Properties

Label 320.3.p
Level $320$
Weight $3$
Character orbit 320.p
Rep. character $\chi_{320}(193,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $44$
Newform subspaces $14$
Sturm bound $144$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 320.p (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 14 \)
Sturm bound: \(144\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(7\), \(13\)

Dimensions

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

Total New Old
Modular forms 216 52 164
Cusp forms 168 44 124
Eisenstein series 48 8 40

Trace form

\( 44 q + 4 q^{5} + O(q^{10}) \) \( 44 q + 4 q^{5} + 4 q^{13} - 20 q^{17} + 8 q^{21} + 44 q^{25} - 40 q^{33} + 4 q^{37} - 8 q^{41} - 96 q^{45} + 292 q^{53} + 32 q^{57} + 72 q^{61} - 116 q^{65} + 44 q^{73} + 296 q^{77} - 52 q^{81} - 284 q^{85} - 632 q^{93} + 76 q^{97} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
320.3.p.a 320.p 5.c $2$ $8.719$ \(\Q(\sqrt{-1}) \) None 10.3.c.a \(0\) \(-4\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-2+2i)q^{3}+5iq^{5}+(-2-2i)q^{7}+\cdots\)
320.3.p.b 320.p 5.c $2$ $8.719$ \(\Q(\sqrt{-1}) \) None 40.3.l.a \(0\) \(-2\) \(-10\) \(-6\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+i)q^{3}-5q^{5}+(-3-3i)q^{7}+\cdots\)
320.3.p.c 320.p 5.c $2$ $8.719$ \(\Q(\sqrt{-1}) \) None 20.3.f.a \(0\) \(-2\) \(6\) \(-14\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+i)q^{3}+(3-4i)q^{5}+(-7-7i)q^{7}+\cdots\)
320.3.p.d 320.p 5.c $2$ $8.719$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) 160.3.p.b \(0\) \(0\) \(-8\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-4-3i)q^{5}+9iq^{9}+(-7+7i)q^{13}+\cdots\)
320.3.p.e 320.p 5.c $2$ $8.719$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) 160.3.p.a \(0\) \(0\) \(8\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(4-3i)q^{5}+9iq^{9}+(17-17i)q^{13}+\cdots\)
320.3.p.f 320.p 5.c $2$ $8.719$ \(\Q(\sqrt{-1}) \) None 40.3.l.a \(0\) \(2\) \(-10\) \(6\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-i)q^{3}-5q^{5}+(3+3i)q^{7}+7iq^{9}+\cdots\)
320.3.p.g 320.p 5.c $2$ $8.719$ \(\Q(\sqrt{-1}) \) None 20.3.f.a \(0\) \(2\) \(6\) \(14\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-i)q^{3}+(3-4i)q^{5}+(7+7i)q^{7}+\cdots\)
320.3.p.h 320.p 5.c $2$ $8.719$ \(\Q(\sqrt{-1}) \) None 10.3.c.a \(0\) \(4\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(2-2i)q^{3}+5iq^{5}+(2+2i)q^{7}+\cdots\)
320.3.p.i 320.p 5.c $4$ $8.719$ \(\Q(i, \sqrt{41})\) None 40.3.l.b \(0\) \(-2\) \(6\) \(-14\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+\beta _{2})q^{3}+(1+2\beta _{1}-\beta _{3})q^{5}+\cdots\)
320.3.p.j 320.p 5.c $4$ $8.719$ \(\Q(i, \sqrt{7})\) None 160.3.p.d \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{2}q^{3}+(-3-4\beta _{1})q^{5}+3\beta _{3}q^{7}+\cdots\)
320.3.p.k 320.p 5.c $4$ $8.719$ \(\Q(i, \sqrt{15})\) None 160.3.p.c \(0\) \(0\) \(20\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{2}q^{3}+5q^{5}-\beta _{3}q^{7}+21\beta _{1}q^{9}+\cdots\)
320.3.p.l 320.p 5.c $4$ $8.719$ \(\Q(i, \sqrt{41})\) None 40.3.l.b \(0\) \(2\) \(6\) \(14\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-\beta _{1}+\beta _{3})q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+\cdots\)
320.3.p.m 320.p 5.c $6$ $8.719$ 6.0.3534400.1 None 160.3.p.e \(0\) \(0\) \(-4\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{2}q^{3}+(-1-\beta _{2}-\beta _{4})q^{5}+(-2+\cdots)q^{7}+\cdots\)
320.3.p.n 320.p 5.c $6$ $8.719$ 6.0.3534400.1 None 160.3.p.e \(0\) \(0\) \(-4\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{2}q^{3}+(-1-\beta _{2}-\beta _{4})q^{5}+(2+2\beta _{3}+\cdots)q^{7}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(320, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)