Properties

Label 320.2.a
Level $320$
Weight $2$
Character orbit 320.a
Rep. character $\chi_{320}(1,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $7$
Sturm bound $96$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 320.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(96\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(320))\).

Total New Old
Modular forms 60 8 52
Cusp forms 37 8 29
Eisenstein series 23 0 23

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
\(+\)\(+\)$+$\(1\)
\(+\)\(-\)$-$\(3\)
\(-\)\(+\)$-$\(3\)
\(-\)\(-\)$+$\(1\)
Plus space\(+\)\(2\)
Minus space\(-\)\(6\)

Trace form

\( 8 q + 8 q^{9} + O(q^{10}) \) \( 8 q + 8 q^{9} + 16 q^{13} + 16 q^{21} + 8 q^{25} - 16 q^{29} - 16 q^{33} - 16 q^{41} + 8 q^{49} - 16 q^{53} - 16 q^{57} - 16 q^{69} - 16 q^{77} - 24 q^{81} - 16 q^{85} - 16 q^{89} - 32 q^{93} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(320))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5
320.2.a.a 320.a 1.a $1$ $2.555$ \(\Q\) None 20.2.a.a \(0\) \(-2\) \(1\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{5}-2q^{7}+q^{9}-2q^{13}+\cdots\)
320.2.a.b 320.a 1.a $1$ $2.555$ \(\Q\) None 160.2.a.a \(0\) \(-2\) \(1\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{5}+2q^{7}+q^{9}-4q^{11}+\cdots\)
320.2.a.c 320.a 1.a $1$ $2.555$ \(\Q\) None 40.2.a.a \(0\) \(0\) \(-1\) \(-4\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-4q^{7}-3q^{9}-4q^{11}+2q^{13}+\cdots\)
320.2.a.d 320.a 1.a $1$ $2.555$ \(\Q\) None 40.2.a.a \(0\) \(0\) \(-1\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+4q^{7}-3q^{9}+4q^{11}+2q^{13}+\cdots\)
320.2.a.e 320.a 1.a $1$ $2.555$ \(\Q\) None 160.2.a.a \(0\) \(2\) \(1\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{5}-2q^{7}+q^{9}+4q^{11}+\cdots\)
320.2.a.f 320.a 1.a $1$ $2.555$ \(\Q\) None 20.2.a.a \(0\) \(2\) \(1\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{5}+2q^{7}+q^{9}-2q^{13}+\cdots\)
320.2.a.g 320.a 1.a $2$ $2.555$ \(\Q(\sqrt{2}) \) None 160.2.a.c \(0\) \(0\) \(-2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-q^{5}+\beta q^{7}+5q^{9}-2\beta q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(320))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(320)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 2}\)