Properties

Label 320.4.c
Level $320$
Weight $4$
Character orbit 320.c
Rep. character $\chi_{320}(129,\cdot)$
Character field $\Q$
Dimension $34$
Newform subspaces $10$
Sturm bound $192$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 320.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(192\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(320, [\chi])\).

Total New Old
Modular forms 156 38 118
Cusp forms 132 34 98
Eisenstein series 24 4 20

Trace form

\( 34 q + 2 q^{5} - 274 q^{9} + O(q^{10}) \) \( 34 q + 2 q^{5} - 274 q^{9} - 104 q^{21} + 42 q^{25} + 4 q^{29} - 476 q^{41} - 786 q^{45} - 1082 q^{49} - 908 q^{61} + 528 q^{65} - 1064 q^{69} + 330 q^{81} + 928 q^{85} + 756 q^{89} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(320, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
320.4.c.a 320.c 5.b $2$ $18.881$ \(\Q(\sqrt{-19}) \) None 20.4.c.a \(0\) \(0\) \(-14\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta q^{3}+(-7+\beta )q^{5}-\beta q^{7}-7^{2}q^{9}+\cdots\)
320.4.c.b 320.c 5.b $2$ $18.881$ \(\Q(\sqrt{-19}) \) None 20.4.c.a \(0\) \(0\) \(-14\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta q^{3}+(-7-\beta )q^{5}-\beta q^{7}-7^{2}q^{9}+\cdots\)
320.4.c.c 320.c 5.b $2$ $18.881$ \(\Q(\sqrt{-1}) \) None 10.4.b.a \(0\) \(0\) \(10\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{3}+(-5\beta+5)q^{5}+13\beta q^{7}+\cdots\)
320.4.c.d 320.c 5.b $2$ $18.881$ \(\Q(\sqrt{-1}) \) None 10.4.b.a \(0\) \(0\) \(10\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{3}+(5\beta+5)q^{5}+13\beta q^{7}+23 q^{9}+\cdots\)
320.4.c.e 320.c 5.b $2$ $18.881$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) 160.4.c.a \(0\) \(0\) \(22\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(\beta+11)q^{5}+27 q^{9}-46\beta q^{13}+\cdots\)
320.4.c.f 320.c 5.b $4$ $18.881$ \(\Q(i, \sqrt{5})\) \(\Q(\sqrt{-5}) \) 160.4.c.c \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-\beta _{1}+2\beta _{3})q^{3}+5\beta _{2}q^{5}+(6\beta _{1}+\cdots)q^{7}+\cdots\)
320.4.c.g 320.c 5.b $4$ $18.881$ \(\Q(i, \sqrt{6})\) None 40.4.c.a \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(1+\beta _{1}+\beta _{3})q^{5}+(-2\beta _{1}+\cdots)q^{7}+\cdots\)
320.4.c.h 320.c 5.b $4$ $18.881$ \(\Q(i, \sqrt{6})\) None 40.4.c.a \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(1+\beta _{2}+\beta _{3})q^{5}+(-2\beta _{1}+\cdots)q^{7}+\cdots\)
320.4.c.i 320.c 5.b $4$ $18.881$ \(\Q(i, \sqrt{29})\) None 160.4.c.b \(0\) \(0\) \(12\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}+(3-\beta _{1})q^{5}+\beta _{2}q^{7}+11q^{9}+\cdots\)
320.4.c.j 320.c 5.b $8$ $18.881$ 8.0.\(\cdots\).22 None 160.4.c.d \(0\) \(0\) \(-32\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-4+\beta _{4})q^{5}+(-\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(320, [\chi])\) into lower level spaces

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