Properties

Label 1280.2.c
Level $1280$
Weight $2$
Character orbit 1280.c
Rep. character $\chi_{1280}(769,\cdot)$
Character field $\Q$
Dimension $44$
Newform subspaces $13$
Sturm bound $384$
Trace bound $15$

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Defining parameters

Level: \( N \) \(=\) \( 1280 = 2^{8} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1280.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 13 \)
Sturm bound: \(384\)
Trace bound: \(15\)
Distinguishing \(T_p\): \(3\), \(7\), \(11\), \(29\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1280, [\chi])\).

Total New Old
Modular forms 216 52 164
Cusp forms 168 44 124
Eisenstein series 48 8 40

Trace form

\( 44 q - 28 q^{9} + O(q^{10}) \) \( 44 q - 28 q^{9} + 4 q^{25} + 8 q^{41} - 28 q^{49} - 40 q^{65} - 20 q^{81} + 40 q^{89} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1280, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1280.2.c.a $2$ $10.221$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-4\) \(0\) \(q+(-2+i)q^{5}+3q^{9}-6iq^{13}+8iq^{17}+\cdots\)
1280.2.c.b $2$ $10.221$ \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{-10}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{5}-2\beta q^{7}+3q^{9}-2q^{11}-2\beta q^{13}+\cdots\)
1280.2.c.c $2$ $10.221$ \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{-10}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{5}+2\beta q^{7}+3q^{9}+2q^{11}-2\beta q^{13}+\cdots\)
1280.2.c.d $2$ $10.221$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(4\) \(0\) \(q+(2+i)q^{5}+3q^{9}-6iq^{13}-8iq^{17}+\cdots\)
1280.2.c.e $4$ $10.221$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(-4\) \(0\) \(q+\beta _{2}q^{3}+(-1-\beta _{1})q^{5}+\beta _{2}q^{7}-3q^{9}+\cdots\)
1280.2.c.f $4$ $10.221$ \(\Q(\sqrt{-2}, \sqrt{5})\) \(\Q(\sqrt{-5}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}+\beta _{3}q^{5}+3\beta _{1}q^{7}-7q^{9}+\cdots\)
1280.2.c.g $4$ $10.221$ \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{3}+(-\beta _{1}+\beta _{2})q^{5}-\beta _{1}q^{7}+\cdots\)
1280.2.c.h $4$ $10.221$ \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{3}+(\beta _{1}+\beta _{2})q^{5}-\beta _{1}q^{7}-3q^{9}+\cdots\)
1280.2.c.i $4$ $10.221$ \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{5}+\beta _{3}q^{7}+\cdots\)
1280.2.c.j $4$ $10.221$ \(\Q(\sqrt{-2}, \sqrt{5})\) \(\Q(\sqrt{-5}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}-\beta _{3}q^{5}-\beta _{2}q^{7}+q^{9}+\beta _{2}q^{15}+\cdots\)
1280.2.c.k $4$ $10.221$ \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+\beta _{3}q^{7}+q^{9}+\cdots\)
1280.2.c.l $4$ $10.221$ \(\Q(\sqrt{-2}, \sqrt{-5})\) \(\Q(\sqrt{-10}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{5}-\beta _{1}q^{7}+3q^{9}-\beta _{3}q^{11}+\cdots\)
1280.2.c.m $4$ $10.221$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(4\) \(0\) \(q+\beta _{2}q^{3}+(1+\beta _{1})q^{5}-\beta _{2}q^{7}-3q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1280, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1280, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(640, [\chi])\)\(^{\oplus 2}\)