
320.3.h.b 320.h 20.d $1$ $8.719$ \(\Q\) \(\Q(\sqrt{-5}) \) \(0\) \(4\) \(5\) \(4\) $\mathrm{U}(1)[D_{2}]$ \(q+4q^{3}+5q^{5}+4q^{7}+7q^{9}+20q^{15}+\cdots\)
320.3.h.c 320.h 20.d $2$ $8.719$ \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-5}) \) \(0\) \(0\) \(-10\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta q^{3}-5q^{5}-3\beta q^{7}+11q^{9}+5\beta q^{15}+\cdots\)
320.3.h.d 320.h 20.d $2$ $8.719$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-6\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-3+i)q^{5}-9q^{9}-6iq^{13}-4iq^{17}+\cdots\)
320.3.h.e 320.h 20.d $4$ $8.719$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(1+\beta _{2})q^{5}-3\beta _{1}q^{7}-q^{9}+\cdots\)
320.3.h.f 320.h 20.d $6$ $8.719$ 6.0.1827904.1 None \(0\) \(-4\) \(2\) \(12\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta _{1})q^{3}+\beta _{3}q^{5}+(2+\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)
320.3.h.g 320.h 20.d $6$ $8.719$ 6.0.1827904.1 None \(0\) \(4\) \(2\) \(-12\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta _{1})q^{3}+(1+\beta _{1}+\beta _{3})q^{5}+(-2+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(320, [\chi])\) into lower level spaces

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