Properties

Label 1280.2.a
Level $1280$
Weight $2$
Character orbit 1280.a
Rep. character $\chi_{1280}(1,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $16$
Sturm bound $384$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 1280 = 2^{8} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1280.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 16 \)
Sturm bound: \(384\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(3\), \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1280))\).

Total New Old
Modular forms 216 32 184
Cusp forms 169 32 137
Eisenstein series 47 0 47

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.
\(+\)\(+\)\(+\)\(6\)
\(+\)\(-\)\(-\)\(10\)
\(-\)\(+\)\(-\)\(10\)
\(-\)\(-\)\(+\)\(6\)
Plus space\(+\)\(12\)
Minus space\(-\)\(20\)

Trace form

\( 32 q + 32 q^{9} + O(q^{10}) \) \( 32 q + 32 q^{9} + 32 q^{25} + 96 q^{49} + 64 q^{57} + 64 q^{73} + 32 q^{81} + 64 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1280))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5
1280.2.a.a 1280.a 1.a $2$ $10.221$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(-2\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}-q^{5}+(1+\beta )q^{7}+(1+\cdots)q^{9}+\cdots\)
1280.2.a.b 1280.a 1.a $2$ $10.221$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(-2\) \(6\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}-q^{5}+(3-\beta )q^{7}+(1+\cdots)q^{9}+\cdots\)
1280.2.a.c 1280.a 1.a $2$ $10.221$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(2\) \(-6\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}+q^{5}+(-3+\beta )q^{7}+\cdots\)
1280.2.a.d 1280.a 1.a $2$ $10.221$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(2\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}+q^{5}+(-1-\beta )q^{7}+\cdots\)
1280.2.a.e 1280.a 1.a $2$ $10.221$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-q^{5}-\beta q^{7}-q^{9}-2\beta q^{11}+\cdots\)
1280.2.a.f 1280.a 1.a $2$ $10.221$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-q^{5}-3\beta q^{7}-q^{9}+4\beta q^{11}+\cdots\)
1280.2.a.g 1280.a 1.a $2$ $10.221$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-q^{5}+3\beta q^{7}-q^{9}+2\beta q^{11}+\cdots\)
1280.2.a.h 1280.a 1.a $2$ $10.221$ \(\Q(\sqrt{10}) \) None \(0\) \(0\) \(-2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-q^{5}+\beta q^{7}+7q^{9}-6q^{13}+\cdots\)
1280.2.a.i 1280.a 1.a $2$ $10.221$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+q^{5}-3\beta q^{7}-q^{9}+2\beta q^{11}+\cdots\)
1280.2.a.j 1280.a 1.a $2$ $10.221$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+q^{5}+3\beta q^{7}-q^{9}+4\beta q^{11}+\cdots\)
1280.2.a.k 1280.a 1.a $2$ $10.221$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+q^{5}+\beta q^{7}-q^{9}-2\beta q^{11}+\cdots\)
1280.2.a.l 1280.a 1.a $2$ $10.221$ \(\Q(\sqrt{10}) \) None \(0\) \(0\) \(2\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+q^{5}-\beta q^{7}+7q^{9}+6q^{13}+\cdots\)
1280.2.a.m 1280.a 1.a $2$ $10.221$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(-2\) \(-6\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}-q^{5}+(-3-\beta )q^{7}+(1+\cdots)q^{9}+\cdots\)
1280.2.a.n 1280.a 1.a $2$ $10.221$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(-2\) \(-2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}-q^{5}+(-1+\beta )q^{7}+(1+\cdots)q^{9}+\cdots\)
1280.2.a.o 1280.a 1.a $2$ $10.221$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(2\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+q^{5}+(1-\beta )q^{7}+(1+2\beta )q^{9}+\cdots\)
1280.2.a.p 1280.a 1.a $2$ $10.221$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(2\) \(6\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+q^{5}+(3+\beta )q^{7}+(1+2\beta )q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1280))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1280)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(128))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(256))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(320))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(640))\)\(^{\oplus 2}\)