Properties

Label 320.4.d
Level $320$
Weight $4$
Character orbit 320.d
Rep. character $\chi_{320}(161,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $4$
Sturm bound $192$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 320.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(192\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

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

Total New Old
Modular forms 156 24 132
Cusp forms 132 24 108
Eisenstein series 24 0 24

Trace form

\( 24 q - 216 q^{9} + O(q^{10}) \) \( 24 q - 216 q^{9} - 600 q^{25} + 1392 q^{33} - 240 q^{41} - 264 q^{49} + 2736 q^{57} - 864 q^{73} - 7272 q^{81} + 2544 q^{89} + 3168 q^{97} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
320.4.d.a 320.d 8.b $4$ $18.881$ \(\Q(i, \sqrt{19})\) None \(0\) \(0\) \(0\) \(-20\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-3\beta _{1}+\beta _{3})q^{3}+5\beta _{1}q^{5}+(-5+\cdots)q^{7}+\cdots\)
320.4.d.b 320.d 8.b $4$ $18.881$ \(\Q(i, \sqrt{19})\) None \(0\) \(0\) \(0\) \(20\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-3\beta _{1}+\beta _{3})q^{3}-5\beta _{1}q^{5}+(5-5\beta _{2}+\cdots)q^{7}+\cdots\)
320.4.d.c 320.d 8.b $8$ $18.881$ 8.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(-64\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}-5\beta _{2}q^{5}+(-8+\beta _{4}-3\beta _{6}+\cdots)q^{7}+\cdots\)
320.4.d.d 320.d 8.b $8$ $18.881$ 8.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(64\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+5\beta _{2}q^{5}+(8-\beta _{4}+3\beta _{6}+\cdots)q^{7}+\cdots\)

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

\( S_{4}^{\mathrm{old}}(320, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)