Properties

Label 320.5.p
Level $320$
Weight $5$
Character orbit 320.p
Rep. character $\chi_{320}(193,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $92$
Newform subspaces $20$
Sturm bound $240$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 320.p (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 20 \)
Sturm bound: \(240\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(320, [\chi])\).

Total New Old
Modular forms 408 100 308
Cusp forms 360 92 268
Eisenstein series 48 8 40

Trace form

\( 92 q + 4 q^{5} + 4 q^{13} + 476 q^{17} + 8 q^{21} - 676 q^{25} - 328 q^{33} + 4 q^{37} - 8 q^{41} - 2496 q^{45} - 20156 q^{53} + 320 q^{57} - 7544 q^{61} - 7396 q^{65} - 5284 q^{73} - 4792 q^{77} - 53860 q^{81}+ \cdots + 30876 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{5}^{\mathrm{new}}(320, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
320.5.p.a 320.p 5.c $2$ $33.078$ \(\Q(\sqrt{-1}) \) None 40.5.l.a \(0\) \(-20\) \(-40\) \(-84\) $\mathrm{SU}(2)[C_{4}]$ \(q+(10 i-10)q^{3}+(-15 i-20)q^{5}+\cdots\)
320.5.p.b 320.p 5.c $2$ $33.078$ \(\Q(\sqrt{-1}) \) None 10.5.c.a \(0\) \(-18\) \(30\) \(58\) $\mathrm{SU}(2)[C_{4}]$ \(q+(9 i-9)q^{3}+(-20 i+15)q^{5}+\cdots\)
320.5.p.c 320.p 5.c $2$ $33.078$ \(\Q(\sqrt{-1}) \) None 5.5.c.a \(0\) \(-12\) \(-40\) \(52\) $\mathrm{SU}(2)[C_{4}]$ \(q+(6 i-6)q^{3}+(-15 i-20)q^{5}+\cdots\)
320.5.p.d 320.p 5.c $2$ $33.078$ \(\Q(\sqrt{-1}) \) None 10.5.c.b \(0\) \(-2\) \(30\) \(-38\) $\mathrm{SU}(2)[C_{4}]$ \(q+(i-1)q^{3}+(20 i+15)q^{5}+(-19 i-19)q^{7}+\cdots\)
320.5.p.e 320.p 5.c $2$ $33.078$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) 160.5.p.b \(0\) \(0\) \(-48\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-7 i-24)q^{5}+81 i q^{9}+(-i+1)q^{13}+\cdots\)
320.5.p.f 320.p 5.c $2$ $33.078$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) 160.5.p.a \(0\) \(0\) \(48\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-7 i+24)q^{5}+81 i q^{9}+(239 i-239)q^{13}+\cdots\)
320.5.p.g 320.p 5.c $2$ $33.078$ \(\Q(\sqrt{-1}) \) None 10.5.c.b \(0\) \(2\) \(30\) \(38\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-i+1)q^{3}+(20 i+15)q^{5}+(19 i+19)q^{7}+\cdots\)
320.5.p.h 320.p 5.c $2$ $33.078$ \(\Q(\sqrt{-1}) \) None 5.5.c.a \(0\) \(12\) \(-40\) \(-52\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-6 i+6)q^{3}+(-15 i-20)q^{5}+\cdots\)
320.5.p.i 320.p 5.c $2$ $33.078$ \(\Q(\sqrt{-1}) \) None 10.5.c.a \(0\) \(18\) \(30\) \(-58\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-9 i+9)q^{3}+(-20 i+15)q^{5}+\cdots\)
320.5.p.j 320.p 5.c $2$ $33.078$ \(\Q(\sqrt{-1}) \) None 40.5.l.a \(0\) \(20\) \(-40\) \(84\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-10 i+10)q^{3}+(-15 i-20)q^{5}+\cdots\)
320.5.p.k 320.p 5.c $4$ $33.078$ \(\Q(i, \sqrt{29})\) None 40.5.l.b \(0\) \(-12\) \(12\) \(-44\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-3+3\beta _{1})q^{3}+(3+6\beta _{1}-\beta _{3})q^{5}+\cdots\)
320.5.p.l 320.p 5.c $4$ $33.078$ \(\Q(i, \sqrt{241})\) None 20.5.f.a \(0\) \(-10\) \(6\) \(-110\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-2+2\beta _{1}+\beta _{3})q^{3}+(6\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
320.5.p.m 320.p 5.c $4$ $33.078$ \(\Q(i, \sqrt{241})\) None 20.5.f.a \(0\) \(10\) \(6\) \(110\) $\mathrm{SU}(2)[C_{4}]$ \(q+(3-3\beta _{1}+\beta _{3})q^{3}+(3+3\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
320.5.p.n 320.p 5.c $4$ $33.078$ \(\Q(i, \sqrt{29})\) None 40.5.l.b \(0\) \(12\) \(12\) \(44\) $\mathrm{SU}(2)[C_{4}]$ \(q+(3-3\beta _{1})q^{3}+(3+6\beta _{1}-\beta _{3})q^{5}+\cdots\)
320.5.p.o 320.p 5.c $6$ $33.078$ 6.0.313431616.3 None 40.5.l.c \(0\) \(-8\) \(4\) \(40\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-\beta _{1}-\beta _{3})q^{3}+(1-7\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
320.5.p.p 320.p 5.c $6$ $33.078$ 6.0.313431616.3 None 40.5.l.c \(0\) \(8\) \(4\) \(-40\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+\beta _{1}+\beta _{3})q^{3}+(1-7\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
320.5.p.q 320.p 5.c $8$ $33.078$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 160.5.p.c \(0\) \(0\) \(40\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{5}q^{3}+(5-5\beta _{4})q^{5}+(\beta _{3}+\beta _{7})q^{7}+\cdots\)
320.5.p.r 320.p 5.c $12$ $33.078$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 160.5.p.e \(0\) \(0\) \(-24\) \(-48\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{8}q^{3}+(-2-\beta _{2}+\beta _{6})q^{5}+(-4+\cdots)q^{7}+\cdots\)
320.5.p.s 320.p 5.c $12$ $33.078$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 160.5.p.e \(0\) \(0\) \(-24\) \(48\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{8}q^{3}+(-2-\beta _{2}+\beta _{6})q^{5}+(4+4\beta _{2}+\cdots)q^{7}+\cdots\)
320.5.p.t 320.p 5.c $12$ $33.078$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None 160.5.p.d \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{6}q^{3}+(1-\beta _{5})q^{5}+(-\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(320, [\chi])\) into lower level spaces

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