Properties

Label 320.4.a
Level $320$
Weight $4$
Character orbit 320.a
Rep. character $\chi_{320}(1,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $19$
Sturm bound $192$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 320.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 19 \)
Sturm bound: \(192\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(320))\).

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

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(5\)FrickeDim.
\(+\)\(+\)\(+\)\(7\)
\(+\)\(-\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(5\)
\(-\)\(-\)\(+\)\(7\)
Plus space\(+\)\(14\)
Minus space\(-\)\(10\)

Trace form

\( 24 q + 216 q^{9} + O(q^{10}) \) \( 24 q + 216 q^{9} - 144 q^{13} + 240 q^{21} + 600 q^{25} + 400 q^{29} + 464 q^{33} + 1024 q^{37} + 80 q^{41} + 1176 q^{49} - 752 q^{53} - 688 q^{57} + 3072 q^{61} + 528 q^{69} - 1904 q^{77} + 1336 q^{81} - 240 q^{85} + 848 q^{89} + 7968 q^{93} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(320))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5
320.4.a.a $1$ $18.881$ \(\Q\) None \(0\) \(-10\) \(5\) \(-18\) $+$ $-$ \(q-10q^{3}+5q^{5}-18q^{7}+73q^{9}+2^{4}q^{11}+\cdots\)
320.4.a.b $1$ $18.881$ \(\Q\) None \(0\) \(-8\) \(-5\) \(4\) $-$ $+$ \(q-8q^{3}-5q^{5}+4q^{7}+37q^{9}+12q^{11}+\cdots\)
320.4.a.c $1$ $18.881$ \(\Q\) None \(0\) \(-6\) \(5\) \(34\) $-$ $-$ \(q-6q^{3}+5q^{5}+34q^{7}+9q^{9}+2^{4}q^{11}+\cdots\)
320.4.a.d $1$ $18.881$ \(\Q\) None \(0\) \(-4\) \(-5\) \(-16\) $+$ $+$ \(q-4q^{3}-5q^{5}-2^{4}q^{7}-11q^{9}+60q^{11}+\cdots\)
320.4.a.e $1$ $18.881$ \(\Q\) None \(0\) \(-4\) \(-5\) \(16\) $+$ $+$ \(q-4q^{3}-5q^{5}+2^{4}q^{7}-11q^{9}-6^{2}q^{11}+\cdots\)
320.4.a.f $1$ $18.881$ \(\Q\) None \(0\) \(-2\) \(5\) \(-6\) $+$ $-$ \(q-2q^{3}+5q^{5}-6q^{7}-23q^{9}+60q^{11}+\cdots\)
320.4.a.g $1$ $18.881$ \(\Q\) None \(0\) \(-2\) \(5\) \(6\) $+$ $-$ \(q-2q^{3}+5q^{5}+6q^{7}-23q^{9}-2^{5}q^{11}+\cdots\)
320.4.a.h $1$ $18.881$ \(\Q\) None \(0\) \(2\) \(5\) \(-6\) $-$ $-$ \(q+2q^{3}+5q^{5}-6q^{7}-23q^{9}+2^{5}q^{11}+\cdots\)
320.4.a.i $1$ $18.881$ \(\Q\) None \(0\) \(2\) \(5\) \(6\) $+$ $-$ \(q+2q^{3}+5q^{5}+6q^{7}-23q^{9}-60q^{11}+\cdots\)
320.4.a.j $1$ $18.881$ \(\Q\) None \(0\) \(4\) \(-5\) \(-16\) $-$ $+$ \(q+4q^{3}-5q^{5}-2^{4}q^{7}-11q^{9}+6^{2}q^{11}+\cdots\)
320.4.a.k $1$ $18.881$ \(\Q\) None \(0\) \(4\) \(-5\) \(16\) $-$ $+$ \(q+4q^{3}-5q^{5}+2^{4}q^{7}-11q^{9}-60q^{11}+\cdots\)
320.4.a.l $1$ $18.881$ \(\Q\) None \(0\) \(6\) \(5\) \(-34\) $+$ $-$ \(q+6q^{3}+5q^{5}-34q^{7}+9q^{9}-2^{4}q^{11}+\cdots\)
320.4.a.m $1$ $18.881$ \(\Q\) None \(0\) \(8\) \(-5\) \(-4\) $+$ $+$ \(q+8q^{3}-5q^{5}-4q^{7}+37q^{9}-12q^{11}+\cdots\)
320.4.a.n $1$ $18.881$ \(\Q\) None \(0\) \(10\) \(5\) \(18\) $-$ $-$ \(q+10q^{3}+5q^{5}+18q^{7}+73q^{9}-2^{4}q^{11}+\cdots\)
320.4.a.o $2$ $18.881$ \(\Q(\sqrt{6}) \) None \(0\) \(-8\) \(-10\) \(8\) $+$ $+$ \(q+(-4+\beta )q^{3}-5q^{5}+(4+5\beta )q^{7}+\cdots\)
320.4.a.p $2$ $18.881$ \(\Q(\sqrt{10}) \) None \(0\) \(0\) \(-10\) \(0\) $-$ $+$ \(q+\beta q^{3}-5q^{5}-3\beta q^{7}+13q^{9}-2\beta q^{11}+\cdots\)
320.4.a.q $2$ $18.881$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(10\) \(0\) $-$ $-$ \(q-\beta q^{3}+5q^{5}-7\beta q^{7}-7q^{9}+2\beta q^{11}+\cdots\)
320.4.a.r $2$ $18.881$ \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(10\) \(0\) $-$ $-$ \(q-\beta q^{3}+5q^{5}+\beta q^{7}+5^{2}q^{9}-6\beta q^{11}+\cdots\)
320.4.a.s $2$ $18.881$ \(\Q(\sqrt{6}) \) None \(0\) \(8\) \(-10\) \(-8\) $+$ $+$ \(q+(4+\beta )q^{3}-5q^{5}+(-4+5\beta )q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(320))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(320)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 7}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 2}\)