Properties

Label 1280.2.o
Level $1280$
Weight $2$
Character orbit 1280.o
Rep. character $\chi_{1280}(127,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $88$
Newform subspaces $22$
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.o (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 22 \)
Sturm bound: \(384\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(3\), \(7\), \(13\)

Dimensions

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

Total New Old
Modular forms 432 104 328
Cusp forms 336 88 248
Eisenstein series 96 16 80

Trace form

\( 88 q + O(q^{10}) \) \( 88 q - 8 q^{17} + 8 q^{25} + 16 q^{33} + 16 q^{41} + 32 q^{57} - 8 q^{65} - 24 q^{73} - 40 q^{81} - 8 q^{97} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1280.2.o.a 1280.o 40.k $2$ $10.221$ \(\Q(\sqrt{-1}) \) None \(0\) \(-4\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-2+2i)q^{3}+(-1-2i)q^{5}+(2+\cdots)q^{7}+\cdots\)
1280.2.o.b 1280.o 40.k $2$ $10.221$ \(\Q(\sqrt{-1}) \) None \(0\) \(-4\) \(2\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-2+2i)q^{3}+(1+2i)q^{5}+(-2+\cdots)q^{7}+\cdots\)
1280.2.o.c 1280.o 40.k $2$ $10.221$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(-4\) \(-6\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+i)q^{3}+(-2+i)q^{5}+(-3+\cdots)q^{7}+\cdots\)
1280.2.o.d 1280.o 40.k $2$ $10.221$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(-4\) \(-2\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+i)q^{3}+(-2-i)q^{5}+(-1+\cdots)q^{7}+\cdots\)
1280.2.o.e 1280.o 40.k $2$ $10.221$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(4\) \(2\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+i)q^{3}+(2+i)q^{5}+(1-i)q^{7}+\cdots\)
1280.2.o.f 1280.o 40.k $2$ $10.221$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(4\) \(6\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+i)q^{3}+(2-i)q^{5}+(3-3i)q^{7}+\cdots\)
1280.2.o.g 1280.o 40.k $2$ $10.221$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-2\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-1-2i)q^{5}+3iq^{9}+(1+i)q^{13}+\cdots\)
1280.2.o.h 1280.o 40.k $2$ $10.221$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-2\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-1+2i)q^{5}+3iq^{9}+(5+5i)q^{13}+\cdots\)
1280.2.o.i 1280.o 40.k $2$ $10.221$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(2\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(1-2i)q^{5}+3iq^{9}+(-5-5i)q^{13}+\cdots\)
1280.2.o.j 1280.o 40.k $2$ $10.221$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(2\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(1+2i)q^{5}+3iq^{9}+(-1-i)q^{13}+\cdots\)
1280.2.o.k 1280.o 40.k $2$ $10.221$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(-4\) \(2\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-i)q^{3}+(-2-i)q^{5}+(1-i)q^{7}+\cdots\)
1280.2.o.l 1280.o 40.k $2$ $10.221$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(-4\) \(6\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-i)q^{3}+(-2+i)q^{5}+(3-3i)q^{7}+\cdots\)
1280.2.o.m 1280.o 40.k $2$ $10.221$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(4\) \(-6\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-i)q^{3}+(2-i)q^{5}+(-3+3i)q^{7}+\cdots\)
1280.2.o.n 1280.o 40.k $2$ $10.221$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(4\) \(-2\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-i)q^{3}+(2+i)q^{5}+(-1+i)q^{7}+\cdots\)
1280.2.o.o 1280.o 40.k $2$ $10.221$ \(\Q(\sqrt{-1}) \) None \(0\) \(4\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(2-2i)q^{3}+(-1-2i)q^{5}+(-2+\cdots)q^{7}+\cdots\)
1280.2.o.p 1280.o 40.k $2$ $10.221$ \(\Q(\sqrt{-1}) \) None \(0\) \(4\) \(2\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(2-2i)q^{3}+(1+2i)q^{5}+(2-2i)q^{7}+\cdots\)
1280.2.o.q 1280.o 40.k $4$ $10.221$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{12}^{2}q^{3}+(-2-\zeta_{12})q^{5}+\zeta_{12}^{2}q^{7}+\cdots\)
1280.2.o.r 1280.o 40.k $4$ $10.221$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{12}^{2}q^{3}+(2+\zeta_{12})q^{5}-\zeta_{12}^{2}q^{7}+\cdots\)
1280.2.o.s 1280.o 40.k $12$ $10.221$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(-4\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{2}q^{3}-\beta _{7}q^{5}+(-1-\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots\)
1280.2.o.t 1280.o 40.k $12$ $10.221$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(-4\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{3}q^{3}-\beta _{6}q^{5}+(1+\beta _{3}+\beta _{5}-\beta _{7}+\cdots)q^{7}+\cdots\)
1280.2.o.u 1280.o 40.k $12$ $10.221$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(4\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{3}q^{3}+\beta _{6}q^{5}+(-1-\beta _{3}-\beta _{5}+\cdots)q^{7}+\cdots\)
1280.2.o.v 1280.o 40.k $12$ $10.221$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(4\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{2}q^{3}+\beta _{7}q^{5}+(1+\beta _{2}-\beta _{4}-\beta _{6}+\cdots)q^{7}+\cdots\)

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

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