Properties

Label 320.6.c
Level $320$
Weight $6$
Character orbit 320.c
Rep. character $\chi_{320}(129,\cdot)$
Character field $\Q$
Dimension $58$
Newform subspaces $12$
Sturm bound $288$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 320.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 12 \)
Sturm bound: \(288\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(320, [\chi])\).

Total New Old
Modular forms 252 62 190
Cusp forms 228 58 170
Eisenstein series 24 4 20

Trace form

\( 58 q + 2 q^{5} - 4378 q^{9} - 968 q^{21} - 3118 q^{25} + 4 q^{29} + 4948 q^{41} + 41790 q^{45} - 110450 q^{49} + 48084 q^{61} + 37776 q^{65} + 306424 q^{69} + 366210 q^{81} + 9568 q^{85} + 76548 q^{89}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(320, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
320.6.c.a 320.c 5.b $2$ $51.323$ \(\Q(\sqrt{-1}) \) None 10.6.b.a \(0\) \(0\) \(-110\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+7\beta q^{3}+(-5\beta-55)q^{5}+79\beta q^{7}+\cdots\)
320.6.c.b 320.c 5.b $2$ $51.323$ \(\Q(\sqrt{-1}) \) None 10.6.b.a \(0\) \(0\) \(-110\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+7\beta q^{3}+(5\beta-55)q^{5}+79\beta q^{7}+\cdots\)
320.6.c.c 320.c 5.b $2$ $51.323$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) 160.6.c.a \(0\) \(0\) \(-82\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-19\beta-41)q^{5}+243 q^{9}+122\beta q^{13}+\cdots\)
320.6.c.d 320.c 5.b $2$ $51.323$ \(\Q(\sqrt{-31}) \) None 20.6.c.a \(0\) \(0\) \(10\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta q^{3}+(5+5\beta )q^{5}+11\beta q^{7}+119q^{9}+\cdots\)
320.6.c.e 320.c 5.b $2$ $51.323$ \(\Q(\sqrt{-31}) \) None 20.6.c.a \(0\) \(0\) \(10\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta q^{3}+(5-5\beta )q^{5}+11\beta q^{7}+119q^{9}+\cdots\)
320.6.c.f 320.c 5.b $2$ $51.323$ \(\Q(\sqrt{-11}) \) None 5.6.b.a \(0\) \(0\) \(90\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-3\beta q^{3}+(45+5\beta )q^{5}+9\beta q^{7}-153q^{9}+\cdots\)
320.6.c.g 320.c 5.b $2$ $51.323$ \(\Q(\sqrt{-11}) \) None 5.6.b.a \(0\) \(0\) \(90\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-3\beta q^{3}+(45-5\beta )q^{5}+9\beta q^{7}-153q^{9}+\cdots\)
320.6.c.h 320.c 5.b $4$ $51.323$ \(\Q(i, \sqrt{5})\) \(\Q(\sqrt{-5}) \) 160.6.c.b \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(5\beta _{1}+\beta _{2})q^{3}-5\beta _{3}q^{5}+(-46\beta _{1}+\cdots)q^{7}+\cdots\)
320.6.c.i 320.c 5.b $8$ $51.323$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None 40.6.c.a \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+(-1+\beta _{2})q^{5}+(-\beta _{2}-\beta _{6}+\cdots)q^{7}+\cdots\)
320.6.c.j 320.c 5.b $8$ $51.323$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None 40.6.c.a \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-1+\beta _{2})q^{5}+(\beta _{2}+\beta _{6}+\cdots)q^{7}+\cdots\)
320.6.c.k 320.c 5.b $12$ $51.323$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None 160.6.c.c \(0\) \(0\) \(60\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{3}+(5+\beta _{5}+\beta _{7})q^{5}+\beta _{9}q^{7}+\cdots\)
320.6.c.l 320.c 5.b $12$ $51.323$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 160.6.c.d \(0\) \(0\) \(60\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}+(5-\beta _{5})q^{5}+(-5\beta _{2}-3\beta _{3}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(320, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(320, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)